[fixed by #5508] `__getitem__` for relative number field elements is ... now fixed

[craigcitro]

Indexing into a relative number field element does unexpected things:

sage: K
 Number Field in b with defining polynomial x^3 - 5 over its base field
sage: K([1,2,3])
 3*b^2 + (-6*a + 2)*b - 2*a + 7
sage: K([1,2,3])[0]
 1
sage: K([1,2,3])[1]
 2

sage: K([1,2,3]).list()
 [-2*a + 7, -6*a + 2, 3]
sage: K([1,2,3]).list()[0]
 -2*a + 7

sage: K([1,2,3]).polynomial()
 3*x^2 + 2*x + 1

The issue is that it's giving you the entries in the representation of the element as an absolute number field element. It should be fixed.

Component: number theory

Issue created by migration from https://trac.sagemath.org/ticket/2551

[sagetrac-fwclarke]

comment:1

This is sorted out by the patch in #5508, in particular the changes there to __getitem__ for the class NumberFieldElement_relative in sage/rings/number_field/number_field_element.pyx.

[sagetrac-mabshoff]

comment:2

To close this we would need a doctest.

Cheers,

Michael

[sagetrac-fwclarke]

comment:4

Replying to @sagetrac-mabshoff:

To close this we would need a doctest.

See lines 2421 to 2445 of sage/rings/number_field/number_field_element.pyx as patched by #5508:

        EXAMPLES::
        
            sage: K.<a, b> = NumberField([x^3 - 5, x^2 + 3])
            sage: c = (a + b)^3; c
            3*b*a^2 - 9*a - 3*b + 5
            sage: c[0]
            -3*b + 5
        
        We illustrate bounds checking::
        
            sage: c[-1]
            Traceback (most recent call last):
            ...
            IndexError: index must be between 0 and the relative degree minus 1.
            sage: c[4]
            Traceback (most recent call last):
            ...
            IndexError: index must be between 0 and the relative degree minus 1.
        
        The list method implicitly calls ``__getitem__``::
        
            sage: list(c)
            [-3*b + 5, -9, 3*b]
            sage: K(list(c)) == c
            True

[sagetrac-mabshoff]

comment:5

Fixed in Sage 3.4.1.alpha0 via #5508. Thanks Francis :)

Cheers,

Michael