sage_input for multivariate polynomials

[AndrewMathas]

Multivariate polynomials do not currently have a _sage_input_ method. This ticket rectifies this:

sage: sage_input(ZZ['u','q'])
ZZ['u,q']

Component: basic arithmetic

Keywords: Multivariate polynomials, days94

Author: Andrew Mathas

Branch/Commit: u/andrew.mathas/sage_input_for_multivariate_polynomials @ a309ff6

Reviewer: Thierry Monteil

Issue created by migration from https://trac.sagemath.org/ticket/25723

[AndrewMathas]

Branch: u/andrew.mathas/sage_input_for_multivariate_polynomials

[AndrewMathas]

Changed keywords from none to Multivariate polynomials

[AndrewMathas]

Description changed:

--- 
+++ 
@@ -1 +1,6 @@
+Multivariate polynomials do not currently have a `_sage_input_` method. This ticket rectifies this:

+```
+sage: sage_input(ZZ['u','q'])
+ZZ['u,q']
+```

[AndrewMathas]

Author: Andrew Mathas

[AndrewMathas]

Commit: a309ff6

[edd8e884-f507-429a-b577-5d554626c0fe]

Reviewer: Thierry Monteil

[edd8e884-f507-429a-b577-5d554626c0fe]

comment:3

The current implementation does not handle the sparsity nor the monomial order of the polynomial ring:

sage: R.<x,y> = PolynomialRing(QQ, order='neglex', sparse=True)
sage: R
Multivariate Polynomial Ring in x, y over Rational Field

sage: sage_input(R)
QQ['x,y']

sage: sage_eval(sage_input(R)) is R
False

sage: sage_input(R, verify=True)
AssertionError: Expected Multivariate Polynomial Ring in x, y over Rational Field == Multivariate Polynomial Ring in x, y over Rational Field

You need to check all those cases with the verify=True option.

See also #22565 and #25762 for similar issues.

[edd8e884-f507-429a-b577-5d554626c0fe]

Changed keywords from Multivariate polynomials to Multivariate polynomials, days94

[AndrewMathas]

comment:4

Replying to @sagetrac-tmonteil:

The current implementation does not handle the sparsity nor the monomial order of the polynomial ring:

sage: R.<x,y> = PolynomialRing(QQ, order='neglex', sparse=True)
sage: R
Multivariate Polynomial Ring in x, y over Rational Field

sage: sage_input(R)
QQ['x,y']

sage: sage_eval(sage_input(R)) is R
False

sage: sage_input(R, verify=True)
AssertionError: Expected Multivariate Polynomial Ring in x, y over Rational Field == Multivariate Polynomial Ring in x, y over Rational Field

You need to check all those cases with the verify=True option.

See also #22565 and #25762 for similar issues.

I agree that the (term) order should be taken into account but looking at both the documentation and the code sparse is not an option for multivariate polynomial rings. (I agree that it is an option for polynomial rings.) Am I missing something?