CC -> PARI: return t_REAL for real numbers

[jdemeyer]

When converting Sage complex numbers to PARI, we should return a PARI t_REAL if the original number was actually real. This fixes a problem with ellwp() in #15767. In PARI's floating point model, the number 1e-19 + 0.0*I has less precision than the real 1e-19.

It is also consistent with the PARI philosophy of returning simplified types (examples: (1.1*I)^2 and ellj(1.1*I) in PARI gives real numbers).

CC: @pjbruin

Component: interfaces

Author: Jeroen Demeyer

Branch/Commit: 7067299

Reviewer: Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/15888

[jdemeyer]

Branch: u/jdemeyer/ticket/15888

[jdemeyer]

New commits:

988c1f8

Improve conversion of complex numbers to PARI

[jdemeyer]

Commit: 988c1f8

[pjbruin]

comment:3

It would seem to make sense to treat purely imaginary numbers similarly, by setting the real component to the t_INT 0, as PARI does. With your patch,

sage: pari(CC(1))
1.00000000000000
sage: pari(CC(I))
0.E-19 + 1.00000000000000*I
sage: _.debug()
[&=0000000004a45468] COMPLEX(lg=3):0c00000000000003 0000000004a45458 0000000004a45440 
  real = [&=0000000004a45458] REAL(lg=2):0400000000000002 (0,expo=-64):1fffffffffffffc0 
  imag = [&=0000000004a45440] REAL(lg=3):0400000000000003 (+,expo=0):6000000000000000 8000000000000000 
sage: pari('1.0*I')
1.00000000000000*I
sage: _.debug()
[&=000000000332b280] COMPLEX(lg=3):0c00000000000003 000000000332b270 000000000332b250 
  real = [&=000000000332b270] INT(lg=2):0200000000000002 (0,lgefint=2):0000000000000002 
  imag = [&=000000000332b250] REAL(lg=4):0400000000000004 (+,expo=0):6000000000000000 8000000000000000 0000000000000000 

[jdemeyer]

Reviewer: Peter Bruin

[sagetrac-git]

Changed commit from 988c1f8 to d6fdd0c

[sagetrac-git]

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

d6fdd0c

CC->PARI: convert purely imaginary numbers to t_COMPLEX with real part exactly 0

[pjbruin]

comment:7

There are a few doctest failures:

File "src/sage/schemes/elliptic_curves/heegner.py", line 3154, in sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve.numerical_approx
Failed example:
    P.numerical_approx()
Expected:
    (-6.68...e-16 + 1.41421356237310*I : 1.00000000000000 - 1.41421356237309*I : 1.00000000000000)
Got:
    (-6.67918322963967e-16 + 1.41421356237310*I : 1.00000000000000 - 1.41421356237309*I : 1.00000000000000)
**********************************************************************
File "src/sage/libs/pari/gen.pyx", line 4835, in sage.libs.pari.gen.gen.tan
Failed example:
    pari(i).tan()
Expected:
    0.E-19 + 0.761594155955765*I
Got:
    0.761594155955765*I
**********************************************************************
File "src/sage/libs/pari/gen.pyx", line 4855, in sage.libs.pari.gen.gen.tanh
Failed example:
    z = pari(i); z
Expected:
    0.E-19 + 1.00000000000000*I
Got:
    1.00000000000000*I
**********************************************************************
File "src/sage/libs/pari/gen.pyx", line 4940, in sage.libs.pari.gen.gen.weber
Failed example:
    pari(i).weber(1)
Expected:
    1.09050773266526 + 0.E-19*I
Got:
    1.09050773266526
**********************************************************************

[sagetrac-git]

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

7067299

CC->PARI conversion: fix doctest failures

[sagetrac-git]

Changed commit from d6fdd0c to 7067299

[vbraun]

Changed branch from u/jdemeyer/ticket/15888 to 7067299