<Shift>-<Enter> or click on the
Evaluate button below it. A trailing semi-colon ; prevents output.
You can assign to variables and define user functions. (Speed is approximately one
eighth of native speed.)
?eulerphi (short help), ??factor (long help in
new tab)
2*3, 10!, (1+x)^10,
exp(Pi*sqrt(163))
factor(2^128+1), factor(x^4+4), isprime(10^50+151)
ploth(x=1,100,[sqrt(2/(Pi*x)),besselj(0,x),-sqrt(2/(Pi*x))])
ploth(x=0,2*Pi,[sin(2*x),cos(3*x)],1)
intnum(x=-oo,oo,1/(1+x^2)), sumpos(n=1, n^(-3))
sin(x), ellj(x + O(x^20))
Mod(x,x^2-x-1)^100000==fibonacci(100000)*x+fibonacci(99999)
g=gamma(1/4+O(5^20)), algdep(g,4), g^4+4*g^2+5
\p100: change default accuracy to 100 decimal digits
K=bnfinit(a^2+23); (huge: don't forget the ;),
K.clgp, bnrclassfield(K)
E=ellinit([1,3]*Mod(1,10^50+151)); ellcard(E)
E=ellinit([-157^2,0]); P=ellheegner(E), ellisoncurve(E,P)
polgalois(x^8-2), ellsearch(11) (loads packages
on demand)lfun(x^3-2, 2) (Dedekind zeta function)
E=ellinit("11a1");L=lfuninit(E,[0,100]);
ploth(x=0,100,lfunhardy(L,x))
ecm(N, B = 1000!, nb = 100)=
{
for(a = 1, nb,
iferr(ellmul(ellinit([a,1], N), [0,1], B),
E, return(gcd(lift(component(E,2)),N))))
}
ecm(2^101-1)
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