CoCoA » CoCoALib

I am not yet sure of the details, but I am hoping that it can be used as in this example:

  ring P = NewPolyRing(...);
  RingElem f(P, "x^2-y");
  homogenizer H(P); // optional second arg saying where the homog indet should be (first/last)
  RingElem f_hom = H(f);
  ideal I = ideal([...]);
  ideal I_hom = H(I);

The ctor for homogenizer will internally create the extended poly ring, P_hom, and
also the mapping of indeterminates of P into P_hom. It will also be possible to
use the homogenizer to dehomogenize (not sure what syntax to use).

Following KISS, it is probably best to try the simple interface first.
If it works well, and we like it, then we can consider offering more
options: e.g. letting the caller specify the extended poly ring, and
how the indeterminates should map.

This way all sanity checking can be done in the ctor for homogenizer,
and all later calls will not need to check much.

The ctor for homogenizer will create the extended polynomial ring.
What properties should this extended ring have?
Same coeff ring, of course.
Term ordering? Presumably compatible with that of the starting ring,
and such that the homogenizing indets have weights like the columns in
an identity matrix. But what happens below the weights in the order
matrix for the big poly ring? Maybe it depends on the intended use?

This is for JOHN Knuckle down and do it!