QuotientRing elements are not callable

[vbraun]

It would be convenient if quotient ring elements would be callable like polynomials. This is currently not the case:

sage: R.<x,y> = QQ[]
sage: I = R.ideal(x)
sage: Q = R.quotient_ring(I)
sage: Q
Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x)
sage: Q.inject_variables()
Defining xbar, ybar
sage: p = xbar + ybar
sage: p(1,1)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/vbraun/opt/sage-4.7.alpha4/devel/sage-main/<ipython console> in <module>()

TypeError: 'QuotientRingElement' object is not callable

The attached patch implements this functionality by handing the argument through to the lift.

Arguably, it should check that the result does not depend on the presentation. Pro: catches errors; Con: potentially slow, ideal membership test necessary if arguments are polynomials.

---

Apply attachment: trac_11199-jhp.patch.

CC: @novoselt

Component: algebra

Author: Volker Braun

Reviewer: John Palmieri

Issue created by migration from https://trac.sagemath.org/ticket/11199

[vbraun]

Initial patch

[vbraun]

comment:1

Attachment: trac_11199_QuotientRingElement_call.patch.gz

[jhpalmieri]

comment:3

Evaluating an element of a quotient ring doesn't make mathematical sense in general, only if it makes sense to evaluate the lift: if you're taking a quotient of a group algebra or the p-adics, what does it mean to evaluate an element of it? I'm attaching a new patch which adds a comment about this to the docstring; is this enough warning?

I'm happy with the original patch as far as it goes, and I'm almost ready to give it a positive review, but I'd like to hear opinions about the issue I raised.

[jhpalmieri]

Reviewer: John Palmieri

[jhpalmieri]

Attachment: trac_11199-delta.patch.gz

for reference only; difference beteen initial patch and jhp patch

[jhpalmieri]

apply this one

[sagetrac-fwclarke]

comment:4

Attachment: trac_11199-jhp.patch.gz

Even with the extra warning in the docstring, users could very easily be misled.
For to make the evaluation independent of the lift it is necessary
for the ideal defining the quotient to annihilate the argument.

I think it would be sensible to have a parameter 'check' with default True, and a
clause like:

if check and any(g(args) !=0 for g in f.parent().defining_ideal().gens()):
    raise ValueError, "argument not in the zero set of the ideal"

That way an unthinking user is not going to be caught out, while someone who
knows what they're doing can speed things up by setting 'check=False'.