Allow conversion of strings to iterated polynomial rings

[novoselt]

It is possible to convert strings and symbolic expressions to iterated polynomial rings in a single variable, but not many if the string contains names of coefficients:

sage: Rs = QQ["a"]["b"]
sage: Rs("a*b")
a*b
sage: Rm = QQ["a"]["b, c"]
sage: Rm("a*b")
Traceback (most recent call last):
...
TypeError: unable to convert string

The patch introduces gens_dict_recursive method and uses it instead of gens_dict in the conversion code:

sage: Rs = QQ["a"]["b"]
sage: Rs("a*b")
a*b
sage: Rm = QQ["a"]["b, c"]
sage: Rm("a*b")
a*b
sage: Rm.gens_dict_recursive()
{'a': a, 'c': c, 'b': b}

Component: commutative algebra

Author: Andrey Novoseltsev

Reviewer: Frédéric Chapoton

Merged: sage-5.4.beta1

Issue created by migration from https://trac.sagemath.org/ticket/13327

[fchapoton]

comment:2

Looks good to me. Maybe one could check

Rm("a*b").parent()

to be sure that it lands where it should ?

[novoselt]

comment:3

Attachment: trac_13327_string_to_iterated_mpolyring.patch.gz

OK, added the check!

[fchapoton]

comment:4

Ok, looks good to me. Positive review.

By the way, what do you think of that :

sage: QQ["a, a"]           
Multivariate Polynomial Ring in a, a over Rational Field

[novoselt]

comment:5

I think this is horrible, as well as

sage: QQ["a"]["a"]
Univariate Polynomial Ring in a over Univariate Polynomial Ring in a over Rational Field

but some people think that it does not matter how something is printing and the name is meaningless.

From my point of view, all generator names should be distinct and different from generator names used in the base ring (recursively). Note that if this is enforced, then it is not possible to create polynomial rings with symbolic coefficients, since "any name is in SR". Since such polynomials are important (at least to me), the first step is to have symbolic rings with only explicitly specified names allows as variables. Then constructors can check for name collisions.

[novoselt]

Reviewer: Frédéric Chapoton

[jdemeyer]

Merged: sage-5.4.beta1