Maxima missing rectform simplification after integral()

[sagetrac-jan]

var('a b c x', domain='real')
A = (sin(a) * x^2+sin(b) *x + sin(c)) * exp(-x^2)
Aint = A.integrate(x,-infinity,infinity)

A.imag() is 0

Aint.imag() is a long expression, which doesn't simplify to 0. This surprising for the user.

A slightly different example, actually a generalization of the one above, just works:

var('a b c x', domain='real')
B = (a * x^2+b *x + c) * exp(-x^2)
Bint = B.integrate(x,-infinity,infinity)

Examples can be found here: http://demo.sagenb.org/home/pub/179

CC: @kcrisman

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/11655

[rwst]

comment:6

This seems to be a missing rectform simplification because

sage: Aint.expand().simplify_rectform()
1/2*sqrt(pi)*sin(a) + sqrt(pi)*sin(c)

The bug is then rather that Maxima does it not in all cases.