evaluating multivariate polynomials yields non-constant

[JohnCremona]

The following behaviour does not agree with the documentation for the {{{call}} function on multivariable polynomials, which states that (as one would expect and hope) the result should lie in the constant field:

sage: K.<t> = NumberField(x^2+47)
sage: R.<X,Y,Z> = K[]
sage: f = X+Y+Z
sage: a = f(t,t,t)
sage: a.parent()
Multivariate Polynomial Ring in X, Y, Z over Number Field in t with defining polynomial x^2 + 47

It is also inconsistent:

sage: R.<X,Y,Z> = QQ[]
sage: f = X+Y+Z
sage: a = f(2,3,4)
sage: a.parent()
Rational Field

This causes strange bugs -- see #8498 for an example.

CC: @categorie @malb

Component: algebra

Keywords: polynomial evaluation

Author: John Cremona

Reviewer: Alex Ghitza

Merged: sage-4.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8502

[JohnCremona]

comment:1

Bug fixed: I added tests for when the resulting value is either 0, or a nonzero constant, in which case an element of the base ring is returned. Otherwise an element of the parent is returned (so you can still evaluate f(x+y,y) and similar.)

Patch up as soon as testing is finished.

malb: I'm CC-ing you as the past person to work on this file.

[JohnCremona]

Author: John Cremona

[JohnCremona]

Applies to 4.3.5

[JohnCremona]

comment:2

Attachment: trac_8502-mpoly.patch.gz

[aghitza]

Reviewer: Alex Ghitza

[aghitza]

comment:3

Looks good.

[jhpalmieri]

Merged: sage-4.4.alpha0

[jhpalmieri]

comment:4

Merged "trac_8502-mpoly.patch" in 4.4.alpha0.