Compute Hom and Ext over SkewCommutative rings

[joel-dodge]

NOT READY FOR REVIEW AT ALL

This is just a draft for now as it also includes changes from #4435 and #4176 that will hopefully be reviewed and merged soon.

[joel-dodge]

Fascinating there is a failure building examples from the BernsteinSato package

	     W = QQ[x, D, WeylAlgebra=>{x=>D}]
	     M = W^1/ideal(D-1)
	     N = W^1/ideal((D-1)^2)
	     DHom(M,N)

That boils down to an issue computing Hom over a non-commutative ring - a check that is added in this PR. I added this based on my understanding that the methods for computing R-module Homs without the use of pushFwd all produce an R-module as the output and that this cannot be correct as these things are not in fact R-modules. I need to dig into Weyl algebras a bit to understand better what should be happening and may relax the invariant in this case if appropriate.

[joel-dodge]

Fascinating. The DHom algorithm indeed relies on computing Hom for modules over the Weyl algebra W but IIUC only does so in the case of computing a dual of a free resoltuion in which case the source of the Hom is free. Of course Hom(M, N) IS a left W-module when N is a bimodule so this works fine. Hom(M, N) has a left R-module structure exctly when M is also a right R-module so in these cases the result actually is a bimodule and I think the existing Hom impl gives the right result!

Unfortunately, It seems that querying whether a given module is a bimodule or not seems to be not well supported in the Core M2 offerings - maybe NCAlgebras does this better... but Weyl algebras / skew symmetric algebras are not part of that package.

I found this old issue that is tangentially related: #58

While this is still WIP I am going to change the invariant check that forbids using bare Hom for non-commutative rings with one that instead checks that the target is free in the non-commutative case. I will expect discussion on this point.