Segmentation fault in pynac when getting real/imag_part of a complex expression

[embray]

From this ​ask question the following crashes pynac with a stack overflow:

sage: n=var('n')
sage: assume(n, 'integer')
sage: (I^n).real_part()
/home/embray/src/sagemath/sage/local/lib/python2.7/site-packages/cysignals/signals.so(+0x80b5)[0x7f5b6da330b5]
/home/embray/src/sagemath/sage/local/lib/python2.7/site-packages/cysignals/signals.so(+0x8158)[0x7f5b6da33158]
/home/embray/src/sagemath/sage/local/lib/python2.7/site-packages/cysignals/signals.so(+0x96ad)[0x7f5b6da346ad]
/lib/x86_64-linux-gnu/libpthread.so.0(+0x10330)[0x7f5b7cf14330]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC7numeric3gcdERKS0_+0x1d)[0x7f594bfdcd7d]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZN5GiNaC3gcdERKNS_7numericES2_+0x9)[0x7f594bfe0e29]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC3add15integer_contentEv+0xcc)[0x7f594bfcc80c]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC3add5powerERKNS_7numericE+0x37)[0x7f594bf09d97]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC5power4evalEi+0x1933)[0x7f594bff6cf3]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZN5GiNaC2ex20construct_from_basicERKNS_5basicE+0x76)[0x7f594bf283a6]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC3mul29combine_ex_with_coeff_to_pairERKNS_2exERKNS_7numericE+0xb8)[0x7f594bfbcfb8]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC9expairseq12evalchildrenEi+0xa7)[0x7f594bf31df7]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC3mul4evalEi+0x36)[0x7f594bfc2d16]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZN5GiNaC2ex20construct_from_basicERKNS_5basicE+0x76)[0x7f594bf283a6]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC3add20recombine_pair_to_exERKNS_6expairE+0x5d)[0x7f594bf050bd]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC3add4infoEj+0x196)[0x7f594bf05ae6]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC5power4evalEi+0x460)[0x7f594bff5820]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZN5GiNaC2ex20construct_from_basicERKNS_5basicE+0x76)[0x7f594bf283a6]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC5power4evalEi+0x12e5)[0x7f594bff66a5]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZN5GiNaC2ex20construct_from_basicERKNS_5basicE+0x76)[0x7f594bf283a6]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC5power9real_partEv+0x50f)[0x7f594bfef0af]
/home/embray/src/sagemath/sage/local/lib/libpynac.so.18(_ZNK5GiNaC5power9real_partEv+0x51)[0x7f594bfeebf1]
...

followed by an infinite recursion in GiNaC::power::real_part(). It doesn't crash without assume(n, 'integer'), and gives a correct answer:

sage: n=var('n')
sage: (I^n).real_part()
cos(1/2*pi*real_part(n))*e^(-1/2*pi*imag_part(n))

so stipulating that assume(n, 'integer') should set imag_part(n) == 0 and real_part(n) == n and give the correct answer...

[gh-DaveWitteMorris]

Diagnosis: Pynac's power::real_part method erroneously assumes that if n is a positive integer, then ((a + b*I)^n).expand() will multiply the factors to write the expression as a sum of monomials. But this is not true when n is symbolic, rather than being equal to a specific integer. Instead, the expression (a + b*I)^n is returned with no change, which leads to an infinite loop.

This pynac patch should fix the bug (for real_part and imag_part).

---

New commits:

​cb80d0b	trac 28357 patch power::real_part
​1850eab	add doctests
​185acd9	increment pynac version

[tscrim]

Merge conflict.

[gh-DaveWitteMorris]

Rebased on 9.4b3

---

New commits:

​eb4e77f	trac 28357 patch power::real_part
​1d579be	add doctests
​c629c30	increment pynac version

[tscrim]

LGTM.

Please also make a PR upstream: ​https://github.com/pynac/pynac.

[gh-DaveWitteMorris]

Thanks! This is now ​pynac PR 380.

[vbraun]

    STDOUT: CONFLICT (content): Merge conflict in build/pkgs/pynac/package-version.txt

[gh-DaveWitteMorris]

Rebased on #31694.

---

New commits:

​e97c1b5	update pynac to 0.7.28
​3c131f7	wip tarball
​11c80aa	updated tarball with PRs 377 and 378
​c9c50e3	build/pkgs/pynac: Upgrade to 0.7.29
​31bbbc1	Merge commit 'c9c50e3d1bb0a6d9ec17ede66a2f47da7cd89b01' of git://trac.sagemath.org/sage into 31694upgradepynac
​ec76ad9	trac 28357 patch power::real_part
​dace50e	add doctests
​248016b	increment pynac version