CoCoA » CoCoA-5

JAA thinks that a good design approach would be to produce a function which takes as args two rings, and returns a RingHom (and not a partial ring hom) which must be applied to map elements of the "simpler" ring into the other ring. The domain and codomain of the ringhom will indicate which value(s) is/are to be mapped.

JAA is not sure what the function should do if no automatic mapping is supported between the two rings. There are two obvious alternatives: throw an exception, or return a boolean (in addition to the RingHom).

JAA is not sure what the function should do if the two rings supplied are equal -- it could return the identity RingHom or it could give an error. At the moment giving an error seems the better option.

Probably the simplest definition is simply that R1 is "simpler" than R2 if the construction of R2 passed explicitly via that of R1.

For instance this means that R is always regarded as being simpler than the quotient R/I.

Proposal for new "constructors": R ring, A matrix, x ringelem (or powerproduct or ...), ... and what else?

Mat(R, A), RingElem(R, x)
checks if object is mappable into R and returns its image in R: equivalent to

phi := CanonicalHom(RingOf(object), R);
apply(phi, object)

Automatic ring in operations is in general very difficult to detect.
Making these new constructors available might be a good and clean intermediate solution.

These "constructors" may be made available in CoCoALib too, but that implies including CanonicalHom.H in all .C files offering them.

It would be handy to have a similar shortcut for homogeneous lists.
Also for ideals, but that raises the same question that came up for BringIn.

The doc for BringIn says that it works for ringelems and matrices, lists and vectors but not ideals.
The CoCoALib fn apply does not appear to be documented!

Assignment of an integer (or rational) to a RingElem will automatically map into the ring.

However, we want to be cautious about extending this automatic mapping to other types of assignment, especially since assignment from a RingElem belonging to another ring does not perform automatic mapping.

Renzo reminds us that this task is important!

No chance of finishing this is in the near future; postponing by 1 version.

Here are done list and todo list copied from issue #1461 comments 7 & 8. Moving them here.

• MatrixOps.C
• MatrixOps-KroneckerProd.C
• module.C (mostly)

• DenseMat: myRowMul, myColMul, myAddRowMul, myAddColMul
• FieldIdeal -- needs vector of RingElem in same ring
• ideal.C many, some need vector of RingElem in same ring
• Matrix.C for SetEntry, also IamEqual
• MatrixSpecial.C for JacobianMat which needs vector of RingElem in same ring
• MatrixView many cases, some need vector of RingElem in same ring
• PolyFamilies for DicksonPoly
• ring.C for operator+= and so on
• RingElemOps-CoprimeFactorBasis needs vector RingElem from same ring.
• SparsePolyOps-XXX many