Testing latest pari + WASM + node.js... and it works?! Wow.
License: GPL3
ubuntu2004
*** too few arguments: abs()
*** ^-
*** at top-level: addell()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: addell(e,z1,z2) ===> elladd(e,z1,z2)
elladd(E,z1,z2): sum of the points z1 and z2 on elliptic curve E.
[]
*** at top-level: adj()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: adj(x) ===> matadjoint(x)
matadjoint(M,{flag=0}): adjoint matrix of M using Leverrier-Faddeev's
algorithm. If flag is 1, compute the characteristic polynomial independently
first.
*** at top-level: akell()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: akell(e,n) ===> ellak(e,n)
ellak(E,n): computes the n-th Fourier coefficient of the L-function of the
elliptic curve E (assumes E is an integral model).
*** at top-level: algdep2()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: algdep2(x,n,dec) ===> algdep(x,n,dec)
algdep(z,k,{flag=0}): algebraic relations up to degree n of z, using
lindep([1,z,...,z^(k-1)], flag).
*** at top-level: algtobasis()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: algtobasis(nf,x) ===> nfalgtobasis(nf,x)
nfalgtobasis(nf,x): transforms the algebraic number x into a column vector on
the integral basis nf.zk.
*** at top-level: anell()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: anell(e,n) ===> ellan(e,n)
ellan(E,n): computes the first n Fourier coefficients of the L-function of the
elliptic curve E defined over a number field (n<2^24 on a 32-bit machine).
*** at top-level: apell()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: apell(e,n) ===> ellap(e,n)
ellap(E,{p}): given an elliptic curve E defined over a finite field Fq, return
the trace of Frobenius a_p = q+1-#E(Fq); for other fields of definition K, p
must define a finite residue field, (p prime for K = Qp or Q; p a maximal ideal
for K a number field), return the order of the (nonsingular) reduction of E.
*** at top-level: apell2()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: apell2(e,n) ===> ellap(e,n)
ellap(E,{p}): given an elliptic curve E defined over a finite field Fq, return
the trace of Frobenius a_p = q+1-#E(Fq); for other fields of definition K, p
must define a finite residue field, (p prime for K = Qp or Q; p a maximal ideal
for K a number field), return the order of the (nonsingular) reduction of E.
*** at top-level: apprpadic()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: apprpadic(x,a) ===> padicappr(x,a)
padicappr(pol,a): p-adic roots of the polynomial pol congruent to a mod p.
*** at top-level: assmat()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: assmat(x) ===> matcompanion(x)
matcompanion(x): companion matrix to polynomial x.
*** at top-level: basis()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: basis(x) ===> nfbasis(x)
nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the
polynomial T, using the round 4 algorithm. An argument [T,listP] is possible,
where listP is a list of primes or a prime bound, to get an order which is
maximal at certain primes only. If present, dK is set to the discriminant of
the returned order.
*** at top-level: basis2()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: basis2(x) ===> nfbasis(x,2)
nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the
polynomial T, using the round 4 algorithm. An argument [T,listP] is possible,
where listP is a list of primes or a prime bound, to get an order which is
maximal at certain primes only. If present, dK is set to the discriminant of
the returned order.
*** at top-level: basistoalg()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: basistoalg(nf,x) ===> nfbasistoalg(nf,x)
nfbasistoalg(nf,x): transforms the column vector x on the integral basis into
an algebraic number.
*** at top-level: bilhell()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: bilhell(e,z1,z2) ===> ellbil(e,z1,z2)
ellbil(E,z1,z2): deprecated alias for ellheight(E,P,Q).
*** at top-level: bin()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: bin(x,y) ===> binomial(x,y)
binomial(x,{k}): binomial coefficient x*(x-1)...*(x-k+1)/k! defined for k in Z
and any x. If k is omitted and x an integer, return the vector
[binomial(x,0),...,binomial(x,x)].
*** at top-level: boundcf()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: boundcf(x,lmax) ===> contfrac(x,,lmax)
contfrac(x,{b},{nmax}): continued fraction expansion of x (x rational,real or
rational function). b and nmax are both optional, where b is the vector of
numerators of the continued fraction, and nmax is a bound for the number of
terms in the continued fraction expansion.
*** at top-level: boundfact()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: boundfact(x,lim) ===> factor(x,lim)
factor(x,{D}): factorization of x over domain D. If x and D are both integers,
return partial factorization, using primes < D.
*** at top-level: buchcertify()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchcertify(bnf) ===> bnfcertify(bnf)
bnfcertify(bnf,{flag = 0}): certify the correctness (i.e. remove the GRH) of
the bnf data output by bnfinit. If flag is present, only certify that the class
group is a quotient of the one computed in bnf (much simpler in general).
*** at top-level: buchfu()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: buchgen()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: buchgenforcefu()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: buchgenfu()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: buchimag()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchimag(D,c1,c2,g) ===> quadclassunit(D,,[c1,c2,g])
quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group
and the regulator of the quadratic field of discriminant D. See manual for the
optional technical parameters.
*** at top-level: buchinit()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchinit(P) ===> bnfinit(P,2)
bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in
ideal and unit group computations, including fundamental units if they are not
too large. flag and tech are both optional. flag can be any of 0: default, 1:
include all data in algebraic form (compact units). See manual for details
about tech.
*** at top-level: buchinitforcefu()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchinitforcefu(P) ===> bnfinit(P,1)
bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in
ideal and unit group computations, including fundamental units if they are not
too large. flag and tech are both optional. flag can be any of 0: default, 1:
include all data in algebraic form (compact units). See manual for details
about tech.
*** at top-level: buchinitfu()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchinitfu(P) ===> bnfinit(P)
bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in
ideal and unit group computations, including fundamental units if they are not
too large. flag and tech are both optional. flag can be any of 0: default, 1:
include all data in algebraic form (compact units). See manual for details
about tech.
*** at top-level: buchnarrow()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchnarrow(bnf) ===> bnfnarrow(bnf)
bnfnarrow(bnf): given a big number field as output by bnfinit, gives as a
3-component vector the structure of the narrow class group.
*** at top-level: buchray()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchray(bnf,ideal) ===> bnrinit(bnf,ideal)
bnrinit(bnf,f,{flag=0},{cycmod}): given a bnf as output by bnfinit and a
modulus f, initializes data linked to the ray class group structure
corresponding to this module. flag is optional, and can be 0: default, 1:
compute also the generators. If the positive integer cycmod is present, only
compute the ray class group modulo cycmod-th powers.
*** at top-level: buchrayinit()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchrayinit(bnf,ideal) ===> bnrinit(bnf,ideal)
bnrinit(bnf,f,{flag=0},{cycmod}): given a bnf as output by bnfinit and a
modulus f, initializes data linked to the ray class group structure
corresponding to this module. flag is optional, and can be 0: default, 1:
compute also the generators. If the positive integer cycmod is present, only
compute the ray class group modulo cycmod-th powers.
*** at top-level: buchrayinitgen()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchrayinitgen(bnf,ideal) ===> bnrinit(bnf,ideal,1)
bnrinit(bnf,f,{flag=0},{cycmod}): given a bnf as output by bnfinit and a
modulus f, initializes data linked to the ray class group structure
corresponding to this module. flag is optional, and can be 0: default, 1:
compute also the generators. If the positive integer cycmod is present, only
compute the ray class group modulo cycmod-th powers.
*** at top-level: buchreal()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: buchreal(D) ===> quadclassunit(D)
quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group
and the regulator of the quadratic field of discriminant D. See manual for the
optional technical parameters.
*** at top-level: bytesize()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: bytesize(x) ===> sizebyte(x)
sizebyte(x): number of bytes occupied by the complete tree of the object x.
*** at top-level: cf()
*** ^----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: cf(x) ===> contfrac(x)
contfrac(x,{b},{nmax}): continued fraction expansion of x (x rational,real or
rational function). b and nmax are both optional, where b is the vector of
numerators of the continued fraction, and nmax is a bound for the number of
terms in the continued fraction expansion.
*** at top-level: cf2()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: cf2(b,x) ===> contfrac(x,b)
contfrac(x,{b},{nmax}): continued fraction expansion of x (x rational,real or
rational function). b and nmax are both optional, where b is the vector of
numerators of the continued fraction, and nmax is a bound for the number of
terms in the continued fraction expansion.
*** at top-level: changevar()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: char()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: char(x,y) ===> charpoly(x,y)
charpoly(A,{v='x},{flag=5}): det(v*Id-A)=characteristic polynomial of the
matrix or polmod A. flag is optional and ignored unless A is a matrix; it may
be set to 0 (Le Verrier), 1 (Lagrange interpolation), 2 (Hessenberg form), 3
(Berkowitz), 4 (modular) if A is integral, or 5 (default, choose best method).
Algorithms 0 (Le Verrier) and 1 (Lagrange) assume that n! is invertible, where
n is the dimension of the matrix.
*** at top-level: char1()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: char1(x,y) ===> charpoly(x,y,1)
charpoly(A,{v='x},{flag=5}): det(v*Id-A)=characteristic polynomial of the
matrix or polmod A. flag is optional and ignored unless A is a matrix; it may
be set to 0 (Le Verrier), 1 (Lagrange interpolation), 2 (Hessenberg form), 3
(Berkowitz), 4 (modular) if A is integral, or 5 (default, choose best method).
Algorithms 0 (Le Verrier) and 1 (Lagrange) assume that n! is invertible, where
n is the dimension of the matrix.
*** at top-level: char2()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: char2(x,y) ===> charpoly(x,y,2)
charpoly(A,{v='x},{flag=5}): det(v*Id-A)=characteristic polynomial of the
matrix or polmod A. flag is optional and ignored unless A is a matrix; it may
be set to 0 (Le Verrier), 1 (Lagrange interpolation), 2 (Hessenberg form), 3
(Berkowitz), 4 (modular) if A is integral, or 5 (default, choose best method).
Algorithms 0 (Le Verrier) and 1 (Lagrange) assume that n! is invertible, where
n is the dimension of the matrix.
*** at top-level: chell()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: chell(x,y) ===> ellchangecurve(x,y)
ellchangecurve(E,v): change data on elliptic curve according to v=[u,r,s,t].
*** at top-level: chptell()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: chptell(x,y) ===> ellchangepoint(x,y)
ellchangepoint(x,v): change data on point or vector of points x on an elliptic
curve according to v=[u,r,s,t].
*** at top-level: classno()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: classno(x) ===> qfbclassno(x)
qfbclassno(D,{flag=0}): class number of discriminant D using Shanks's method by
default. If (optional) flag is set to 1, use Euler products.
*** at top-level: classno2()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: classno2(x) ===> qfbclassno(x,1)
qfbclassno(D,{flag=0}): class number of discriminant D using Shanks's method by
default. If (optional) flag is set to 1, use Euler products.
*** at top-level: coeff()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: coeff(x,s) ===> polcoeff(x,s)
polcoeff(x,n,{v}): deprecated alias for polcoef.
*** at top-level: compimag()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: compimag(x,y) ===> x*y
x*y: product of x and y.
*** at top-level: compo()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: compo(x,s) ===> component(x,s)
component(x,n): the n'th component of the internal representation of x. For
vectors or matrices, it is simpler to use x[]. For list objects such as nf,
bnf, bnr or ell, it is much easier to use member functions starting with ".".
*** at top-level: compositum()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: compositum(pol1,pol2) ===> polcompositum(pol1,pol2)
polcompositum(P,Q,{flag=0}): vector of all possible compositums of the number
fields defined by the polynomials P and Q; flag is optional, whose binary
digits mean 1: output for each compositum, not only the compositum polynomial
pol, but a vector [R,a,b,k] where a (resp. b) is a root of P (resp. Q)
expressed as a polynomial modulo R, and a small integer k such that al2+k*al1
is the chosen root of R; 2: assume that the number fields defined by P and Q
are linearly disjoint.
*** at top-level: compositum2()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: compositum2(pol1,pol2) ===> polcompositum(pol1,pol2,1)
polcompositum(P,Q,{flag=0}): vector of all possible compositums of the number
fields defined by the polynomials P and Q; flag is optional, whose binary
digits mean 1: output for each compositum, not only the compositum polynomial
pol, but a vector [R,a,b,k] where a (resp. b) is a root of P (resp. Q)
expressed as a polynomial modulo R, and a small integer k such that al2+k*al1
is the chosen root of R; 2: assume that the number fields defined by P and Q
are linearly disjoint.
*** at top-level: comprealraw()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: comprealraw(x,y) ===> qfbcompraw(x,y)
qfbcompraw(x,y): Gaussian composition without reduction of the binary quadratic
forms x and y.
*** at top-level: conductor()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: conductor(a1) ===> bnrconductor(a1)
bnrconductor(A,{B},{C},{flag=0}): conductor f of the subfield of the ray class
field given by A,B,C. flag is optional and can be 0: default, 1: returns [f,
Cl_f, H], H subgroup of the ray class group modulo f defining the extension, 2:
returns [f, bnr(f), H].
*** at top-level: conductorofchar()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: conductorofchar(bnr,chi) ===> bnrconductorofchar(bnr,chi)
bnrconductorofchar(bnr,chi): this function is obsolete, use bnrconductor.
*** at top-level: convol()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: convol(x,y) ===> serconvol(x,y)
serconvol(x,y): convolution (or Hadamard product) of two power series.
*** at top-level: core2()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: core2(x) ===> core(x,1)
core(n,{flag=0}): unique squarefree integer d dividing n such that n/d is a
square. If (optional) flag is nonzero, output the two-component row vector
[d,f], where d is the unique squarefree integer dividing n such that n/d=f^2 is
a square.
*** at top-level: coredisc2()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: coredisc2(x) ===> coredisc(x,1)
coredisc(n,{flag=0}): discriminant of the quadratic field Q(sqrt(n)). If
(optional) flag is nonzero, output a two-component row vector [d,f], where d is
the discriminant of the quadratic field Q(sqrt(n)) and n=df^2. f may be a half
integer.
*** at top-level: cvtoi()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: cvtoi(x) ===> truncate(x,&e)
truncate(x,{&e}): truncation of x; when x is a power series,take away the
O(X^). If e is present, do not take into account loss of integer part
precision, and set e = error estimate in bits.
*** at top-level: cyclo()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: cyclo(n) ===> polcyclo(n)
polcyclo(n,{a = 'x}): n-th cyclotomic polynomial evaluated at a.
*** at top-level: decodefactor()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: decodefactor(fa) ===> factorback(fa)
factorback(f,{e}): given a factorization f, gives the factored object back. If
e is present, f has to be a vector of the same length, and we return the
product of the f[i]^e[i].
*** at top-level: decodemodule()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: decodemodule(nf,fa) ===> bnfdecodemodule(nf,fa)
bnfdecodemodule(nf,m): given a coded module m as in bnrdisclist, gives the true
module.
*** at top-level: degree()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: degree(x) ===> poldegree(x)
poldegree(x,{v}): degree of the polynomial or rational function x with respect
to main variable if v is omitted, with respect to v otherwise. For scalar x,
return 0 if x is nonzero and -oo otherwise.
*** at top-level: denom()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: denom(x) ===> denominator(x)
denominator(f,{D}): denominator of f.
*** at top-level: deplin()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: deplin(x) ===> lindep(x,-1)
lindep(v,{flag=0}): integral linear dependencies between components of v. flag
is optional, and can be 0: default, guess a suitable accuracy, or positive:
accuracy to use for the computation, in decimal digits.
*** at top-level: det()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: det(x) ===> matdet(x)
matdet(x,{flag=0}): determinant of the matrix x using an appropriate algorithm
depending on the coefficients. If (optional) flag is set to 1, use classical
Gaussian elimination (usually worse than the default).
*** at top-level: det2()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: det2(x) ===> matdet(x,1)
matdet(x,{flag=0}): determinant of the matrix x using an appropriate algorithm
depending on the coefficients. If (optional) flag is set to 1, use classical
Gaussian elimination (usually worse than the default).
*** at top-level: detint()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: detint(x) ===> matdetint(x)
matdetint(B): some multiple of the determinant of the lattice generated by the
columns of B (0 if not of maximal rank). Useful with mathnfmod.
*** at top-level: diagonal()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: diagonal(x) ===> matdiagonal(x)
matdiagonal(x): creates the diagonal matrix whose diagonal entries are the
entries of the vector x.
*** at top-level: disc()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: disc(x) ===> poldisc(x)
poldisc(pol,{v}): discriminant of the polynomial pol, with respect to main
variable if v is omitted, with respect to v otherwise.
*** at top-level: discf()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discf(x) ===> nfdisc(x)
nfdisc(T): discriminant of the number field defined by the polynomial T. An
argument [T,listP] is possible, where listP is a list of primes or a prime
bound.
*** at top-level: discf2()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discf2(x) ===> nfdisc(x,2)
nfdisc(T): discriminant of the number field defined by the polynomial T. An
argument [T,listP] is possible, where listP is a list of primes or a prime
bound.
*** at top-level: discrayabs()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayabs(bnr,subgroup) ===> bnrdisc(bnr,subgroup)
bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field
defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus]
or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit,
and subgroup is the HNF matrix of a subgroup of the corresponding ray class
group (if omitted, the trivial subgroup). flag is optional whose binary digits
mean 1: give relative data; 2: return 0 if modulus is not the conductor.
*** at top-level: discrayabscond()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayabscond(bnr) ===> bnrdisc(bnr,,,2)
bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field
defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus]
or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit,
and subgroup is the HNF matrix of a subgroup of the corresponding ray class
group (if omitted, the trivial subgroup). flag is optional whose binary digits
mean 1: give relative data; 2: return 0 if modulus is not the conductor.
*** at top-level: discrayabslist()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayabslist(bnf,list) ===> bnrdisclist(bnf,list)
bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all
conductors up to norm bound. The ramified Archimedean places are given by arch;
all possible values are taken if arch is omitted. Supports the alternative
syntax bnrdisclist(bnf,list), where list is as output by ideallist or
ideallistarch (with units).
*** at top-level: discrayabslistarch()
*** ^--------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayabslistarch(bnf,arch,bound) ===> bnrdisclist(bnf,bound,arch)
bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all
conductors up to norm bound. The ramified Archimedean places are given by arch;
all possible values are taken if arch is omitted. Supports the alternative
syntax bnrdisclist(bnf,list), where list is as output by ideallist or
ideallistarch (with units).
*** at top-level: discrayabslistarchall()
*** ^-----------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayabslistarchall(bnf,bound) ===> bnrdisclist(bnf,bound,,1)
bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all
conductors up to norm bound. The ramified Archimedean places are given by arch;
all possible values are taken if arch is omitted. Supports the alternative
syntax bnrdisclist(bnf,list), where list is as output by ideallist or
ideallistarch (with units).
*** at top-level: discrayabslistlong()
*** ^--------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayabslistlong(bnf,bound) ===> bnrdisclist(bnf,bound)
bnrdisclist(bnf,bound,{arch}): list of discriminants of ray class fields of all
conductors up to norm bound. The ramified Archimedean places are given by arch;
all possible values are taken if arch is omitted. Supports the alternative
syntax bnrdisclist(bnf,list), where list is as output by ideallist or
ideallistarch (with units).
*** at top-level: discrayrel()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayrel(bnr,subgroup) ===> bnrdisc(bnr,subgroup,,1)
bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field
defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus]
or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit,
and subgroup is the HNF matrix of a subgroup of the corresponding ray class
group (if omitted, the trivial subgroup). flag is optional whose binary digits
mean 1: give relative data; 2: return 0 if modulus is not the conductor.
*** at top-level: discrayrelcond()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: discrayrelcond(bnr,subgroup) ===> bnrdisc(bnr,subgroup,,3)
bnrdisc(A,{B},{C},{flag=0}): absolute or relative [N,R1,discf] of the field
defined by A,B,C. [A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf, modulus]
or [bnf,modulus,subgroup], where bnf is as output by bnfinit, bnr by bnrinit,
and subgroup is the HNF matrix of a subgroup of the corresponding ray class
group (if omitted, the trivial subgroup). flag is optional whose binary digits
mean 1: give relative data; 2: return 0 if modulus is not the conductor.
*** at top-level: divres()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: divres(x,y) ===> divrem(x,y)
divrem(x,y,{v}): euclidean division of x by y giving as a 2-dimensional column
vector the quotient and the remainder, with respect to v (to main variable if v
is omitted).
*** at top-level: divsum()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: divsum(n,X,expr) ===> sumdiv(n,X,expr)
sumdiv(n,X,expr): sum of expression expr, X running over the divisors of n.
*** at top-level: eigen()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: eigen(x) ===> mateigen(x)
mateigen(x,{flag=0}): complex eigenvectors of the matrix x given as columns of
a matrix H. If flag=1, return [L,H], where L contains the eigenvalues and H the
corresponding eigenvectors.
*** at top-level: euler()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: euler ===> Euler
Euler=Euler(): Euler's constant with current precision.
*** at top-level: extract()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: extract(x,y) ===> vecextract(x,y)
vecextract(x,y,{z}): extraction of the components of the matrix or vector x
according to y and z. If z is omitted, y represents columns, otherwise y
corresponds to rows and z to columns. y and z can be vectors (of indices),
strings (indicating ranges as in "1..10") or masks (integers whose binary
representation indicates the indices to extract, from left to right 1, 2, 4, 8,
etc.).
*** at top-level: fact()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: fact(x) ===> factorial(x)
factorial(x): factorial of x, the result being given as a real number.
*** at top-level: factcantor()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factcantor(x,p) ===> factorcantor(x,p)
factorcantor(x,p): this function is obsolete, use factormod.
*** at top-level: factfq()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factfq(x,p,a) ===> factorff(x,p,a)
factorff(x,{p},{a}): obsolete, use factormod.
*** at top-level: factmod()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factmod(x,p) ===> factormod(x,p)
factormod(f,{D},{flag=0}): factors the polynomial f over the finite field
defined by the domain D; flag is optional, and can be 0: default or 1: only the
degrees of the irreducible factors are given.
*** at top-level: factoredbasis()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factoredbasis(x,p) ===> nfbasis(x,,p)
nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the
polynomial T, using the round 4 algorithm. An argument [T,listP] is possible,
where listP is a list of primes or a prime bound, to get an order which is
maximal at certain primes only. If present, dK is set to the discriminant of
the returned order.
*** at top-level: factoreddiscf()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factoreddiscf(x,p) ===> nfdisc(x,,p)
nfdisc(T): discriminant of the number field defined by the polynomial T. An
argument [T,listP] is possible, where listP is a list of primes or a prime
bound.
*** at top-level: factoredpolred()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factoredpolred(x,p) ===> polred(x,,p)
polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T
(gives minimal polynomials only). The following binary digits of (optional)
flag are significant 1: partial reduction, 2: gives also elements.
*** at top-level: factoredpolred2()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factoredpolred2(x,p) ===> polred(x,2,p)
polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T
(gives minimal polynomials only). The following binary digits of (optional)
flag are significant 1: partial reduction, 2: gives also elements.
*** at top-level: factorpadic2()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factorpadic2(x,p,r) ===> factorpadic(x,p,r,1)
factorpadic(pol,p,r): p-adic factorization of the polynomial pol to precision
r.
*** at top-level: factpol()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factpol(x,l,hint) ===> factor(x)
factor(x,{D}): factorization of x over domain D. If x and D are both integers,
return partial factorization, using primes < D.
*** at top-level: factpol2()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: factpol2(x,l,hint) ===> factor(x)
factor(x,{D}): factorization of x over domain D. If x and D are both integers,
return partial factorization, using primes < D.
*** at top-level: fibo()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: fibo(x) ===> fibonacci(x)
fibonacci(x): fibonacci number of index x (x C-integer).
*** at top-level: fpn()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: fpn(p,n) ===> ffinit(p,n)
ffinit(p,n,{v='x}): monic irreducible polynomial of degree n over F_p[v].
*** at top-level: galois()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: galois(x) ===> polgalois(x)
polgalois(T): Galois group of the polynomial T (see manual for group coding).
Return [n, s, k, name] where n is the group order, s the signature, k the index
and name is the GAP4 name of the transitive group.
*** at top-level: galoisapply()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: galoisapply(nf,aut,x) ===> nfgaloisapply(nf,aut,x)
nfgaloisapply(nf,aut,x): apply the Galois automorphism aut to the object x
(element or ideal) in the number field nf.
*** at top-level: galoisconj()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: galoisconj(nf) ===> nfgaloisconj(nf)
nfgaloisconj(nf,{flag=0},{d}): list of conjugates of a root of the polynomial
x=nf.pol in the same number field. flag is optional (set to 0 by default),
meaning 0: use combination of flag 4 and 1, always complete; 1: use nfroots; 4:
use Allombert's algorithm, complete if the field is Galois of degree <= 35 (see
manual for details). nf can be simply a polynomial.
*** at top-level: galoisconj1()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: galoisconj1(nf) ===> nfgaloisconj(nf,2)
nfgaloisconj(nf,{flag=0},{d}): list of conjugates of a root of the polynomial
x=nf.pol in the same number field. flag is optional (set to 0 by default),
meaning 0: use combination of flag 4 and 1, always complete; 1: use nfroots; 4:
use Allombert's algorithm, complete if the field is Galois of degree <= 35 (see
manual for details). nf can be simply a polynomial.
*** at top-level: galoisconjforce()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: galoisconjforce ===> nfgaloisconj(nf,1)
nfgaloisconj(nf,{flag=0},{d}): list of conjugates of a root of the polynomial
x=nf.pol in the same number field. flag is optional (set to 0 by default),
meaning 0: use combination of flag 4 and 1, always complete; 1: use nfroots; 4:
use Allombert's algorithm, complete if the field is Galois of degree <= 35 (see
manual for details). nf can be simply a polynomial.
*** at top-level: gamh()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: gamh(x) ===> gammah(x)
gammah(x): gamma of x+1/2 (x integer).
*** at top-level: gauss()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: gauss(a,b) ===> matsolve(a,b)
matsolve(M,B): solution of MX=B (M matrix, B column vector or matrix).
*** at top-level: gaussmodulo()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: gaussmodulo(M,D,Y) ===> matsolvemod(M,D,Y)
matsolvemod(M,D,B,{flag=0}): one solution of system of congruences MX=B mod D
(M matrix, B and D column vectors). If (optional) flag is nonzero return all
solutions.
*** at top-level: gaussmodulo2()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: gaussmodulo2(M,D,Y) ===> matsolvemod(M,D,Y,1)
matsolvemod(M,D,B,{flag=0}): one solution of system of congruences MX=B mod D
(M matrix, B and D column vectors). If (optional) flag is nonzero return all
solutions.
*** at top-level: globalred()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: globalred(x,y) ===> ellglobalred(x,y)
ellglobalred(E): E being an elliptic curve over a number field, returns [N, v,
c, faN, L], where N is the conductor of E, c is the product of the local
Tamagawa numbers c_p, faN is the factorization of N and L[i] is elllocalred(E,
faN[i,1]); v is an obsolete field.
*** at top-level: goto()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: hclassno()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hclassno(x) ===> qfbhclassno(x)
qfbhclassno(x): Hurwitz-Kronecker class number of x>0.
*** at top-level: hell()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hell(e,x) ===> ellheight(e,x)
ellheight(E,{P},{Q}): Faltings height of the curve E, resp. canonical height of
the point P on elliptic curve E, resp. the value of the attached bilinear form
at (P,Q).
*** at top-level: hell2()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hell2(e,x) ===> ellheight(e,x,1)
ellheight(E,{P},{Q}): Faltings height of the curve E, resp. canonical height of
the point P on elliptic curve E, resp. the value of the attached bilinear form
at (P,Q).
*** at top-level: hermite()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hermite(x) ===> mathnf(x)
mathnf(M,{flag=0}): (upper triangular) Hermite normal form of M, basis for the
lattice formed by the columns of M. flag is optional whose value range from 0
to 3 have a binary meaning. Bit 1: complete output, returns a 2-component
vector [H,U] such that H is the HNF of M, and U is an invertible matrix such
that MU=H. Bit 2: allow polynomial entries, otherwise assume that M is
integral. These use a naive algorithm; larger values correspond to more
involved algorithms and are restricted to integer matrices; flag = 4: returns
[H,U] using LLL reduction along the way; flag = 5: return [H,U,P] where P is a
permutation of row indices such that P applied to M U is H.
*** at top-level: hermite2()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hermite2(x) ===> mathnf(x,1)
mathnf(M,{flag=0}): (upper triangular) Hermite normal form of M, basis for the
lattice formed by the columns of M. flag is optional whose value range from 0
to 3 have a binary meaning. Bit 1: complete output, returns a 2-component
vector [H,U] such that H is the HNF of M, and U is an invertible matrix such
that MU=H. Bit 2: allow polynomial entries, otherwise assume that M is
integral. These use a naive algorithm; larger values correspond to more
involved algorithms and are restricted to integer matrices; flag = 4: returns
[H,U] using LLL reduction along the way; flag = 5: return [H,U,P] where P is a
permutation of row indices such that P applied to M U is H.
*** at top-level: hermitehavas()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: hermitemod()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hermitemod(x,d) ===> mathnfmod(x,d)
mathnfmod(x,d): (upper triangular) Hermite normal form of x, basis for the
lattice formed by the columns of x, where d is a multiple of the nonzero
determinant of this lattice.
*** at top-level: hermitemodid()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hermitemodid(x,d) ===> mathnfmodid(x,d)
mathnfmodid(x,d): (upper triangular) Hermite normal form of x concatenated with
matdiagonal(d).
*** at top-level: hermiteperm()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hermiteperm(x) ===> mathnf(x,3)
mathnf(M,{flag=0}): (upper triangular) Hermite normal form of M, basis for the
lattice formed by the columns of M. flag is optional whose value range from 0
to 3 have a binary meaning. Bit 1: complete output, returns a 2-component
vector [H,U] such that H is the HNF of M, and U is an invertible matrix such
that MU=H. Bit 2: allow polynomial entries, otherwise assume that M is
integral. These use a naive algorithm; larger values correspond to more
involved algorithms and are restricted to integer matrices; flag = 4: returns
[H,U] using LLL reduction along the way; flag = 5: return [H,U,P] where P is a
permutation of row indices such that P applied to M U is H.
*** at top-level: hess()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hess(x) ===> mathess(x)
mathess(x): Hessenberg form of x.
*** at top-level: hilb()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hilb(x,y) ===> hilbert(x,y)
hilbert(x,y,{p}): Hilbert symbol at p of x,y.
*** at top-level: hilbp()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hilbp(x,y,p) ===> hilbert(x,y,p)
hilbert(x,y,{p}): Hilbert symbol at p of x,y.
*** at top-level: hvector()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: hvector(n,X,expr) ===> vector(n,X,expr)
vector(n,{X},{expr=0}): row vector with n components of expression expr (X
ranges from 1 to n). By default, fills with 0s.
*** at top-level: i()
*** ^---
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: i ===> I
I=I(): square root of -1.
*** at top-level: idealaddmultone()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealaddmultone(nf,list) ===> idealaddtoone(nf,list)
idealaddtoone(nf,x,{y}): if y is omitted, when the sum of the ideals in the
number field K defined by nf and given in the vector x is equal to Z_K, gives a
vector of elements of the corresponding ideals who sum to 1. Otherwise, x and y
are ideals, and if they sum up to 1, find one element in each of them such that
the sum is 1.
*** at top-level: idealaddone()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealaddone(nf,x,y) ===> idealaddtoone(nf,x,y)
idealaddtoone(nf,x,{y}): if y is omitted, when the sum of the ideals in the
number field K defined by nf and given in the vector x is equal to Z_K, gives a
vector of elements of the corresponding ideals who sum to 1. Otherwise, x and y
are ideals, and if they sum up to 1, find one element in each of them such that
the sum is 1.
*** at top-level: idealapprfact()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealapprfact(nf,x) ===> idealappr(nf,x,1)
idealappr(nf,x,{flag}): x being a fractional ideal, gives an element b such
that v_p(b)=v_p(x) for all prime ideals p dividing x, and v_p(b)>=0 for all
other p; x may also be a prime ideal factorization with possibly zero
exponents. flag is deprecated (ignored), kept for backward compatibility.
*** at top-level: idealdivexact()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealdivexact(nf,x,y) ===> idealdiv(nf,x,y,1)
idealdiv(nf,x,y,{flag=0}): quotient x/y of two ideals x and y in HNF in the
number field nf. If (optional) flag is nonzero, the quotient is supposed to be
an integral ideal (slightly faster).
*** at top-level: idealhermite()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealhermite(nf,x) ===> idealhnf(nf,x)
idealhnf(nf,u,{v}): hermite normal form of the ideal u in the number field nf
if v is omitted. If called as idealhnf(nf,u,v), the ideal is given as uZ_K +
vZ_K in the number field K defined by nf.
*** at top-level: idealhermite2()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealhermite2(nf,x) ===> idealhnf(nf,x)
idealhnf(nf,u,{v}): hermite normal form of the ideal u in the number field nf
if v is omitted. If called as idealhnf(nf,u,v), the ideal is given as uZ_K +
vZ_K in the number field K defined by nf.
*** at top-level: idealinv2()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealinv2(nf,x) ===> idealinv(nf,x,1)
idealinv(nf,x): inverse of the ideal x in the number field nf.
*** at top-level: ideallistarchgen()
*** ^------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallistarchgen(nf,list,arch) ===> ideallistarch(nf,list,arch)
ideallistarch(nf,list,arch): list is a vector of vectors of bid's as output by
ideallist. Return a vector of vectors with the same number of components as the
original list. The leaves give information about moduli whose finite part is as
in original list, in the same order, and Archimedean part is now arch. The
information contained is of the same kind as was present in the input.
*** at top-level: ideallistunit()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallistunit(nf,list) ===> ideallist(nf,list,2)
ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all
ideals of norm<=bound. If (optional) flag is present, its binary digits are
toggles meaning 1: give generators; 2: add units; 4: give only the ideals and
not the bid.
*** at top-level: ideallistunitarch()
*** ^-------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallistunitarch ===> ideallistarch(nf,list,arch)
ideallistarch(nf,list,arch): list is a vector of vectors of bid's as output by
ideallist. Return a vector of vectors with the same number of components as the
original list. The leaves give information about moduli whose finite part is as
in original list, in the same order, and Archimedean part is now arch. The
information contained is of the same kind as was present in the input.
*** at top-level: ideallistunitarchgen()
*** ^----------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallistunitarchgen ===> ideallistarch(nf,list,arch)
ideallistarch(nf,list,arch): list is a vector of vectors of bid's as output by
ideallist. Return a vector of vectors with the same number of components as the
original list. The leaves give information about moduli whose finite part is as
in original list, in the same order, and Archimedean part is now arch. The
information contained is of the same kind as was present in the input.
*** at top-level: ideallistunitgen()
*** ^------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallistunitgen ===> ideallist(nf,list,3)
ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all
ideals of norm<=bound. If (optional) flag is present, its binary digits are
toggles meaning 1: give generators; 2: add units; 4: give only the ideals and
not the bid.
*** at top-level: ideallistzstar()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallistzstar(nf,bound) ===> ideallist(nf,bound)
ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all
ideals of norm<=bound. If (optional) flag is present, its binary digits are
toggles meaning 1: give generators; 2: add units; 4: give only the ideals and
not the bid.
*** at top-level: ideallistzstargen()
*** ^-------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallistzstargen(nf,bound) ===> ideallist(nf,bound,1)
ideallist(nf,bound,{flag=4}): vector of vectors L of all idealstar of all
ideals of norm<=bound. If (optional) flag is present, its binary digits are
toggles meaning 1: give generators; 2: add units; 4: give only the ideals and
not the bid.
*** at top-level: ideallllred()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ideallllred(nf,x,vdir) ===> idealred(nf,x,vdir)
idealred(nf,I,{v=0}): LLL reduction of the ideal I in the number field nf along
direction v, in HNF.
*** at top-level: idealmulred()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealmulred(nf,x,y) ===> idealmul(nf,x,y,1)
idealmul(nf,x,y,{flag=0}): product of the two ideals x and y in the number
field nf. If (optional) flag is nonzero, reduce the result.
*** at top-level: idealpowred()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealpowred(nf,x,y) ===> idealpow(nf,x,y,1)
idealpow(nf,x,k,{flag=0}): k-th power of the ideal x in HNF in the number field
nf. If (optional) flag is nonzero, reduce the result.
*** at top-level: idealtwoelt2()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idealtwoelt2(nf,x,a) ===> idealtwoelt(nf,x,a)
idealtwoelt(nf,x,{a}): two-element representation of an ideal x in the number
field nf. If (optional) a is nonzero, first element will be equal to a.
*** at top-level: idmat()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: idmat(n) ===> matid(n)
matid(n): identity matrix of order n.
*** at top-level: image()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: image(x) ===> matimage(x)
matimage(x,{flag=0}): basis of the image of the matrix x. flag is optional and
can be set to 0 or 1, corresponding to two different algorithms.
*** at top-level: image2()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: image2(x) ===> matimage(x,1)
matimage(x,{flag=0}): basis of the image of the matrix x. flag is optional and
can be set to 0 or 1, corresponding to two different algorithms.
*** at top-level: imagecompl()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: imagecompl(x) ===> matimagecompl(x)
matimagecompl(x): vector of column indices not corresponding to the indices
given by the function matimage.
*** at top-level: incgam1()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: incgam2()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: incgam3()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: incgam4()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: incgam4(s,x,y) ===> incgam(s,x,y)
incgam(s,x,{g}): incomplete gamma function. g is optional and is the
precomputed value of gamma(s).
*** at top-level: indexrank()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: indexrank(x) ===> matindexrank(x)
matindexrank(M): gives two extraction vectors (rows and columns) for the matrix
M such that the extracted matrix is square of maximal rank.
*** at top-level: indsort()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: indsort(x) ===> vecsort(x,,1)
vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in
ascending order, according to the comparison function cmpf, if not omitted. (If
cmpf is an integer k, sort according to the value of the k-th component of each
entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return
the permutation instead of the permuted vector, 4: use descending instead of
ascending order, 8: remove duplicate entries.
*** at top-level: initalg()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: initalg(pol) ===> nfinit(pol)
nfinit(pol,{flag=0}): pol being a nonconstant irreducible polynomial, gives the
vector: [pol,[r1,r2],discf,index,[M,MC,T2,T,different] (see manual),r1+r2 first
roots, integral basis, matrix of power basis in terms of integral basis,
multiplication table of basis]. flag is optional and can be set to 0: default;
1: do not compute different; 2: first use polred to find a simpler polynomial;
3: outputs a two-element vector [nf,Mod(a,P)], where nf is as in 2 and Mod(a,P)
is a polmod equal to Mod(x,pol) and P=nf.pol.
*** at top-level: initalgred()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: initalgred(x) ===> nfinit(x,2)
nfinit(pol,{flag=0}): pol being a nonconstant irreducible polynomial, gives the
vector: [pol,[r1,r2],discf,index,[M,MC,T2,T,different] (see manual),r1+r2 first
roots, integral basis, matrix of power basis in terms of integral basis,
multiplication table of basis]. flag is optional and can be set to 0: default;
1: do not compute different; 2: first use polred to find a simpler polynomial;
3: outputs a two-element vector [nf,Mod(a,P)], where nf is as in 2 and Mod(a,P)
is a polmod equal to Mod(x,pol) and P=nf.pol.
*** at top-level: initalgred2()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: initalgred2(x) ===> nfinit(x,3)
nfinit(pol,{flag=0}): pol being a nonconstant irreducible polynomial, gives the
vector: [pol,[r1,r2],discf,index,[M,MC,T2,T,different] (see manual),r1+r2 first
roots, integral basis, matrix of power basis in terms of integral basis,
multiplication table of basis]. flag is optional and can be set to 0: default;
1: do not compute different; 2: first use polred to find a simpler polynomial;
3: outputs a two-element vector [nf,Mod(a,P)], where nf is as in 2 and Mod(a,P)
is a polmod equal to Mod(x,pol) and P=nf.pol.
*** at top-level: initell()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: initell(x) ===> ellinit(x)
ellinit(x,{D=1}): let x be a vector [a1,a2,a3,a4,a6], or [a4,a6] if a1=a2=a3=0,
defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6; x can also be
a string, in which case the curve with matching name is retrieved from the
elldata database, if available. This function initializes an elliptic curve
over the domain D (inferred from coefficients if omitted).
*** at top-level: initzeta()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: integ()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: integ(x,y) ===> intformal(x,y)
intformal(x,{v}): formal integration of x with respect to v, or to the main
variable of x if v is omitted.
*** at top-level: intersect()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: intersect(x,y) ===> matintersect(x,y)
matintersect(x,y): intersection of the vector spaces whose bases are the
columns of x and y.
*** at top-level: intgen()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: intgen(x=a,b,s) ===> intnum(x=a,b,s,1)
intnum(X=a,b,expr,{tab}): numerical integration of expr from a to b with
respect to X. Plus/minus infinity is coded as +oo/-oo. Finally tab is either
omitted (let the program choose the integration step), a nonnegative integer m
(divide integration step by 2^m), or data precomputed with intnuminit.
*** at top-level: intinf()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: intinf(x=a,b,s) ===> intnum(x=a,b,s,2)
intnum(X=a,b,expr,{tab}): numerical integration of expr from a to b with
respect to X. Plus/minus infinity is coded as +oo/-oo. Finally tab is either
omitted (let the program choose the integration step), a nonnegative integer m
(divide integration step by 2^m), or data precomputed with intnuminit.
*** at top-level: intopen()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: intopen(x=a,b,s) ===> intnum(x=a,b,s,3)
intnum(X=a,b,expr,{tab}): numerical integration of expr from a to b with
respect to X. Plus/minus infinity is coded as +oo/-oo. Finally tab is either
omitted (let the program choose the integration step), a nonnegative integer m
(divide integration step by 2^m), or data precomputed with intnuminit.
*** at top-level: inverseimage()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: inverseimage(x,y) ===> matinverseimage(x,y)
matinverseimage(x,y): an element of the inverse image of the vector y by the
matrix x if one exists, the empty vector otherwise.
*** at top-level: isdiagonal()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isdiagonal(x) ===> matisdiagonal(x)
matisdiagonal(x): true(1) if x is a diagonal matrix, false(0) otherwise.
*** at top-level: isfund()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isfund(x) ===> isfundamental(x)
isfundamental(D): true(1) if D is a fundamental discriminant (including 1),
false(0) if not.
*** at top-level: isideal()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isideal(nf,x) ===> nfisideal(nf,x)
nfisideal(nf,x): true(1) if x is an ideal in the number field nf, false(0) if
not.
*** at top-level: isincl()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isincl(x,y) ===> nfisincl(x,y)
nfisincl(f,g,{flag=0}): let f and g define number fields, either irreducible
rational polynomials or number fields as output by nfinit; tests whether the
number field f is isomorphic to a subfield of g. Return 0 if not, and otherwise
all the embeddings (flag=0, default) or only one (flag=1).
*** at top-level: isinclfast()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isinclfast(nf1,nf2) ===> nfisincl(nf1,nf2,1)
nfisincl(f,g,{flag=0}): let f and g define number fields, either irreducible
rational polynomials or number fields as output by nfinit; tests whether the
number field f is isomorphic to a subfield of g. Return 0 if not, and otherwise
all the embeddings (flag=0, default) or only one (flag=1).
*** at top-level: isirreducible()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isirreducible(x) ===> polisirreducible(x)
polisirreducible(pol): true(1) if pol is an irreducible nonconstant polynomial,
false(0) if pol is reducible or constant.
*** at top-level: isisom()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isisom(x,y) ===> nfisisom(x,y)
nfisisom(f,g): as nfisincl but tests whether f is isomorphic to g.
*** at top-level: isisomfast()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isisomfast(x,y) ===> nfisisom(x,y)
nfisisom(f,g): as nfisincl but tests whether f is isomorphic to g.
*** too few arguments: isoncurve()
*** ^-
*** at top-level: isprincipal()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isprincipal(bnf,x) ===> bnfisprincipal(bnf,x,0)
bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where
e is the vector of exponents on the class group generators and t is the
generator of the resulting principal ideal. In particular x is principal if and
only if e is the zero vector. flag is optional, whose binary digits mean 1:
output [e,t] (only e if unset); 2: increase precision until t can be computed
(do not insist if unset); 4: return t in factored form (compact
representation).
*** at top-level: isprincipalforce()
*** ^------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isprincipalforce(bnf,x) ===> bnfisprincipal(bnf,x,2)
bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where
e is the vector of exponents on the class group generators and t is the
generator of the resulting principal ideal. In particular x is principal if and
only if e is the zero vector. flag is optional, whose binary digits mean 1:
output [e,t] (only e if unset); 2: increase precision until t can be computed
(do not insist if unset); 4: return t in factored form (compact
representation).
*** at top-level: isprincipalgen()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isprincipalgen(bnf,x) ===> bnfisprincipal(bnf,x)
bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where
e is the vector of exponents on the class group generators and t is the
generator of the resulting principal ideal. In particular x is principal if and
only if e is the zero vector. flag is optional, whose binary digits mean 1:
output [e,t] (only e if unset); 2: increase precision until t can be computed
(do not insist if unset); 4: return t in factored form (compact
representation).
*** at top-level: isprincipalgenforce()
*** ^---------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isprincipalgenforce(bnf,x) ===> bnfisprincipal(bnf,x,3)
bnfisprincipal(bnf,x,{flag=1}): bnf being output by bnfinit, gives [e,t], where
e is the vector of exponents on the class group generators and t is the
generator of the resulting principal ideal. In particular x is principal if and
only if e is the zero vector. flag is optional, whose binary digits mean 1:
output [e,t] (only e if unset); 2: increase precision until t can be computed
(do not insist if unset); 4: return t in factored form (compact
representation).
*** at top-level: isprincipalray()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isprincipalray(bnf,x) ===> bnrisprincipal(bnf,x)
bnrisprincipal(bnr,x,{flag=1}): bnr being output by bnrinit and x being an
ideal coprime to bnr.mod, returns [v,alpha], where v is the vector of exponents
on the ray class group generators and alpha is the generator of the resulting
principal ideal. If (optional) flag is set to 0, output only v.
*** at top-level: isprincipalraygen()
*** ^-------------------
*** not a function in function call
*** at top-level: ispsp()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ispsp(x) ===> ispseudoprime(x)
ispseudoprime(x,{flag}): true(1) if x is a strong pseudoprime, false(0) if not.
If flag is 0 or omitted, use BPSW test, otherwise use strong Rabin-Miller test
for flag randomly chosen bases.
*** at top-level: isqrt()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isqrt(x) ===> sqrtint(x)
sqrtint(x,{&r}): integer square root y of x, where x is a nonnegative integer.
If r is present, set it to the remainder x - y^2.
*** at top-level: isset()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isset(x) ===> setisset(x)
setisset(x): true(1) if x is a set (row vector with strictly increasing
entries), false(0) if not.
*** at top-level: issqfree()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: issqfree(x) ===> issquarefree(x)
issquarefree(x): true(1) if x is squarefree, false(0) if not.
*** at top-level: isunit()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: isunit(bnf,x) ===> bnfisunit(bnf,x)
bnfisunit(bnf,x, {U}): bnf being output by bnfinit, give the column vector of
exponents of x on the fundamental units and the roots of unity if x is a unit,
the empty vector otherwise. If U is present, as given by bnfunits, decompose x
on the attached S-units generators.
*** at top-level: jacobi()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: jacobi(x) ===> qfjacobi(x)
qfjacobi(A): eigenvalues and orthogonal matrix of eigenvectors of the real
symmetric matrix A.
*** at top-level: jbesselh()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: jbesselh(n,x) ===> besseljh(n,x)
besseljh(n,x): J-bessel function of index n+1/2 and argument x, where n is a
nonnegative integer.
*** at top-level: jell()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: jell(x) ===> ellj(x)
ellj(x): elliptic j invariant of x.
*** at top-level: karamul()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: kbessel()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: kbessel(nu,x) ===> besselk(nu,x)
besselk(nu,x): K-bessel function of index nu and argument x.
*** at top-level: kbessel2()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: kbessel2(nu,x) ===> besselk(nu,x)
besselk(nu,x): K-bessel function of index nu and argument x.
*** at top-level: ker()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ker(x) ===> matker(x)
matker(x,{flag=0}): basis of the kernel of the matrix x. flag is optional, and
may be set to 0: default; nonzero: x is known to have integral entries.
*** at top-level: keri()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: keri(x) ===> matker(x,1)
matker(x,{flag=0}): basis of the kernel of the matrix x. flag is optional, and
may be set to 0: default; nonzero: x is known to have integral entries.
*** at top-level: kerint()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: kerint(x) ===> matkerint(x)
matkerint(x,{flag=0}): LLL-reduced Z-basis of the kernel of the matrix x with
integral entries. flag is deprecated, and may be set to 0 or 1 for backward
compatibility.
*** at top-level: kerint1()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: kerint1(x) ===> matkerint(x,1)
matkerint(x,{flag=0}): LLL-reduced Z-basis of the kernel of the matrix x with
integral entries. flag is deprecated, and may be set to 0 or 1 for backward
compatibility.
*** at top-level: kerint2()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: kro()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: kro(x,y) ===> kronecker(x,y)
kronecker(x,y): kronecker symbol (x/y).
*** at top-level: label()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: lambdak()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: laplace()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: laplace(x) ===> serlaplace(x)
serlaplace(x): replaces the power series sum of a_n*x^n/n! by sum of a_n*x^n.
For the reverse operation, use serconvol(x,exp(X)).
*** at top-level: legendre()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: legendre(n) ===> pollegendre(n)
pollegendre(n,{a='x},{flag=0}): legendre polynomial of degree n evaluated at a.
If flag is 1, return [P_{n-1}(a), P_n(a)].
*** at top-level: lexsort()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lexsort(x) ===> vecsort(x,,2)
vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in
ascending order, according to the comparison function cmpf, if not omitted. (If
cmpf is an integer k, sort according to the value of the k-th component of each
entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return
the permutation instead of the permuted vector, 4: use descending instead of
ascending order, 8: remove duplicate entries.
*** at top-level: lindep2()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lindep2(x) ===> lindep(x,1)
lindep(v,{flag=0}): integral linear dependencies between components of v. flag
is optional, and can be 0: default, guess a suitable accuracy, or positive:
accuracy to use for the computation, in decimal digits.
*** at top-level: lll()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lll(x) ===> qflll(x)
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is
optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is
integral, returns a partially reduced basis, 4: assumes x is integral, returns
[K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same
as 4 but x may have polynomial coefficients, 8: same as 0 but x may have
polynomial coefficients.
*** at top-level: lll1()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: lllgen()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllgen(x) ===> qflll(x,8)
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is
optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is
integral, returns a partially reduced basis, 4: assumes x is integral, returns
[K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same
as 4 but x may have polynomial coefficients, 8: same as 0 but x may have
polynomial coefficients.
*** at top-level: lllgram()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllgram(x) ===> qflllgram(x)
qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G
(gives the unimodular transformation matrix). flag is optional and can be 0:
default,1: assumes x is integral, 4: assumes x is integral, returns [K,T],
where K is the integer kernel of x and T the LLL reduced image, 5: same as 4
but x may have polynomial coefficients, 8: same as 0 but x may have polynomial
coefficients.
*** at top-level: lllgram1()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: lllgramgen()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllgramgen(x) ===> qflllgram(x,8)
qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G
(gives the unimodular transformation matrix). flag is optional and can be 0:
default,1: assumes x is integral, 4: assumes x is integral, returns [K,T],
where K is the integer kernel of x and T the LLL reduced image, 5: same as 4
but x may have polynomial coefficients, 8: same as 0 but x may have polynomial
coefficients.
*** at top-level: lllgramint()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllgramint(x) ===> qflllgram(x,1)
qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G
(gives the unimodular transformation matrix). flag is optional and can be 0:
default,1: assumes x is integral, 4: assumes x is integral, returns [K,T],
where K is the integer kernel of x and T the LLL reduced image, 5: same as 4
but x may have polynomial coefficients, 8: same as 0 but x may have polynomial
coefficients.
*** at top-level: lllgramkerim()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllgramkerim(x) ===> qflllgram(x,4)
qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G
(gives the unimodular transformation matrix). flag is optional and can be 0:
default,1: assumes x is integral, 4: assumes x is integral, returns [K,T],
where K is the integer kernel of x and T the LLL reduced image, 5: same as 4
but x may have polynomial coefficients, 8: same as 0 but x may have polynomial
coefficients.
*** at top-level: lllgramkerimgen()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllgramkerimgen(x) ===> qflllgram(x,5)
qflllgram(G,{flag=0}): LLL reduction of the lattice whose gram matrix is G
(gives the unimodular transformation matrix). flag is optional and can be 0:
default,1: assumes x is integral, 4: assumes x is integral, returns [K,T],
where K is the integer kernel of x and T the LLL reduced image, 5: same as 4
but x may have polynomial coefficients, 8: same as 0 but x may have polynomial
coefficients.
*** at top-level: lllint()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllint(x) ===> qflll(x,1)
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is
optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is
integral, returns a partially reduced basis, 4: assumes x is integral, returns
[K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same
as 4 but x may have polynomial coefficients, 8: same as 0 but x may have
polynomial coefficients.
*** at top-level: lllintpartial()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllintpartial(x) ===> qflll(x,2)
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is
optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is
integral, returns a partially reduced basis, 4: assumes x is integral, returns
[K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same
as 4 but x may have polynomial coefficients, 8: same as 0 but x may have
polynomial coefficients.
*** at top-level: lllkerim()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllkerim(x) ===> qflll(x,4)
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is
optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is
integral, returns a partially reduced basis, 4: assumes x is integral, returns
[K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same
as 4 but x may have polynomial coefficients, 8: same as 0 but x may have
polynomial coefficients.
*** at top-level: lllkerimgen()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lllkerimgen(x) ===> qflll(x,5)
qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x (gives the
unimodular transformation matrix T such that x*T is LLL-reduced). flag is
optional, and can be 0: default, 1: assumes x is integral, 2: assumes x is
integral, returns a partially reduced basis, 4: assumes x is integral, returns
[K,T] where K is the integer kernel of x and T the LLL reduced image, 5: same
as 4 but x may have polynomial coefficients, 8: same as 0 but x may have
polynomial coefficients.
*** at top-level: lllrat()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: ln()
*** ^----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ln(x) ===> log(x)
log(x): natural logarithm of x.
*** at top-level: localred()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: localred(e) ===> elllocalred(e)
elllocalred(E,{p}): E being an elliptic curve, returns [f,kod,[u,r,s,t],c],
where f is the conductor's exponent, kod is the Kodaira type for E at p,
[u,r,s,t] is the change of variable needed to make E minimal at p, and c is the
local Tamagawa number c_p.
*** at top-level: logagm()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: logagm(x) ===> log(x,1)
log(x): natural logarithm of x.
*** at top-level: lseriesell()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lseriesell(e,s,N,A) ===> elllseries(e,s,A)
elllseries(E,s,{A=1}): L-series at s of the elliptic curve E, where A a cut-off
point close to 1.
*** at top-level: makebigbnf()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: makebigbnf(sbnf) ===> bnfinit(sbnf)
bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future use in
ideal and unit group computations, including fundamental units if they are not
too large. flag and tech are both optional. flag can be any of 0: default, 1:
include all data in algebraic form (compact units). See manual for details
about tech.
*** at top-level: mat()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: mat(x) ===> Mat(x)
Mat({x=[]}): transforms any GEN x into a matrix. Empty matrix if x is omitted.
*** at top-level: matextract()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: matextract(x,y,z) ===> vecextract(x,y,z)
vecextract(x,y,{z}): extraction of the components of the matrix or vector x
according to y and z. If z is omitted, y represents columns, otherwise y
corresponds to rows and z to columns. y and z can be vectors (of indices),
strings (indicating ranges as in "1..10") or masks (integers whose binary
representation indicates the indices to extract, from left to right 1, 2, 4, 8,
etc.).
*** at top-level: mathell()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: mathell(e,x) ===> ellheightmatrix(e,x)
ellheightmatrix(E,x): gives the height matrix for vector of points x on
elliptic curve E.
*** at top-level: matrixqz2()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: matrixqz2(x,p) ===> matrixqz(x,-1)
matrixqz(A,{p=0}): if p>=0, transforms the rational or integral mxn (m>=n)
matrix A into an integral matrix with gcd of maximal determinants coprime to p.
If p=-1, finds a basis of the intersection with Z^n of the lattice spanned by
the columns of A. If p=-2, finds a basis of the intersection with Z^n of the
Q-vector space spanned by the columns of A.
*** at top-level: matrixqz3()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: matrixqz3(x,p) ===> matrixqz(x,-2)
matrixqz(A,{p=0}): if p>=0, transforms the rational or integral mxn (m>=n)
matrix A into an integral matrix with gcd of maximal determinants coprime to p.
If p=-1, finds a basis of the intersection with Z^n of the lattice spanned by
the columns of A. If p=-2, finds a basis of the intersection with Z^n of the
Q-vector space spanned by the columns of A.
*** at top-level: minideal()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: minideal(nf,ix,vdir) ===> idealmin(nf,ix,vdir)
idealmin(nf,ix,{vdir}): pseudo-minimum of the ideal ix in the direction vdir in
the number field nf.
*** at top-level: minim()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: minim(x,bound,maxnum) ===> qfminim(x,bound,maxnum)
qfminim(x,{B},{m},{flag=0}): x being a square and symmetric matrix representing
a positive definite quadratic form, this function deals with the vectors of x
whose norm is less than or equal to B, enumerated using the Fincke-Pohst
algorithm, storing at most m vectors (no limit if m is omitted). The function
searches for the minimal nonzero vectors if B is omitted. The precise behavior
depends on flag. 0: returns at most 2m vectors (unless m omitted), returns
[N,M,V] where N is the number of vectors enumerated, M the maximum norm among
these, and V lists half the vectors (the other half is given by -V). 1: ignores
m and returns the first vector whose norm is less than B. 2: as 0 but uses a
more robust, slower implementation
*** at top-level: minim2()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: minim2(x,bound) ===> qfminim(x,bound,,1)
qfminim(x,{B},{m},{flag=0}): x being a square and symmetric matrix representing
a positive definite quadratic form, this function deals with the vectors of x
whose norm is less than or equal to B, enumerated using the Fincke-Pohst
algorithm, storing at most m vectors (no limit if m is omitted). The function
searches for the minimal nonzero vectors if B is omitted. The precise behavior
depends on flag. 0: returns at most 2m vectors (unless m omitted), returns
[N,M,V] where N is the number of vectors enumerated, M the maximum norm among
these, and V lists half the vectors (the other half is given by -V). 1: ignores
m and returns the first vector whose norm is less than B. 2: as 0 but uses a
more robust, slower implementation
*** at top-level: mod()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: mod(x,y) ===> Mod(x,y)
Mod(a,b): create 'a modulo b'.
*** at top-level: modp()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: modp(x,y,p) ===> Mod(x,y)
Mod(a,b): create 'a modulo b'.
*** at top-level: modulargcd()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: modulargcd(x,y) ===> gcd(x,y,1)
gcd(x,{y}): greatest common divisor of x and y.
*** at top-level: mu()
*** ^----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: mu(n) ===> moebius(n)
moebius(x): Moebius function of x.
*** at top-level: nfdiv()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfdiv(nf,a,b) ===> nfeltdiv(nf,a,b)
nfeltdiv(nf,x,y): element x/y in nf.
*** at top-level: nfdiveuc()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfdiveuc(nf,a,b) ===> nfeltdiveuc(nf,a,b)
nfeltdiveuc(nf,x,y): gives algebraic integer q such that x-qy is small.
*** at top-level: nfdivres()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfdivres(nf,a,b) ===> nfeltdivrem(nf,a,b)
nfeltdivrem(nf,x,y): gives [q,r] such that r=x-qy is small.
*** at top-level: nfhermite()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfhermite(nf,x) ===> nfhnf(nf,x)
nfhnf(nf,x,{flag=0}): if x=[A,I], gives a pseudo-basis [B,J] of the module sum
A_jI_j. If flag is nonzero, return [[B,J], U], where U is the transformation
matrix such that AU = [0|B].
*** at top-level: nfhermitemod()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfhermitemod(nf,x,detx) ===> nfhnfmod(nf,x,detx)
nfhnfmod(nf,x,detx): if x=[A,I], and detx is a multiple of the ideal
determinant of x, gives a pseudo-basis of the module sum A_jI_j.
*** at top-level: nfmod()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfmod(nf,a,b) ===> nfeltmod(nf,a,b)
nfeltmod(nf,x,y): gives r such that r=x-qy is small with q algebraic integer.
*** at top-level: nfmul()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfmul(nf,a,b) ===> nfeltmul(nf,a,b)
nfeltmul(nf,x,y): element x.y in nf.
*** at top-level: nfpow()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfpow(nf,a,k) ===> nfeltpow(nf,a,k)
nfeltpow(nf,x,k): element x^k in nf.
*** at top-level: nfreduce()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfreduce(nf,a,id) ===> nfeltreduce(nf,a,id)
nfeltreduce(nf,a,id): gives r such that a-r is in the ideal id and r is small.
*** at top-level: nfsmith()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfsmith(nf,x) ===> nfsnf(nf,x)
nfsnf(nf,x,{flag=0}): if x=[A,I,J], outputs D=[d_1,...d_n] Smith normal form of
x. If flag is nonzero return [D,U,V], where UAV = Id.
*** at top-level: nfval()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nfval(nf,a,pr) ===> nfeltval(nf,a,pr)
nfeltval(nf,x,pr,{&y}): valuation of element x at the prime pr as output by
idealprimedec.
*** at top-level: nucomp()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nucomp(x,y,l) ===> qfbnucomp(x,y,l)
qfbnucomp(x,y,L): composite of primitive positive definite quadratic forms x
and y using nucomp and nudupl, where L=[|D/4|^(1/4)] is precomputed.
*** at top-level: numer()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: numer(x) ===> numerator(x)
numerator(f,{D}): numerator of f.
*** at top-level: nupow()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: nupow(x,n) ===> qfbnupow(x,n)
qfbnupow(x,n,{L}): n-th power of primitive positive definite quadratic form x
using nucomp and nudupl.
*** at top-level: o()
*** ^---
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: o(x) ===> O(x)
O(p^e): p-adic or power series zero with precision given by e.
*** at top-level: ordell()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ordell(e,x) ===> ellordinate(e,x)
ellordinate(E,x): y-coordinates corresponding to x-ordinate x on elliptic curve
E.
*** at top-level: order()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: order(x) ===> znorder(x)
znorder(x,{o}): order of the integermod x in (Z/nZ)*. Optional o represents a
multiple of the order of the element.
*** at top-level: orderell()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: orderell(e,x) ===> ellorder(e,x)
ellorder(E,z,{o}): order of the point z on the elliptic curve E over a number
field or a finite field, 0 if nontorsion. The parameter o, if present,
represents a nonzero multiple of the order of z.
*** at top-level: ordred()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ordred(x) ===> polredord(x)
polredord(x): this function is obsolete, use polredbest.
*** at top-level: pascal()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: pascal(n) ===> matpascal(n)
matpascal(n,{q}): Pascal triangle of order n if q is omitted. q-Pascal triangle
otherwise.
*** at top-level: perf()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: perf(a) ===> qfperfection(a)
qfperfection(G): rank of matrix of xx~ for x minimal vectors of a gram matrix
G.
*** at top-level: permutation()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: permutation(n,k) ===> numtoperm(n,k)
numtoperm(n,k): permutation number k (mod n!) of n letters (n C-integer).
*** at top-level: permutation2num()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: permutation2num(vect) ===> permtonum(vect)
permtonum(x): ordinal (between 0 and n!-1) of permutation x.
*** at top-level: pf()
*** ^----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: pf(x,p) ===> qfbprimeform(x,p)
qfbprimeform(x,p): returns the prime form of discriminant x, whose first
coefficient is p.
*** at top-level: phi()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: phi(x) ===> eulerphi(x)
eulerphi(x): Euler's totient function of x.
*** at top-level: pi()
*** ^----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: pi ===> Pi
Pi=Pi(): the constant pi, with current precision.
*** at top-level: pnqn()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: pnqn(x) ===> contfracpnqn(x)
contfracpnqn(x, {n=-1}): [p_n,p_{n-1}; q_n,q_{n-1}] corresponding to the
continued fraction x. If n >= 0 is present, returns all convergents from
p_0/q_0 up to p_n/q_n.
*** at top-level: pointell()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: pointell(e,z) ===> ellztopoint(e,z)
ellztopoint(E,z): inverse of ellpointtoz. Returns the coordinates of point P on
the curve E corresponding to a complex or p-adic z.
*** at top-level: polint()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polint(xa,ya,x) ===> polinterpolate(xa,ya,p)
polinterpolate(X,{Y},{t = 'x},{&e}): polynomial interpolation at t according to
data vectors X, Y, i.e., given P of minimal degree such that P(X[i]) = Y[i] for
all i, return P(t). If Y is omitted, take P such that P(i) = X[i]. If present
and t is numeric, e will contain an error estimate on the returned value
(Neville's algorithm).
*** at top-level: polred2()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polred2(x) ===> polred(x,2)
polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T
(gives minimal polynomials only). The following binary digits of (optional)
flag are significant 1: partial reduction, 2: gives also elements.
*** at top-level: polredabs2()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polredabs2(x) ===> polredabs(x,1)
polredabs(T,{flag=0}): a smallest generating polynomial of the number field for
the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is
optional, whose binary digit mean 1: give the element whose characteristic
polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm
(give only one of P(x) and P(-x)).
*** at top-level: polredabsall()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polredabsall(x) ===> polredabs(x,4)
polredabs(T,{flag=0}): a smallest generating polynomial of the number field for
the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is
optional, whose binary digit mean 1: give the element whose characteristic
polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm
(give only one of P(x) and P(-x)).
*** at top-level: polredabsfast()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polredabsfast(x) ===> polredabs(x,8)
polredabs(T,{flag=0}): a smallest generating polynomial of the number field for
the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is
optional, whose binary digit mean 1: give the element whose characteristic
polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm
(give only one of P(x) and P(-x)).
*** at top-level: polredabsnored()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polredabsnored(x) ===> polredabs(x,2)
polredabs(T,{flag=0}): a smallest generating polynomial of the number field for
the T2 norm on the roots, with smallest index for the minimal T2 norm. flag is
optional, whose binary digit mean 1: give the element whose characteristic
polynomial is the given polynomial. 4: give all polynomials of minimal T2 norm
(give only one of P(x) and P(-x)).
*** at top-level: polvar()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polvar(x) ===> variable(x)
variable({x}): main variable of object x. Gives p for p-adic x, 0 if no
variable can be attached to x. Returns the list of user variables if x is
omitted.
*** at top-level: poly()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: poly(x,v) ===> Pol(x,v)
Pol(t,{v='x}): convert t (usually a vector or a power series) into a polynomial
with variable v, starting with the leading coefficient.
*** at top-level: polylogd()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polylogd(m,x) ===> polylog(m,x,1)
polylog(m,x,{flag=0}): m-th polylogarithm of x. flag is optional, and can be 0:
default, 1: D_m~-modified m-th polylog of x, 2: D_m-modified m-th polylog of x,
3: P_m-modified m-th polylog of x.
*** at top-level: polylogdold()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polylogdold(m,x) ===> polylog(m,x,2)
polylog(m,x,{flag=0}): m-th polylogarithm of x. flag is optional, and can be 0:
default, 1: D_m~-modified m-th polylog of x, 2: D_m-modified m-th polylog of x,
3: P_m-modified m-th polylog of x.
*** at top-level: polylogp()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polylogp(m,x) ===> polylog(m,x,3)
polylog(m,x,{flag=0}): m-th polylogarithm of x. flag is optional, and can be 0:
default, 1: D_m~-modified m-th polylog of x, 2: D_m-modified m-th polylog of x,
3: P_m-modified m-th polylog of x.
*** at top-level: polyrev()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polyrev(x,v) ===> Polrev(x,v)
Polrev(t,{v='x}): convert t (usually a vector or a power series) into a
polynomial with variable v, starting with the constant term.
*** at top-level: polzag()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: polzag(n,m) ===> polzagier(n,m)
polzagier(n,m): Zagier's polynomials of index n,m.
*** at top-level: powell()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: powell(e,x,n) ===> ellmul(e,x,n)
ellmul(E,z,n): n times the point z on elliptic curve E (n in Z).
*** at top-level: powrealraw()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: powrealraw(x,n) ===> qfbpowraw(x,n)
qfbpowraw(x,n): n-th power without reduction of the binary quadratic form x.
*** at top-level: prec()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: prec(x,n) ===> precision(x,n)
precision(x,{n}): if n is present, return x at precision n. If n is omitted,
return real precision of object x.
*** at top-level: primedec()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: primedec(nf,p) ===> idealprimedec(nf,p)
idealprimedec(nf,p,{f=0}): prime ideal decomposition of the prime number p in
the number field nf as a vector of prime ideals. If f is present and nonzero,
restrict the result to primes of residue degree <= f.
*** at top-level: primroot()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: primroot(n) ===> znprimroot(n)
znprimroot(n): returns a primitive root of n when it exists.
*** at top-level: principalideal()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: principalidele()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: prodinf1()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: prodinf1(X=a,expr) ===> prodinf(X=a,expr,1)
prodinf(X=a,expr,{flag=0}): infinite product (X goes from a to infinity) of
real or complex expression. flag can be 0 (default) or 1, in which case compute
the product of the 1+expr instead.
*** at top-level: qfi()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: qfi(a,b,c) ===> Qfb(a,b,c)
Qfb(a,{b},{c}): binary quadratic form a*x^2+b*x*y+c*y^2.
*** at top-level: qfr()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: qfr(a,b,c,d) ===> Qfb(a,b,c,d)
Qfb(a,{b},{c}): binary quadratic form a*x^2+b*x*y+c*y^2.
1546275796
*** at top-level: rank()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rank(x) ===> matrank(x)
matrank(x): rank of the matrix x.
*** at top-level: rayclassno()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rayclassno(bnf,x) ===> bnrclassno(bnf,x)
bnrclassno(A,{B},{C}): relative degree of the class field defined by A,B,C.
[A,{B},{C}] is of type [bnr], [bnr,subgroup], [bnf,modulus], or
[bnf,modulus,subgroup]. Faster than bnrinit if only the ray class number is
wanted.
*** at top-level: rayclassnolist()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rayclassnolist(bnf,liste) ===> bnrclassnolist(bnf,liste)
bnrclassnolist(bnf,list): if list is as output by ideallist or similar, gives
list of corresponding ray class numbers.
*** at top-level: recip()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: recip(x) ===> polrecip(x)
polrecip(pol): reciprocal polynomial of pol.
*** at top-level: redimag()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: redimag(x) ===> qfbred(x)
qfbred(x,{flag=0},{isd},{sd}): reduction of the binary quadratic form x. All
other args. are optional. The argument isd and sd, if present, supply the
values of floor(sqrt(d)) and sqrt(d) respectively, where d is the discriminant.
If d<0, its value is not used and all references to Shanks's distance hereafter
are meaningless. flag can be any of 0: default; 1: do a single reduction step;
*** at top-level: redreal()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: redreal(x) ===> qfbred(x)
qfbred(x,{flag=0},{isd},{sd}): reduction of the binary quadratic form x. All
other args. are optional. The argument isd and sd, if present, supply the
values of floor(sqrt(d)) and sqrt(d) respectively, where d is the discriminant.
If d<0, its value is not used and all references to Shanks's distance hereafter
are meaningless. flag can be any of 0: default; 1: do a single reduction step;
*** at top-level: redrealnod()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: redrealnod(x,d) ===> qfbred(x,2,,d)
qfbred(x,{flag=0},{isd},{sd}): reduction of the binary quadratic form x. All
other args. are optional. The argument isd and sd, if present, supply the
values of floor(sqrt(d)) and sqrt(d) respectively, where d is the discriminant.
If d<0, its value is not used and all references to Shanks's distance hereafter
are meaningless. flag can be any of 0: default; 1: do a single reduction step;
*** at top-level: reduceddisc()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: reduceddisc(f) ===> poldiscreduced(f)
poldiscreduced(f): vector of elementary divisors of Z[a]/f'(a)Z[a], where a is
a root of the polynomial f.
*** at top-level: regula()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: regula(x) ===> quadregulator(x)
quadregulator(x): regulator of the real quadratic field of discriminant x.
*** at top-level: reorder()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: resultant()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: resultant(x,y) ===> polresultant(x,y)
polresultant(x,y,{v},{flag=0}): resultant of the polynomials x and y, with
respect to the main variables of x and y if v is omitted, with respect to the
variable v otherwise. flag is optional, and can be 0: default, uses either the
subresultant algorithm, a modular algorithm or Sylvester's matrix, depending on
the inputs; 1 uses Sylvester's matrix (should always be slower than the
default).
*** at top-level: resultant2()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: resultant2(x,y) ===> polresultant(x,y,1)
polresultant(x,y,{v},{flag=0}): resultant of the polynomials x and y, with
respect to the main variables of x and y if v is omitted, with respect to the
variable v otherwise. flag is optional, and can be 0: default, uses either the
subresultant algorithm, a modular algorithm or Sylvester's matrix, depending on
the inputs; 1 uses Sylvester's matrix (should always be slower than the
default).
*** at top-level: reverse()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: reverse(x) ===> serreverse(x)
serreverse(s): reversion of the power series s.
*** at top-level: rhoreal()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rhoreal(x) ===> qfbred(x,1)
qfbred(x,{flag=0},{isd},{sd}): reduction of the binary quadratic form x. All
other args. are optional. The argument isd and sd, if present, supply the
values of floor(sqrt(d)) and sqrt(d) respectively, where d is the discriminant.
If d<0, its value is not used and all references to Shanks's distance hereafter
are meaningless. flag can be any of 0: default; 1: do a single reduction step;
*** at top-level: rhorealnod()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rhorealnod(x,d) ===> qfbred(x,3,,d)
qfbred(x,{flag=0},{isd},{sd}): reduction of the binary quadratic form x. All
other args. are optional. The argument isd and sd, if present, supply the
values of floor(sqrt(d)) and sqrt(d) respectively, where d is the discriminant.
If d<0, its value is not used and all references to Shanks's distance hereafter
are meaningless. flag can be any of 0: default; 1: do a single reduction step;
*** at top-level: rndtoi()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rndtoi(x) ===> round(x,&e)
round(x,{&e}): take the nearest integer to all the coefficients of x. If e is
present, do not take into account loss of integer part precision, and set e =
error estimate in bits.
*** at top-level: rnfdiscf()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rnfdiscf(nf,pol) ===> rnfdisc(nf,pol)
rnfdisc(nf,T): given a polynomial T with coefficients in nf, gives a
2-component vector [D,d], where D is the relative ideal discriminant, and d is
the relative discriminant in nf^*/nf*^2.
*** at top-level: rnfequation2()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rnfequation2(nf,pol) ===> rnfequation(nf,pol,1)
rnfequation(nf,pol,{flag=0}): given a pol with coefficients in nf, gives an
absolute equation z of the number field defined by pol. flag is optional, and
can be 0: default, or nonzero, gives [z,al,k], where z defines the absolute
equation L/Q as in the default behavior, al expresses as an element of L a root
of the polynomial defining the base field nf, and k is a small integer such
that t = b + k al is a root of z, for b a root of pol.
*** at top-level: rnfhermitebasis()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rnfhermitebasis(bnf,order) ===> rnfhnfbasis(bnf,order)
rnfhnfbasis(bnf,x): given an order x as output by rnfpseudobasis, gives either
a true HNF basis of the order if it exists, zero otherwise.
*** at top-level: rootmod()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rootmod(x,p) ===> polrootsmod(x,p)
polrootsmod(f,{D}): roots of the polynomial f over the finite field defined by
the domain D.
*** at top-level: rootmod2()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rootmod2(x,p) ===> polrootsmod(x,p)
polrootsmod(f,{D}): roots of the polynomial f over the finite field defined by
the domain D.
*** at top-level: rootpadic()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rootpadic(x,p,r) ===> polrootspadic(x,p,r)
polrootspadic(f,p,r): p-adic roots of the polynomial f to precision r.
*** at top-level: roots()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: roots(x) ===> polroots(x)
polroots(T): complex roots of the polynomial T using Schonhage's method, as
modified by Gourdon.
*** too few arguments: rootsof1()
*** ^-
*** at top-level: rootsold()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: rounderror()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rounderror(x) ===> round(x,&e)
round(x,{&e}): take the nearest integer to all the coefficients of x. If e is
present, do not take into account loss of integer part precision, and set e =
error estimate in bits.
*** at top-level: series()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: series(x,v) ===> Ser(x,v)
Ser(s,{v='x},{d=seriesprecision}): convert s into a power series with variable
v and precision d, starting with the constant coefficient.
*** at top-level: set()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: set(x) ===> Set(x)
Set({x=[]}): convert x into a set, i.e. a row vector with strictly increasing
coefficients. Empty set if x is omitted.
*** at top-level: sigmak()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sigmak(k,x) ===> sigma(x,k)
sigma(x,{k=1}): sum of the k-th powers of the divisors of x. k is optional and
if omitted is assumed to be equal to 1.
*** at top-level: signat()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: signat(x) ===> qfsign(x)
qfsign(x): signature of the symmetric matrix x.
*** at top-level: signunit()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: signunit(bnf) ===> bnfsignunit(bnf)
bnfsignunit(bnf): matrix of signs of the real embeddings of the system of
fundamental units found by bnfinit.
*** at top-level: simplefactmod()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: simplefactmod(x,p) ===> factormod(x,p,1)
factormod(f,{D},{flag=0}): factors the polynomial f over the finite field
defined by the domain D; flag is optional, and can be 0: default or 1: only the
degrees of the irreducible factors are given.
*** at top-level: size()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: size(x) ===> sizedigit(x)
sizedigit(x): rough upper bound for the number of decimal digits of (the
components of) x. DEPRECATED.
*** at top-level: smallbasis()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smallbasis(x) ===> nfbasis(x,1)
nfbasis(T, {&dK}): integral basis of the field Q[a], where a is a root of the
polynomial T, using the round 4 algorithm. An argument [T,listP] is possible,
where listP is a list of primes or a prime bound, to get an order which is
maximal at certain primes only. If present, dK is set to the discriminant of
the returned order.
*** at top-level: smallbuchinit()
*** ^---------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: smalldiscf()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smalldiscf(x) ===> nfdisc(x,1)
nfdisc(T): discriminant of the number field defined by the polynomial T. An
argument [T,listP] is possible, where listP is a list of primes or a prime
bound.
*** at top-level: smallfact()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smallfact(x) ===> factor(x,0)
factor(x,{D}): factorization of x over domain D. If x and D are both integers,
return partial factorization, using primes < D.
*** at top-level: smallinitell()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smallinitell(x) ===> ellinit(x,1)
ellinit(x,{D=1}): let x be a vector [a1,a2,a3,a4,a6], or [a4,a6] if a1=a2=a3=0,
defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6; x can also be
a string, in which case the curve with matching name is retrieved from the
elldata database, if available. This function initializes an elliptic curve
over the domain D (inferred from coefficients if omitted).
*** at top-level: smallpolred()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smallpolred(x) ===> polred(x,1)
polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T
(gives minimal polynomials only). The following binary digits of (optional)
flag are significant 1: partial reduction, 2: gives also elements.
*** at top-level: smallpolred2()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smallpolred2(x) ===> polred(x,3)
polred(T,{flag=0}): deprecated, use polredbest. Reduction of the polynomial T
(gives minimal polynomials only). The following binary digits of (optional)
flag are significant 1: partial reduction, 2: gives also elements.
*** at top-level: smith()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smith(x) ===> matsnf(x)
matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix
X, expressed as a vector d; X must have integer or polynomial entries. Binary
digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the
diagonal d is returned, 4: removes all information corresponding to entries
equal to 1 in d.
*** at top-level: smith2()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smith2(x) ===> matsnf(x,1)
matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix
X, expressed as a vector d; X must have integer or polynomial entries. Binary
digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the
diagonal d is returned, 4: removes all information corresponding to entries
equal to 1 in d.
*** at top-level: smithclean()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smithclean(x) ===> matsnf(x,4)
matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix
X, expressed as a vector d; X must have integer or polynomial entries. Binary
digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the
diagonal d is returned, 4: removes all information corresponding to entries
equal to 1 in d.
*** at top-level: smithpol()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: smithpol(x) ===> matsnf(x,2)
matsnf(X,{flag=0}): Smith normal form (i.e. elementary divisors) of the matrix
X, expressed as a vector d; X must have integer or polynomial entries. Binary
digits of flag mean 1: returns [u,v,d] where d=u*X*v, otherwise only the
diagonal d is returned, 4: removes all information corresponding to entries
equal to 1 in d.
*** at top-level: sort()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sort(x) ===> vecsort(x)
vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in
ascending order, according to the comparison function cmpf, if not omitted. (If
cmpf is an integer k, sort according to the value of the k-th component of each
entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return
the permutation instead of the permuted vector, 4: use descending instead of
ascending order, 8: remove duplicate entries.
*** at top-level: sqred()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sqred(x) ===> qfgaussred(x)
qfgaussred(q): square reduction of the (symmetric) matrix q (returns a square
matrix whose i-th diagonal term is the coefficient of the i-th square in which
the coefficient of the i-th variable is 1).
*** at top-level: srgcd()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: srgcd(x,y) ===> gcd(x,y,2)
gcd(x,{y}): greatest common divisor of x and y.
*** at top-level: sturm()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sturm(x) ===> polsturm(x)
polsturm(T,{ab}): number of distinct real roots of the polynomial T (in the
interval ab = [a,b] if present).
*** at top-level: sturmpart()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sturmpart(x,a,b) ===> polsturm(x,a,b)
polsturm(T,{ab}): number of distinct real roots of the polynomial T (in the
interval ab = [a,b] if present).
*** at top-level: subcyclo()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: subcyclo(p,d) ===> polsubcyclo(p,d)
polsubcyclo(n,d,{v='x}): finds an equation (in variable v) for the d-th degree
subfields of Q(zeta_n). Output is a polynomial, or a vector of polynomials if
there are several such fields or none.
*** at top-level: subell()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: subell(e,a,b) ===> ellsub(e,a,b)
ellsub(E,z1,z2): difference of the points z1 and z2 on elliptic curve E.
*** at top-level: sumalt2()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sumalt2(X=a,expr) ===> sumalt(X=a,expr,1)
sumalt(X=a,expr,{flag=0}): Cohen-Villegas-Zagier's acceleration of alternating
series expr, X starting at a. flag is optional, and can be 0: default, or 1:
uses a slightly different method using Zagier's polynomials.
*** at top-level: sumpos2()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sumpos2(X=a,expr) ===> sumpos(X=a,expr,1)
sumpos(X=a,expr,{flag=0}): sum of positive (or negative) series expr, the
formal variable X starting at a. flag is optional, and can be 0: default, or 1:
uses a slightly different method using Zagier's polynomials.
*** at top-level: supplement()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: supplement(x) ===> matsupplement(x)
matsupplement(x): supplement the columns of the matrix x to an invertible
matrix.
*** at top-level: sylvestermatrix()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: sylvestermatrix(x,y) ===> polsylvestermatrix(x,y)
polsylvestermatrix(x,y): forms the sylvester matrix attached to the two
polynomials x and y. Warning: the polynomial coefficients are in columns, not
in rows.
*** at top-level: taniyama()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: taniyama(e) ===> elltaniyama(e)
elltaniyama(E, {n = seriesprecision}): modular parametrization of elliptic
curve E/Q.
*** at top-level: tchebi()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: tchebi(n) ===> polchebyshev(n)
polchebyshev(n,{flag=1},{a='x}): Chebyshev polynomial of the first (flag = 1)
or second (flag = 2) kind, of degree n, evaluated at a.
*** at top-level: teich()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: teich(x) ===> teichmuller(x)
teichmuller(x,{tab}): Teichmuller character of p-adic number x. If x = [p,n],
return the lifts of all teichmuller(i + O(p^n)) for i = 1, ..., p-1. Such a
vector can be fed back to teichmuller, as the optional argument tab, to speed
up later computations.
*** at top-level: threetotwo()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: threetotwo2()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: torsell()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: torsell(e) ===> elltors(e)
elltors(E): torsion subgroup of elliptic curve E: order, structure, generators.
*** at top-level: trans()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: trans(x) ===> mattranspose(x)
mattranspose(x): x~ = transpose of x.
*** at top-level: trunc()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: trunc(x) ===> truncate(x)
truncate(x,{&e}): truncation of x; when x is a power series,take away the
O(X^). If e is present, do not take into account loss of integer part
precision, and set e = error estimate in bits.
*** at top-level: tschirnhaus()
*** ^-------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: tschirnhaus(x) ===> poltschirnhaus(x)
poltschirnhaus(x): random Tschirnhausen transformation of the polynomial x.
*** at top-level: twototwo()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: unit()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: unit(x) ===> quadunit(x)
quadunit(D,{v = 'w}): fundamental unit u of the quadratic field of discriminant
D where D must be positive. If v is given, the variable name is used to display
u, else 'w' is used.
*** at top-level: vec()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: vec(x) ===> Vec(x)
Vec(x, {n}): transforms the object x into a vector of dimension n.
*** at top-level: vecindexsort()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: vecindexsort(x) ===> vecsort(x,,1)
vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in
ascending order, according to the comparison function cmpf, if not omitted. (If
cmpf is an integer k, sort according to the value of the k-th component of each
entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return
the permutation instead of the permuted vector, 4: use descending instead of
ascending order, 8: remove duplicate entries.
*** at top-level: veclexsort()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: veclexsort(x) ===> vecsort(x,,2)
vecsort(x,{cmpf},{flag=0}): sorts the vector of vectors (or matrix) x in
ascending order, according to the comparison function cmpf, if not omitted. (If
cmpf is an integer k, sort according to the value of the k-th component of each
entry.) Binary digits of flag (if present) mean: 1: indirect sorting, return
the permutation instead of the permuted vector, 4: use descending instead of
ascending order, 8: remove duplicate entries.
*** at top-level: vvector()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: vvector(n,X,expr) ===> vectorv(n,X,expr)
vectorv(n,{X},{expr=0}): column vector with n components of expression expr (X
ranges from 1 to n). By default, fill with 0s.
*** at top-level: weipell()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: weipell(e) ===> ellwp(e)
ellwp(w,{z='x},{flag=0}): computes the value at z of the Weierstrass P function
attached to the lattice w, as given by ellperiods. Optional flag means 0
(default), compute only P(z), 1 compute [P(z),P'(z)].
*** at top-level: wf()
*** ^----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: wf(x) ===> weber(x)
weber(x,{flag=0}): one of Weber's f function of x. flag is optional, and can be
0: default, function f(x)=exp(-i*Pi/24)*eta((x+1)/2)/eta(x), 1: function
f1(x)=eta(x/2)/eta(x) 2: function f2(x)=sqrt(2)*eta(2*x)/eta(x). Note that j =
(f^24-16)^3/f^24 = (f1^24+16)^3/f1^24 = (f2^24+16)^3/f2^24.
*** at top-level: wf2()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: wf2(x) ===> weber(x,2)
weber(x,{flag=0}): one of Weber's f function of x. flag is optional, and can be
0: default, function f(x)=exp(-i*Pi/24)*eta((x+1)/2)/eta(x), 1: function
f1(x)=eta(x/2)/eta(x) 2: function f2(x)=sqrt(2)*eta(2*x)/eta(x). Note that j =
(f^24-16)^3/f^24 = (f1^24+16)^3/f1^24 = (f2^24+16)^3/f2^24.
*** at top-level: zell()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: zell(e,P) ===> ellpointtoz(e,P)
ellpointtoz(E,P): lattice point z corresponding to the point P on the elliptic
curve E.
*** at top-level: zideallog()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: zideallog(nf,x,bid) ===> ideallog(nf,x,bid)
ideallog({nf},x,bid): if bid is a big ideal, as given by idealstar(nf,D,...),
gives the vector of exponents on the generators bid.gen (even if these
generators have not been explicitly computed).
*** at top-level: zidealstar()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: zidealstar(nf,I) ===> idealstar(nf,I)
idealstar({nf},N,{flag=1},{cycmod}): gives the structure of (Z_K/N)^*, where N
is a modulus (an ideal in any form or a vector [f0, foo], where f0 is an ideal
and foo is a {0,1}-vector with r1 components. If the positive integer cycmod is
present, only compute the group modulo cycmod-th powers. flag is optional, and
can be 0: structure as an abelian group [h,d,g] where h is the order, d the
orders of the cyclic factors and g the generators; if flag=1 (default), gives a
bid structure used in ideallog to compute discrete logarithms; underlying
generators are well-defined but not explicitly computed, which saves time; if
flag=2, same as with flag=1 except that the generators are also given. If nf is
omitted, N must be an integer and we return the structure of (Z/NZ)^*.
*** at top-level: zidealstarinit()
*** ^----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: zidealstarinit(nf,id) ===> idealstar(nf,id,1)
idealstar({nf},N,{flag=1},{cycmod}): gives the structure of (Z_K/N)^*, where N
is a modulus (an ideal in any form or a vector [f0, foo], where f0 is an ideal
and foo is a {0,1}-vector with r1 components. If the positive integer cycmod is
present, only compute the group modulo cycmod-th powers. flag is optional, and
can be 0: structure as an abelian group [h,d,g] where h is the order, d the
orders of the cyclic factors and g the generators; if flag=1 (default), gives a
bid structure used in ideallog to compute discrete logarithms; underlying
generators are well-defined but not explicitly computed, which saves time; if
flag=2, same as with flag=1 except that the generators are also given. If nf is
omitted, N must be an integer and we return the structure of (Z/NZ)^*.
*** at top-level: zidealstarinitgen()
*** ^-------------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: zidealstarinitgen(nf,id) ===> idealstar(nf,id,2)
idealstar({nf},N,{flag=1},{cycmod}): gives the structure of (Z_K/N)^*, where N
is a modulus (an ideal in any form or a vector [f0, foo], where f0 is an ideal
and foo is a {0,1}-vector with r1 components. If the positive integer cycmod is
present, only compute the group modulo cycmod-th powers. flag is optional, and
can be 0: structure as an abelian group [h,d,g] where h is the order, d the
orders of the cyclic factors and g the generators; if flag=1 (default), gives a
bid structure used in ideallog to compute discrete logarithms; underlying
generators are well-defined but not explicitly computed, which saves time; if
flag=2, same as with flag=1 except that the generators are also given. If nf is
omitted, N must be an integer and we return the structure of (Z/NZ)^*.
*** at top-level: box()
*** ^-----
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: box(x,a) ===> plotbox(x,a)
plotbox(w,x2,y2,{filled=0}): if the cursor is at position (x1,y1), draw a box
with diagonal (x1,y1) and (x2,y2) in rectwindow w (cursor does not move). If
filled=1, fill the box.
*** at top-level: color()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: color(w,c) ===> plotcolor(w,c)
plotcolor(w,c): in rectwindow w, set default color to c. Possible values for c
are [R,G,B] values, a color name or an index in the graphcolormap default:
factory settings are 1=black, 2=blue, 3=sienna, 4=red, 5=green, 6=grey,
7=gainsborough. Return [R,G,B] value attached to color.
*** at top-level: cursor()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: cursor(w) ===> plotcursor(w)
plotcursor(w): current position of cursor in rectwindow w.
*** at top-level: draw()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: draw(list) ===> plotdraw(list)
plotdraw(w, {flag=0}): draw rectwindow w. More generally, w can be of the form
[w1,x1,y1, w2,x2,y2,etc.]: draw rectwindows wi at given xi,yi positions. If
flag!=0, the xi,yi express fractions of the size of the current output device.
*** at top-level: initrect()
*** ^----------
*** not a function in function call
*** at top-level: killrect()
*** ^----------
*** not a function in function call
*** at top-level: line()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: line(w,x2,y2) ===> plotlines(w,x2,y2)
plotlines(w,X,Y,{flag=0}): draws an open polygon in rectwindow w where X and Y
contain the x (resp. y) coordinates of the vertices. If X and Y are both single
values (i.e not vectors), draw the corresponding line (and move cursor). If
(optional) flag is nonzero, close the polygon.
*** at top-level: lines()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: lines(w,x2,y2) ===> plotlines(w,x2,y2)
plotlines(w,X,Y,{flag=0}): draws an open polygon in rectwindow w where X and Y
contain the x (resp. y) coordinates of the vertices. If X and Y are both single
values (i.e not vectors), draw the corresponding line (and move cursor). If
(optional) flag is nonzero, close the polygon.
*** at top-level: move()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: move(w,x,y) ===> plotmove(w,x,y)
plotmove(w,x,y): move cursor to position x,y in rectwindow w.
*** at top-level: ploth2()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: ploth2(X=a,b,expr) ===> ploth(X=a,b,expr,1)
ploth(X=a,b,expr,{flag=0},{n=0}): plot of expression expr, X goes from a to b
in high resolution. Both flag and n are optional. Binary digits of flag mean:
1=Parametric, 2=Recursive, 4=no_Rescale, 8=no_X_axis, 16=no_Y_axis,
32=no_Frame, 64=no_Lines (do not join points), 128=Points_too (plot both lines
and points), 256=Splines (use cubic splines), 512=no_X_ticks, 1024= no_Y_ticks,
2048=Same_ticks (plot all ticks with the same length), 4096=Complex (the two
coordinates of each point are encoded as a complex number). n specifies number
of reference points on the graph (0=use default value). Returns a vector for
the bounding box.
*** at top-level: plothmult()
*** ^-----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: plothmult(X=a,b,expr) ===> ploth(X=a,b,expr)
ploth(X=a,b,expr,{flag=0},{n=0}): plot of expression expr, X goes from a to b
in high resolution. Both flag and n are optional. Binary digits of flag mean:
1=Parametric, 2=Recursive, 4=no_Rescale, 8=no_X_axis, 16=no_Y_axis,
32=no_Frame, 64=no_Lines (do not join points), 128=Points_too (plot both lines
and points), 256=Splines (use cubic splines), 512=no_X_ticks, 1024= no_Y_ticks,
2048=Same_ticks (plot all ticks with the same length), 4096=Complex (the two
coordinates of each point are encoded as a complex number). n specifies number
of reference points on the graph (0=use default value). Returns a vector for
the bounding box.
*** at top-level: point()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: point(w,x,y) ===> plotpoints(w,x,y)
plotpoints(w,X,Y): draws in rectwindow w the points whose x (resp y)
coordinates are in X (resp Y). If X and Y are both single values (i.e not
vectors), draw the corresponding point (and move cursor).
*** at top-level: points()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: points(w,x,y) ===> plotpoints(w,x,y)
plotpoints(w,X,Y): draws in rectwindow w the points whose x (resp y)
coordinates are in X (resp Y). If X and Y are both single values (i.e not
vectors), draw the corresponding point (and move cursor).
*** at top-level: postdraw()
*** ^----------
*** not a function in function call
*** at top-level: postploth()
*** ^-----------
*** not a function in function call
*** at top-level: postploth2()
*** ^------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: postploth2(X=a,b,expr) ===> psploth(X=a,b,expr,1)
psploth(X=a,b,expr,{flags=0},{n=0}): obsolete function.
*** at top-level: postplothraw()
*** ^--------------
*** not a function in function call
*** at top-level: pprint()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: pprint1()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
This function no longer exists
*** at top-level: rbox()
*** ^------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rbox(w,dx,dy) ===> plotrbox(w,dx,dy)
plotrbox(w,dx,dy,{filled}): if the cursor is at (x1,y1), draw a box with
diagonal (x1,y1)-(x1+dx,y1+dy) in rectwindow w (cursor does not move). If
filled=1, fill the box.
*** at top-level: read()
*** ^------
*** read: You never gave me anything to read!.
*** at top-level: rline()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rline(w,dx,dy) ===> plotrline(w,dx,dy)
plotrline(w,dx,dy): if the cursor is at (x1,y1), draw a line from (x1,y1) to
(x1+dx,y1+dy) (and move the cursor) in the rectwindow w.
*** at top-level: rlines()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
*** at top-level: rlines()
*** ^--------
*** bug in whatnow, please report.
*** at top-level: rmove()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rmove(w,dx,dy) ===> plotrmove(w,dx,dy)
plotrmove(w,dx,dy): move cursor to position (dx,dy) relative to the present
position in the rectwindow w.
*** at top-level: rpoint()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: rpoint(w,dx,dy) ===> plotrpoint(w,dx,dy)
plotrpoint(w,dx,dy): draw a point (and move cursor) at position dx,dy relative
to present position of the cursor in rectwindow w.
*** at top-level: rpoints()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
*** at top-level: rpoints()
*** ^---------
*** bug in whatnow, please report.
*** at top-level: scale()
*** ^-------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: scale(w,x1,x2,y1,y2) ===> plotscale(w,x1,x2,y1,y2)
plotscale(w,x1,x2,y1,y2): scale the coordinates in rectwindow w so that x goes
from x1 to x2 and y from y1 to y2 (y2<y1 is allowed).
*** at top-level: setprecision()
*** ^--------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: setprecision(n) ===> default(realprecision,n)
default({key},{val}): returns the current value of the default key. If val is
present, set opt to val first. If no argument is given, print a list of all
defaults as well as their values.
*** at top-level: setserieslength()
*** ^-----------------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: setserieslength(n) ===> default(seriesprecision,n)
default({key},{val}): returns the current value of the default key. If val is
present, set opt to val first. If no argument is given, print a list of all
defaults as well as their values.
*** at top-level: settype()
*** ^---------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: settype(x,t) ===> type(x,t)
type(x): return the type of the GEN x.
*** at top-level: string()
*** ^--------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: string(w,x) ===> plotstring(w,x)
plotstring(w,x,{flags=0}): draw in rectwindow w the string corresponding to x.
Bits 1 and 2 of flag regulate horizontal alignment: left if 0, right if 2,
center if 1. Bits 4 and 8 regulate vertical alignment: bottom if 0, top if 8,
v-center if 4. Can insert additional gap between point and string: horizontal
if bit 16 is set, vertical if bit 32 is set.
*** at top-level: texprint()
*** ^----------
*** not a function in function call
A function with that name existed in GP-1.39.15. Please update your script.
New syntax: texprint(x) ===> printtex(x)
printtex({str}*): outputs its string arguments in TeX format.
Total time spent: 5