Bug with NumberField.abs_val at zero

[mercatp]

The following code fails:

sage: x = polygen(ZZ)
sage: K = NumberField(x^3 - 3, 'a')
sage: v = tuple(K.primes_above(3))[0]
sage: K.abs_val(v, K.zero())
Traceback (most recent call last)
...
TypeError: unsupported operand parent(s) for ^:
'The Infinity Ring' and 'The Infinity Ring'

It should return 0. We fix the bug and add a doctest.

Related:

• #28241: Fix number field abs_val at non-real places

[mercatp]

New commits:

​9261c0b

Correct a bug with NumberField.abs_val and add a doctest to check that it's corected

[alexjbest]

I set this to needs review as it seems it is done, so the patchbots can check it.

The other way to do this would be to ensure that p^(-Infinity) returns 0 in some way, but I don't suppose that really matters.

[gh-mwageringel]

Returning 0 gives an int which is of the wrong type, so please change it to return R.zero() instead. Moreover, a blank line is needed after TESTS:: and please remove the trailing whitespace in the line above that. Also enter your full name in the authors field.

I am not too familiar with the theory, so it would be good if someone can confirm this is mathematically correct.

[embray]

Ticket retargeted after milestone closed

[mkoeppe]

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

[mkoeppe]

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[chapoton]

here is a brand new branch, please review

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New commits:

​1d7248c

fix absolute value of zero in number fields

[chapoton]

green bot, please review this very simple ticket