Polynomials should support definite integration

[jdemeyer]

Symbolic expressions support definite and indefinite integration:

sage: var('x')
x
sage: (x^3).integral(x)
1/4*x^4
sage: (x^3).integral(x, 0, 1)
1/4

Polynomials on the other hand support only indefinite integration:

sage: R.<x> = QQ[]
sage: (x^3).integral(x)
1/4*x^4
sage: (x^3).integral(x, 0, 1)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-7-2a9c71b6b709> in <module>()
----> 1 (x**Integer(3)).integral(x, Integer(0), Integer(1))

/usr/local/src/sage-config/src/sage/rings/polynomial/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial.integral (build/cythonized/sage/rings/polynomial/polynomial_element.c:35807)()
   3361         return self._parent([n*coeffs[n] for n from 1 <= n <= degree])
   3362 
-> 3363     def integral(self,var=None):
   3364         """
   3365         Return the integral of this polynomial.

TypeError: integral() takes at most 1 positional argument (3 given)

Component: commutative algebra

Author: Frédéric Chapoton

Branch/Commit: u/chapoton/22033 @ 8254627

Issue created by migration from https://trac.sagemath.org/ticket/22033

[fchapoton]

Commit: 2735f04

[fchapoton]

Changed author from Jeroen Demeyer to Frédéric Chapoton

[fchapoton]

New commits:

2735f04

definite integral for polynomials

[fchapoton]

Branch: u/chapoton/22033

[fchapoton]

comment:3

one should be more careful in the substitution to handle multivariate polynomials too

[sagetrac-git]

Changed commit from 2735f04 to 8254627

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8254627

work in progress

[fchapoton]

comment:5

there is another method "integral" for singular polynomials that needs the same treatment