intformal

Function: intformal
Section: polynomials
C-Name: integ
Prototype: GDn
Help: intformal(x,{v}): formal integration of x with respect to v, or to the
 main variable of x if v is omitted.
Doc: \idx{formal integration} of $x$ with respect to the variable $v$ (wrt.
 the main variable if $v$ is omitted). Since PARI cannot represent
 logarithmic or arctangent terms, any such term in the result will yield an
 error:
 \bprog
  ? intformal(x^2)
  %1 = 1/3*x^3
  ? intformal(x^2, y)
  %2 = y*x^2
  ? intformal(1/x)
    ***   at top-level: intformal(1/x)
    ***                 ^--------------
    *** intformal: domain error in intformal: residue(series, pole) != 0
 @eprog
 The argument $x$ can be of any type. When $x$ is a rational function, we
 assume that the base ring is an integral domain of characteristic zero.

   By  definition,   the main variable of a \typ{POLMOD} is the main variable
 among the  coefficients  from  its  two  polynomial  components
 (representative and modulus); in other words, assuming a polmod represents an
 element of $R[X]/(T(X))$, the variable $X$ is a mute variable and the
 integral is taken with respect to the main variable used in the base ring $R$.
 In particular, it is meaningless to integrate with respect to the main
 variable of \kbd{x.mod}:
 \bprog
 ? intformal(Mod(1,x^2+1), 'x)
 *** intformal: incorrect priority in intformal: variable x = x
 @eprog