Elim ordering and matrix ordering
in cocoa-4 we had an easy way to use an elimination ordering:
MyRing ::= QQ[x[1..N], t], Elim(t);
and to define a matrix ordering
MyRing ::= QQ[x[1..N], t], Ord(M);
This is not currently allowed in CoCoA-5 because we are still working on the ring interface and we fear there could be ambiguities allowing "(" in a ring definition. (one should use NewPolyRing instead)
Even though it is quite clear how to make an elimination ordering (matrix), the construction seems quite tedious and verbose.
This "issue" is to make a decision about allowing "Elim(..)" in a ring definition or to propose "the right way" to construct an elimination matrix.
#4 Updated by John Abbott about 4 years ago
- Status changed from New to In Progress
- Priority changed from Normal to High
In issue #313 I have posted an impl of
ElimOrdMat which creates a matrix for elimination orderings. This fn lets one create elim order matrices easily -- JAA could simply put this in some C5 package!
It would be handy to have the
, Ord(...) syntax working; the current solution for creating poly rings with orders defined by matrices is unpleasantly cumbersome. Any chance of having this working before next term?
#5 Updated by John Abbott about 4 years ago
- % Done changed from 10 to 50
Just an idea... it might be nice if the matrix created contained only non-negative entries (e.g. it is easy to have a non-neg matrix for degrevlex).
If I recall well, CoCoALib always arranges for the internal matrix to be non-negative.
What do you think?
#9 Updated by Anna Maria Bigatti over 2 years ago
- Assignee set to Anna Maria Bigatti
- Estimated time set to 6.00 h
One problem is how to make it easy to use an elimination ordering.
Currently one has to write:
OrdM := ElimMat(3, ); -- elim the first out of 3 indets X := <list of names/symbols>; P := NewPolyRing(QQ, AllIndetNames, OrdM, 0); Use P;
How to make this easier? Here is a possible shortcut:
P := NewPolyRingElim(QQ, ElimIndetNames, OtherIndetNames); Use P;
this has the advantage that it can be similarly implemented in CoCoALib.
Another shortcut is this (but I'm not 100% sure it can be done):
Ord := record[M := ..., GrDim := ..]; Use P ::= QQ[<indets>], Ord;