Add coercion complex -> CC

[jdemeyer]

This works fine:

sage: CC(complex('13.8+6.2j'))
13.8000000000000 + 6.20000000000000*I
sage: CDF(complex('13.8+6.2j'))
13.8 + 6.2*I

However, it is a conversion while it should be a coercion.

sage: CC.has_coerce_map_from(complex)
False

This is inconsistent with

sage: CC.has_coerce_map_from(float)
True

CC: @robertwb

Component: coercion

Author: Jeroen Demeyer

Branch/Commit: d00b706

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/17166

[jdemeyer]

Branch: u/jdemeyer/ticket/17166

[jdemeyer]

Commit: d00b706

[jdemeyer]

New commits:

d00b706

Add coercion complex -> CC

[kcrisman]

comment:3

What did the old doctest

a=matrix([[1, 1e-4r, 1+1e-100jr], [1e-8+3j, 0, 1e-58r]])

do with the changes in question if you didn't change the ring? (I'm just wondering about breaking existing third-party code.)

[jdemeyer]

comment:4

Replying to @kcrisman:

What did the old doctest

a=matrix([[1, 1e-4r, 1+1e-100jr], [1e-8+3j, 0, 1e-58r]])

do with the changes in question if you didn't change the ring?

Return a matrix over CC instead of CDF.

[jdemeyer]

comment:5

But your question makes sense: why should it have changed?

[jdemeyer]

comment:6

Replying to @jdemeyer:

But your question makes sense: why should it have changed?

The change makes sense because the parent of the entry 1e-8+3j is CC. Therefore, it is logical that the matrix is defined over CC.

[vbraun]

comment:7

IMHO the coercion should be complex -> CDF -> CC and not complex -> CC -> CDF. Pretty much the only difference is that the matrix would default to CDF, but since matrices over CDF are much more useful than matrices over CC this is probably what the user prefers.

[jdemeyer]

comment:8

Replying to @vbraun:

IMHO the coercion should be complex -> CDF -> CC and not complex -> CC -> CDF.

Coercion goes both ways in this case (CDF -> CC and CC -> CDF), so the result is the same really. Interestingly, this has the following consequence:

sage: Sequence([CDF(1), CC(1)]).parent()
Category of sequences in Complex Double Field
sage: Sequence([CC(1), CDF(1)]).parent()
Category of sequences in Complex Field with 53 bits of precision

Let me know what you think, if you think the coercion should be added to ComplexDoubleField._coerce_map_from(), I could do that.

[vbraun]

comment:9

I also noticed that we have coercions both way CDF <-> CC. This sounds a bit wonky, IMHO it shoud be ComplexField(>=53) -> CDF -> ComplexField(<53). Though this has been around for a long time, perhaps there is a deeper reason for that? Maybe Robert knows? Possibly stuff for another ticket, though.

What I originally meant was just that Python complex should coerce to CDF and not CC.

[jdemeyer]

comment:10

Replying to @vbraun:

What I originally meant was just that Python complex should coerce to CDF and not CC.

Having a coercion complex -> CDF and CDF -> CC but not complex -> CC sounds strange to me (isn't coercion supposed to be transitive?). Moreover, that would be inconsistent with

sage: RR.has_coerce_map_from(float)
True
sage: RDF.has_coerce_map_from(float)
True

Whatever the outcome of this ticket is, the behaviour of complex / CDF / CC should be the same as float / RDF / RR.

[jdemeyer]

comment:11

Replying to @vbraun:

IMHO it shoud be ComplexField(>=53) -> CDF -> ComplexField(<53).

I would prefer CDF -> ComplexField(53) simply because there are numbers in CC which cannot be represented in CDF:

sage: CC(1e1000)
1.00000000000000e1000
sage: CDF(1e1000)
+infinity

[robertwb]

comment:12

Yes, it should be ComplexField(>53) -> CDF -> ComplexField(<=53). We should also have complex -> CDF. This does induce a coercion complex -> ComplexField(<=53).

[jdemeyer]

comment:13

Can this ticket please be reviewed as just making complex/CC consistent with float/RR? Further discussions about changing coercion between CC and CDF can still go to another ticket.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:14

I'm okay with pushing the issues with the other coercions to another ticket, and the current branch LGTM. So I'm setting a positive review.

[vbraun]

Changed branch from u/jdemeyer/ticket/17166 to d00b706