conversion in multivariate polynomial ring fails

[dkrenn]

sage: K = QQ
sage: QQabc = PolynomialRing(K, ['a', 'b', 'c'])
sage: QQxy = PolynomialRing(K, ['x', 'y'])
sage: Pxy = PolynomialRing(QQabc, ['x', 'y'])
sage: Pabc = PolynomialRing(QQxy, ['a', 'b', 'c'])
sage: Pabc(QQabc.0 * Pxy.1)

fails with a TypeError.

Component: algebra

Issue created by migration from https://trac.sagemath.org/ticket/23629

[dkrenn]

comment:1

Maybe #22333 would fix this issue.

[tscrim]

comment:2

To begin, we can simplify this a little bit by taking K = QQ. I updated the description accordingly.

I don't think that #22333 would fix the issue as I think the conversion is getting confused. Actually, this code block in _mpoly_dict_recursive() seems to be where problems start:

        elif not my_vars[-1] in vars:
            x = base_ring(self) if base_ring is not None else self
            const_ix = ETuple((0,)*len(vars))
            return { const_ix: x }

You get into a chicken-and-egg problem of needing to extract out all of your variables from the input x, but first you need to know there are none of your variables in x as a polynomial in its current form. This is what leads to the current problem, it thinks a*y should be treated as a constant polynomial with respect to the variables abc. The recurse is made and it would then extract the y variable, but it doesn't know what to do with the a because the base ring is K. This is what raises the error.

I feel like the problem is that the polynomial code that calls this only passes variable_names() rather than variable_names_recursive(). However, even with doing that, it doesn't extract the correct variables first due to the ordering of variable_names_recursive() with your variables being last. I think the code that tries to construct the mapping is making way too many assumptions about the input, especially for how general I feel this code should work.

Thus, I think two things need to be fixed. The first is that we should be using variable_names_recursive() when calling _mpoly_dict_recursive in __call__. The second is that the handling of variables when my_vars is a subset of vars needs to be done without assuming my_vars are the last variables of vars.

---

Additionally, this "works" however:

sage: K = QQ
sage: QQabc = PolynomialRing(K, ['a', 'b', 'c'])
sage: QQxyz = PolynomialRing(K, ['x', 'y', 'z'])
sage: Pxyz = PolynomialRing(QQabc, ['x', 'y', 'z'])
sage: Pabc = PolynomialRing(QQxyz, ['a', 'b', 'c'])
sage: Pabc(QQabc.0 * Pxyz.1)
x*b

because it goes through a slightly different code path. However, the result is wrong:

sage: QQabc.0 * Pxyz.1
a*y

This result is because it first matches the number of variables and does:

sage: QQabc(QQxyz.1)
b

So this may even be considered "correct" behavior, but it is deserving of a sage-devel ask and would be a separate ticket (if considered a bug).

[dkrenn]

comment:3

See also #23631.