Univariate Laurent polynomial do not properly handle __call__

[tscrim]

Univariate Laurent polynomials behave very differently with __call__ compared to other polynomials. In particular, the following does not (correctly) work:

sage: R.<t> = LaurentPolynomialRing(ZZ)
sage: f = t^(-2) + t^2
sage: f(t=-1)  # Boom
sage: f(x=-1)  # Boom
sage: f()  # Boom
sage: f(1,2)  # Should be an error
2

The original symptom (which has been fixed by other means, see comment:3) came from

sage: R.<q> = QQ[]
sage: p = q^4 + q^2 - 2*q + 3
sage: L.<x,y> = LaurentPolynomialRing(QQ)
sage: p(q=x)
x^4 + x^2 - 2*x + 3

but if we change things to a univariate Laurent polynomial ring, we get:

sage: L.<x> = LaurentPolynomialRing(QQ)
sage: p(q=x)
...
IndexError: tuple index out of range

See comment:2.

Component: commutative algebra

Keywords: Laurent polynomial, substitution

Author: Travis Scrimshaw

Branch/Commit: 7f41391

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/17554

[nbruin]

comment:2

The following seems to be the issue

sage: p() #evaluating with no arguments should probably be a no-op
q^4 + q^2 - 2*q + 3
sage: x() #but it raises an error for laurent polynomials
IndexError: tuple index out of range

The problem gets triggered by sage.rings.polynomial.polynomial_element.Polynomial.__call__, which for keyword arguments does:

          P = self.parent()
            name = P.variable_name()
            if name in kwds:
                if len(x) > 0:
                    raise ValueError("must not specify both a keyword and positional argument")
                a = self(kwds[name])
                del kwds[name]
                try:
                    return a(**kwds)
                except TypeError:
                    return a

The command return a(**kwds) fails, because it's effectively a(*(),**{}). Furthermore, it fails with an IndexError which doesn't get caught.

The better solution is probably to amend laurentpolynomial's __call__ to do the right thing. Presently, it doesn't support keyword arguments at all and it expects non-empty arguments. Its implementation is

    def __call__(self, *x):
        if isinstance(x[0], tuple):
            x = x[0]
        return self.__u(x) * (x[0]**self.__n)

which expects there is at least one argument and doesn't handle keyword arguments.

[fchapoton]

comment:3

This seems to work now (8.0.b11)

[tscrim]

comment:4

However, there are still serious issues with __call__ that I am recycling this ticket for (sorry it completely fell off my radar). The attached branch makes the behavior standard with the rest of polynomials Sage (with some mild cleanup of the multivariate __call__).

---

New commits:

7f41391

Make univariate Laurent polynomials behave like other polynomials.

[tscrim]

Description changed:

--- 
+++ 
@@ -1,4 +1,16 @@
-We can do
+Univariate Laurent polynomials behave very differently with `__call__` compared to other polynomials. In particular, the following does not (correctly) work:
+
+```
+sage: R.<t> = LaurentPolynomialRing(ZZ)
+sage: f = t^(-2) + t^2
+sage: f(t=-1)  # Boom
+sage: f(x=-1)  # Boom
+sage: f()  # Boom
+sage: f(1,2)  # Should be an error
+2
+```
+
+The original symptom (which has been fixed by other means, see [comment:3](#comment%3A3)) came from
 
 ```
 sage: R.<q> = QQ[]
@@ -15,3 +27,4 @@
 ...
 IndexError: tuple index out of range
 ```
+See [comment:2](#comment%3A2).

[tscrim]

Author: Travis Scrimshaw

[tscrim]

Commit: 7f41391

[tscrim]

Branch: public/rings/laurent_polynomial_call-17554