coefficients(RationalMap) -- coefficient matrix of a rational map

Synopsis

Function: coefficients
Usage:

coefficients phi
Inputs:
- phi, a rational map
Optional inputs:
- Monomials => ..., default value null,
- Variables => ..., default value null,
Outputs:
- a matrix, the coefficient matrix of the polynomials defining phi

Description

i1 : K = QQ; ringP9 = K[x_0..x_9];

i3 : M = random(K^10,K^10)

o3 = | 9/2 7/10 2    1/2 5/3  4/3  2/3 1/8  1   5/2 |
     | 1/2 1/2  6    10  7/2  3/7  6   10/3 7/5 5/2 |
     | 9/4 7/10 5/4  3   2/5  9/10 5/4 3/4  3/2 1/6 |
     | 1/2 7/3  2/9  3   6/5  4/7  2/9 4    1/5 3/4 |
     | 1   7    5    3/2 5/4  5/2  8/5 1/4  5   4   |
     | 3/4 3/7  3/10 4/3 5/7  5/9  9/4 1/3  5/7 8/5 |
     | 3/2 5/2  1    7/8 5/9  5/9  2/9 4/3  3/8 10  |
     | 3/4 6/7  3/7  5/6 5/3  6/7  3   9/10 3   2   |
     | 7/4 2/3  5    5   4/5  2    9/8 5/4  1   1/3 |
     | 7/9 1    10/9 2/5 1/10 1    1/2 1/7  1/2 5/2 |

              10       10
o3 : Matrix QQ   <-- QQ

i4 : phi = rationalMap ((vars ringP9) * (transpose M));

o4 : RationalMap (linear rational map from PP^9 to PP^9)

i5 : M' = coefficients phi

o5 = | 9/2 7/10 2    1/2 5/3  4/3  2/3 1/8  1   5/2 |
     | 1/2 1/2  6    10  7/2  3/7  6   10/3 7/5 5/2 |
     | 9/4 7/10 5/4  3   2/5  9/10 5/4 3/4  3/2 1/6 |
     | 1/2 7/3  2/9  3   6/5  4/7  2/9 4    1/5 3/4 |
     | 1   7    5    3/2 5/4  5/2  8/5 1/4  5   4   |
     | 3/4 3/7  3/10 4/3 5/7  5/9  9/4 1/3  5/7 8/5 |
     | 3/2 5/2  1    7/8 5/9  5/9  2/9 4/3  3/8 10  |
     | 3/4 6/7  3/7  5/6 5/3  6/7  3   9/10 3   2   |
     | 7/4 2/3  5    5   4/5  2    9/8 5/4  1   1/3 |
     | 7/9 1    10/9 2/5 1/10 1    1/2 1/7  1/2 5/2 |

              10       10
o5 : Matrix QQ   <-- QQ

i6 : M == M'

o6 = true

Ways to use this method: