Inconsistency in polynomial .reverse(n)

[defeo]

The optional argument of the .reverse() method of univariate polynomials is interpreted inconsistently through different classes.

Rationals interpret is as "length":

sage: _.<x> = QQ[]
sage: (x+1).reverse(1)
1
sage: (x).reverse(1)
0

The docstring for generic polynomials (inherited by CC, number fields, Polynomial_GF2X, Polynomial_ZZ_pEX, ...) says:

If an optional degree argument is given the coefficient list will
be truncated or zero padded as necessary and the reverse polynomial
will have the specified degree.

but the behaviour is inconsistent with it

sage: _.<x> = GF(2)[]
sage: (x+1).reverse(1)
x + 1
sage: (x).reverse(1)
1
sage: ['reverse' in cl.__dict__ for cl in  inspect.getmro(x.__class__)]
[False, False, True, False, False, False, False, False, False, False]
sage: inspect.getmro(x.__class__)[2]
<type 'sage.rings.polynomial.polynomial_element.Polynomial'>

Polynomial_zmod_flint and Polynomial_integer_dense_flint have the exact same docstring and behaviour, though they do not inherit .reverse() from the generic class:

sage: _.<x> = ZZ[]
sage: (x+1).reverse(1)
x + 1
sage: (x).reverse(1)
1
sage: ['reverse' in cl.__dict__ for cl in  inspect.getmro(x.__class__)]
[True, True, False, False, False, False, False, False, False]
<type 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>

Reals take no optional argument. The docstring says

Returns x!^d f(1/x) where d is the degree of f.

and the behaviour is consistent with it

sage: (x+1).reverse()
x + 1.00000000000000
sage: x.reverse()
1.00000000000000

In my opinion the best behaviour is the one of the generic class, but the docstring should be amended to something similar to the last one, which is the proper mathematical definition. The behaviour of rationals should be corrected to conform to the other classes.

CC: @mezzarobba @jhpalmieri

Component: commutative algebra

Keywords: polynomial univariate reverse

Author: Bruno Grenet

Branch/Commit: bd32a84

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/15077

[sagetrac-jakobkroeker]

Stopgaps: inconsistentAnswer

[fchapoton]

comment:6

This is obsolete. QQ['x'] now works as the other cases.

[jhpalmieri]

comment:7

There remain two issues: unifying the documentation, and also the version for RR does not allow for an optional argument. Low priority, but I say we keep this open.