Fix some more deepcopy/caching issues in the quadratic forms code (followup to #5403)

[sagetrac-mabshoff]

Gonzalo found some problem in the QF code when working on #5403. These problems are related to deepcopy.

Cheers,

Michael

Component: quadratic forms

Issue created by migration from https://trac.sagemath.org/ticket/5417

[tornaria]

comment:1

The patch in #5403 fixes the function scale_by_factor in quadratic_form__variable_substitutions.py, by replacing the use of copy.deepcopy + __init__ by a call to the constructor.

The issue with this is that the caches for some functions are copied, hence the results may be incorrect. There seem to be more instances of this bug in the quadratic_forms code, hence this ticket, but that one is the only one currently triggered by the following doctest (this only happens after applying the import * fix in #5403 without the deepcopy fix):

        sage: Q = QuadraticForm(ZZ, 3, [2, -2, 0, 3, -5, 4])
        sage: Q.jordan_blocks_in_unimodular_list_by_scale_power(2)
        Traceback (most recent call last):
        ...
        TypeError: Oops!  The given quadratic form has a Jordan component with a negative scale exponent!
        This routine requires an integer-matrix quadratic form for the output indexing to work properly!

        sage: Q.scale_by_factor(2).jordan_blocks_in_unimodular_list_by_scale_power(2)
        [Quadratic form in 2 variables over Integer Ring with coefficients: 
        [ 0 2 ]
        [ * 0 ]
        ,
        Quadratic form in 0 variables over Integer Ring with coefficients: 
        ,
        Quadratic form in 1 variables over Integer Ring with coefficients: 
        [ 345 ]
        ]

In this example, after the first call to jordan_blocks_in_unimodular_list_by_scale_power, the result is cached, and the function scale_by_factor copies this cached result, so that the second call returns the answer for the original quadratic form.