cmp for number field elements

[robertwb]

See discussion at http://groups.google.com/group/sage-nt/browse_thread/thread/422606e40805d5d0?hl=en

Note that cmp(list(a), list(b)) can be slow...

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/6132

[rlmill]

comment:1

Minor, but I just fixed two of these elsewhere: it's spelled "consistent"

[robertwb]

Attachment: 6132-nf-elt-cmp.patch.gz

[aghitza]

comment:3

The patch applies with some fuzz to 4.0.rc2, but I'm seeing a bunch of doctest failures in sage/rings:

The following tests failed:


	sage -t  "devel/sage-main/sage/rings/number_field/number_field.py"
	sage -t  "devel/sage-main/sage/rings/number_field/number_field_rel.py"
	sage -t  "devel/sage-main/sage/rings/number_field/order.py"
	sage -t  "devel/sage-main/sage/rings/number_field/galois_group.py"
	sage -t  "devel/sage-main/sage/rings/number_field/number_field_element.pyx"
	sage -t  "devel/sage-main/sage/rings/number_field/number_field_ideal.py"
	sage -t  "devel/sage-main/sage/rings/number_field/number_field_ideal_rel.py"
	sage -t  "devel/sage-main/sage/rings/number_field/unit_group.py"
	sage -t  "devel/sage-main/sage/rings/polynomial/complex_roots.py"
	sage -t  "devel/sage-main/sage/rings/polynomial/polynomial_element.pyx"

[nbruin]

comment:4

In Python 3, "greater than" etc. comparisons between objects where no natural ordering exist are supposed to raise a "TypeError"

Already, comparing complex numbers in Python 2.6.2 raises
TypeError: no ordering relation is defined for complex numbers

Changing this will probably lead to even more doctest failures, but brings us closer to Python's way of doing things and to mathematical sanity.

[robertwb]

comment:6

Note that to follow this convention, we have to use __richcmp__ as == and != should still work for unordered elements.

[kcrisman]

comment:7

Apparently related to #7160 and #10064, see this sage-devel discussion.

[williamstein]

comment:8

See also #9572.

[kcrisman]

comment:9

Replying to @williamstein:

See also #9572.

That is a SageNB release ticket. ?

[williamstein]

comment:10

See #7160 for a related ticket/discussion.

[mwhansen]

comment:11

I think we can close this as a duplicate of those other tickets now that they are merged.