Doctest fixes for bugs with real_part and is_real

[mforets]

The real_part method of a variable in the integer domain behaves unexpectedly,

sage: SR.var('x', domain='integer').real_part()
real_part(x)

compare to

sage: SR.var('x', domain='real').real_part()
x

[nbruin]

You can get the desired result by explicitly doing assume(x,'real'). Is it the case that integer should be implying real? Gaussian integers aren't real ... (but then the algebraic integers aren't discrete in R, so perhaps that's not what integer means).

[mforets]

well, true, one can add that as an additional assumption, and I don't know if integer should be implying real in the most general case in Sage.

the use case at hand was an expression involving complex exponentials and some variables that are discretized, hence the integer assumption ​(integers being understood as a subset of the real numbers.)

[rws]

Internally in Pynac there are the info flags ìnteger and cinteger and the internal bool numeric::is_cinteger() uses py_is_cinteger which looks like return py_is_integer(x) or (py_is_crational(x) and py_denom(x) == 1), but the functions are buggy (maybe since the parent of I changed some time ago):

sage: from sage.libs.pynac.pynac import py_is_crational_for_doctest
sage: py_is_crational_for_doctest(1)
True
sage: py_is_crational_for_doctest(2*I)
False
sage: py_is_cinteger_for_doctest(2*I)
False

is_cinteger is not used in Pynac. For crational I opened the (unrelated to this ticket) ​https://github.com/pynac/pynac/issues/253 because it's used in Pynac. It's not exposed to the Sage user.

So from the info flag level integer would mean real integer, so this ticket is about a bug in Pynac with setting flags in symbol::set_domain. I cannot say atm if there are more bugs revealed in consequence.

This also means that the docstring for x.is_integer? should be adapted to this because Expression.is_integer() directly queries the integer info flag.

[rws]

See also #20132.

[rws]

Fixed in pynac master. I will also add here doctests for the (new) bug sqrt(-2).is_real().

[rws]

New commits:

​593c379

23093: doctests for some issues with the symbolic real/integer domain

[tscrim]

LGTM. Feel free to set to positive review if this is ready for review.

[vbraun]

See patchbot

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​58c2a27	Merge branch 'develop' into t/23093/doctest_fixes_for_bugs_with_real_part_and_is_real
​bd732ec	23134: version/chksum/delete old patch
​31340ea	23134: doctest fixes
​c83582f	Merge branch 'develop' into t/23134/upgrade_to_pynac_0_7_8
​caf7065	Merge branch 'u/rws/23199-1' of git://trac.sagemath.org/sage into t/23134/upgrade_to_pynac_0_7_8
​e46e07c	Merge branch 'u/rws/23199-1' of git://trac.sagemath.org/sage into t/23134/upgrade_to_pynac_0_7_8
​5f9a991	Merge branch 'develop' into t/23134/upgrade_to_pynac_0_7_8
​86f8933	23134: last minute patch for doc build failures on Debian
​20bddee	Merge commit '86f8933d83ba2ac11adeea91e26703b08263f1b4' of git://trac.sagemath.org/sage into t/23093/doctest_fixes_for_bugs_with_real_part_and_is_real
​13954c4	23093: fix doctests

[rws]

Merging the dependency makes the failing tests pass. However the problem is uncovered that the added doctests change x to integer, making subsequent tests fail.

So I just merged the dependency and added forget().