randomPointsMat -- matrix of homogeneous coordinates of random points in projective space

Synopsis

Usage:

m=randomPointsMat(R,n)
Inputs:
- R, a ring, homogeneous coordinate ring of projective space Pm
- n, an integer, number of points
Optional inputs:
- AllRandom => ..., default value false
Outputs:
- m, a matrix, of ZZ

Description

Produces a random m+1 x n matrix of scalars, with columns representing the coordinates of the point. The first m+1 x m+1 submatrix is the identity.

i1 : R = ZZ/31991[vars(0..3)]

o1 = R

o1 : PolynomialRing

i2 : randomPointsMat(R,3)

o2 = | 1 0 0 |
     | 0 1 0 |
     | 0 0 1 |
     | 0 0 0 |

             4      3
o2 : Matrix R  <-- R

i3 : randomPointsMat(R,3, AllRandom=>true)

o3 = | 107   3783   8444   |
     | 4376  -5295  -10468 |
     | -5558 8570   10359  |
     | 3187  -15332 -7452  |

             4      3
o3 : Matrix R  <-- R

i4 : randomPointsMat(R,7)

o4 = | 1 0 0 0 1 -8239 12365  |
     | 0 1 0 0 1 2653  -13496 |
     | 0 0 1 0 1 5071  -9468  |
     | 0 0 0 1 1 -6191 -11938 |

             4      7
o4 : Matrix R  <-- R

Ways to use randomPointsMat :

randomPointsMat(Ring,ZZ)

For the programmer

The object randomPointsMat is a method function with options.