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

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

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

              10       10
o5 : Matrix QQ   <-- QQ

i6 : M == M'

o6 = true

Ways to use this method:

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

The source of this document is in Cremona/documentation.m2:538:0.