Description
This function uses the Buchberger-Moeller algorithm to compute a the matrix
A in which the columns are indexed by standard monomials, the rows are indexed by points, and the entries are given by evaluation. The ordering of the standard monomials is recorded in the matrix
stds which has a single column. Here is a simple example.
i1 : M = random(ZZ^3, ZZ^5)
o1 = | 8 7 3 8 8 |
| 1 8 7 5 5 |
| 3 3 8 7 2 |
3 5
o1 : Matrix ZZ <-- ZZ
|
i2 : R = QQ[x,y,z]
o2 = R
o2 : PolynomialRing
|
i3 : (A,stds) = affinePointsMat(M,R)
o3 = (| 1 3 1 8 9 |, {0} | 1 |)
| 1 3 8 7 9 | {-1} | z |
| 1 8 7 3 64 | {-1} | y |
| 1 7 5 8 49 | {-1} | x |
| 1 2 5 8 4 | {-2} | z2 |
o3 : Sequence
|