Add some methods to projective morphisms (rational maps)

[kwankyu]

Add graph(), projective_degrees() and degree() methods to projective morphisms (rational maps).

Projective morphisms in Sage represent rational maps. That is, the domain of the definition of the morphism could be a dense subset of its domain.

Depends on #33950

Component: algebraic geometry

Author: Kwankyu Lee

Branch/Commit: ac60efe

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/33953

[kwankyu]

Author: Kwankyu Lee

[kwankyu]

Branch: u/klee/33953

[sagetrac-git]

Commit: a39ca95

[sagetrac-git]

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

d2b1b06	Add modules over domain
83cbb2b	Merge branch 'develop' into module-over-domain
5e5b8f1	Add submodule.py
74a3930	Clean up doc tree of modules
c725f74	Small fix on the main toc
c4e61db	Add free resolutions
a39ca95	Add projective_degrees() and degrees() methods

[kwankyu]

New commits:

d2b1b06	Add modules over domain
83cbb2b	Merge branch 'develop' into module-over-domain
5e5b8f1	Add submodule.py
74a3930	Clean up doc tree of modules
c725f74	Small fix on the main toc
c4e61db	Add free resolutions
a39ca95	Add projective_degrees() and degrees() methods

[kwankyu]

Dependencies: #33950

[sagetrac-git]

Changed commit from a39ca95 to 5c1e6e0

[sagetrac-git]

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

5c1e6e0

Fix a doctest; now gives the correct answer

[sagetrac-git]

Changed commit from 5c1e6e0 to 4c3f8ce

[sagetrac-git]

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

4c3f8ce

Modify two doctests

[sagetrac-git]

Changed commit from 4c3f8ce to 4c2e151

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

b2870da	Refactor FreeModule_generic
fcb51da	Add coercion map from a submodule to the free module
c4e89b9	A fix to cooperate with matrix infrastructure
9f12e32	Rename to Module_free_ambient and fix doctests
59226b1	Add free resolutions
4c2e151	Add some methods to projective morphisms

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

e8db541

Add some methods to projective morphisms

[sagetrac-git]

Changed commit from 4c2e151 to e8db541

[sagetrac-git]

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

0232e9e	Add free resolutions
bdbb479	Merge branch 'develop' into t/33950/free-resolution
fcb1842	Merge branch 't/33950/free-resolution' into t/33953/degree-morphism

[sagetrac-git]

Changed commit from e8db541 to fcb1842

[sagetrac-git]

Changed commit from fcb1842 to dabe765

[sagetrac-git]

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

817e341	Merge branch 'develop' into t/33953/degree-morphism
736d448	Moving the main computation to be done on demand.
5285e67	Moving Singular conversion code to libs/singular; converting resoltuion files to Python files.
5917129	Changing the doc for clarity and to add some more descriptions.
3f1d1c3	Merge branch 'develop' into t/33950/public/rings/free_multigraded_resolutions-33950
ab725f2	Fix spaces
dabe765	Merge branch 't/33950/public/rings/free_multigraded_resolutions-33950' into t/33953/degree-morphism

[tscrim]

comment:14

There seems to be some real doctest failures reported by the patchbot:

sage -t --long --random-seed=28903988791302297014049808319140034392 src/sage/schemes/projective/projective_morphism.py  # 1 doctest failed

which I can reproduce. The others

sage -t --long --random-seed=28903988791302297014049808319140034392 src/sage/homology/graded_resolution.py  # 1 doctest failed
sage -t --long --random-seed=28903988791302297014049808319140034392 src/sage/homology/free_resolution.py  # 5 doctests failed

I cannot.

Here are my comments:

Since projective_degrees() potentially is an expensive computation, I would cache the result (which would also mean it returns a tuple).

Perhaps we should call morphism() instead as_morphim() to indicate that it is an equivalent but different type of object?

[tscrim]

comment:15

Also, if you could split this line:

-n1 = n + 1; m1 = m + 1
+n1 = n + 1
+m1 = m + 1

for our style guidelines (see patchbot).

[kwankyu]

comment:16

Replying to @tscrim:

There seems to be some real doctest failures reported by the patchbot:

sage -t --long --random-seed=28903988791302297014049808319140034392 src/sage/schemes/projective/projective_morphism.py  # 1 doctest failed

which I can reproduce.

Yes. It is related with a deep-rooted problem of conic curves modules. I am working on it. If I fail, then I would simply change the doctest slightly.

[sagetrac-git]

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

3947c02	Refactor conic curves
ac60efe	Fixes for reviewer comments

[sagetrac-git]

Changed commit from dabe765 to ac60efe

[kwankyu]

comment:18

Replying to @tscrim:

There seems to be some real doctest failures reported by the patchbot:

sage -t --long --random-seed=28903988791302297014049808319140034392 src/sage/schemes/projective/projective_morphism.py  # 1 doctest failed

which I can reproduce.

Fixed.

Since projective_degrees() potentially is an expensive computation, I would cache the result (which would also mean it returns a tuple).

Done. Also graph() is cached.

Perhaps we should call morphism() instead as_morphim() to indicate that it is an equivalent but different type of object?

Yes. Done.

[kwankyu]

comment:19

Replying to @tscrim:

Also, if you could split this line:

-n1 = n + 1; m1 = m + 1
+n1 = n + 1
+m1 = m + 1

for our style guidelines (see patchbot).

Done. Thanks.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:21

Thank you. Green bot => positive review.

[vbraun]

Changed branch from u/klee/33953 to ac60efe