CoCoA » CoCoALib

Dear Anna and John,

let me collect all the points that came up in the development of nmzIntegrate (Christof has everything and can show it to you):

1) Input of polynomials. We have made such a function for nmzIntegrate, but is not good for general use.

2) A default constructor for RingElem. Not absolutely necessary, but makes programming easier.

3) Coefficients and power products should automatically be considered as polynomials for arithmetic. This is too natural for every mathematician.

4) Spaces separating terms of polynomials?

5) A simpler solution for using OpenMP

6) Nice conversion from coefficients of polynomials to integers and rationals that can be used outside CoCoA (for example in Normaliz).

7) More liberal treatment of external libraries by avoiding hardwired paths

8) Function for homogeneous components (nmzIntegrate contains a function for standard gradimg)

9) Standard grading of polynomial rings by default

10) At one point you ask whether one should use the term "multiplicity" in connection with factorization. I think this is the right choice. I think you are using "exponent" at present.

11) One could think of a clean up function for polynomials in the following sense: suppose I build a polynomial by freely using PushBack without paying attention to the monomial order. Then I could run such a function to sort the terms and convert my wild list into a correct polynomial.