New module complex_mpc using lib mpc for complex multiprecision arithmetic

[sagetrac-thevenyp]

Herewith and there (http://www.loria.fr/~thevenyp/complex_mpc.patch 38K) is a patch with new classes using the MPC library for complex multi-precision arithmetic (see ticket #4308 for the associated spackage).

This is an adaptation of the module real_mpfr and of ComplexField and ComplexNumber classes. It adds a class MPComplexField with precision (common to both part) and rounding modes (specific to each part) and a class MPComplexNumber.

This first attempt implements only the complex arithmetic.

The test suite does fail due to coercion problems I can't solve.

CC: @robertwb @williamstein @mwhansen @sagetrac-mvngu @haraldschilly @nexttime

Component: basic arithmetic

Author: Philippe Theveny, Alex Ghitza, Yann Laigle-Chapuy

Reviewer: William Stein, David Kirkby, Paul Zimmermann, Mitesh Patel

Merged: sage-4.6.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/4446

[sagetrac-thevenyp]

Attachment: complex_mpc.patch.gz

[aghitza]

Attachment: trac4446-complex_mpc.patch.gz

replace the previous patch (rebase against 3.2)

[aghitza]

comment:2

There seems to have been some bitrot due to recent changes in Sage. I have uploaded a very slightly modified version of Philippe's patch, which applies cleanly against 3.2. A number of doctests fail for various reasons. I will try to look into this soon.

[sagetrac-thevenyp]

Attachment: complex_mpc.p0.patch.gz

coercion problems resolved, more functions

[sagetrac-thevenyp]

comment:3

The coercion problems have been solved, all doctests now succeed in new version. The whole set of mpc functions involving complex numbers is now in the interface.

[aghitza]

apply after complex_mpc.p0.patch

[aghitza]

comment:4

Attachment: trac4446_fix.patch.gz

Philippe,

Great work! I'll do my best to review this for 3.2.2. Right now I notice that the patch doesn't work in 3.2.1 because of #4580. I'm attaching a tiny patch that fixes that (should be applied after complex_mpc.p0.patch.