Lie algebra morphism defined by values on a Lie generating subset

[gh-ehaka]

Implementation of a method to define a Lie algebra morphism by giving the images on any Lie-generating subset which need not be the entire basis.

[tscrim]

Thank you for implementing this! I will have some minor tweaks, but mostly it looks like a good first step. However, we should make this into an actual Morphism subclass (so we can define, e.g., compositions and coercions) and we should add a hook to a finite-dimensional Lie algebra so that it is exposed to the users. It probably a good idea to subclass LieAlgebraHomomorphism_im_gens for this. I can do this too if you would want or on a followup.

[gh-ehaka]

Thanks for the comment, I am still figuring out the morphism framework, so this is very helpful information. By a hook I take it you mean adding a method named for example lie_algebra_morphism in sage.categories.lie_algebras.LieAlgebras.FiniteDimensional? I will add this and change LieAlgebraMorphism_from_generators to a subclass of LieAlgebraHomomorphism_im_gens as you suggested.

On another note, I noticed that the test suites skip _test_elements. Would it be valid to append

if not issubclass(self.__class__, parent._abstract_element_class):
    self.__class__ = parent.__make_element_class__(self.__class__)

at the end of initialization as in sage.modules.with_basis.morphism.ModuleMorphism.__init__ to make the morphisms proper subclasses of the parent Hom-space, or would this cause some problems?

[git]

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

​544750b

Converted morphism creator into a subclass and added a hook into the finite dimensional Lie algebras category

[gh-ehaka]

I converted the function to a subclass and added the hook into sage.categories.lie_algebras.LieAlgebras.FiniteDimensional.ParentMethods. However, the test suite for _test_pickling of the new class fails since the class is creating a parent LieAlgebraHomset, which does not have unique behavior. I opened a new ticket #26039 about this, since it seems to be an issue unrelated to the new code.

[tscrim]

Thank you for making it into a class. I am planning to change the hook (yes, you interpreted correctly) to just morphism since we already know it is a Lie algebra. :)

As I mentioned on #26039, you should be using Hom to create the parent, not directly constructing LieAlgebraHomset (I know that is a stupid pitfall, but there are [annoying] reasons for it). I will be doing some reviewer modifications now, including fixing that. (Also, the morphism framework probably could use some larger scale refactoring now that we have been adding more types of morphisms, but that is my opinion and a large-scale project.)

In regards to your question about setting the __class__, that might work, but I would be very worried that will cause problems when the homset does not have an explicit Element set (because it can have many different types of elements).

[tscrim]

Okay, this fixes the pickling issue(s), as well as gives a better interface. Now you can also use the morphism on you Lie algebra elements. If my changes are good, then you can set a positive review.

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New commits:

​24d0fd7	Renaming and moving lie_algebra_morphism() to morphism(); fixing some other problems.
​3c34d3d	Removed trailing whitespace.
​bfe5c97	Making the Homset be able to construct these morphisms and other improvements.
​4d9b050	Add richcmp to morphisms (rather than use the default).

[git]

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

​ed5b1e9

Fixed doctest to refer to new name of function and new punctuation in error message.

[gh-ehaka]

Looks good to me. I fixed the doctest in finite_dimensional_lie_algebras_with_basis to use the correct method name and the punctuation change in the error message.

[tscrim]

Whoops, forgot to test that file too. Thank you!