next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Points :: affinePointsMat

affinePointsMat -- produces the matrix of values of the standard monomials on a set of points

Synopsis

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

Caveat

Program does not check that the points are distinct.

See also

Ways to use affinePointsMat :

For the programmer

The object affinePointsMat is a method function.