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

## Synopsis

• Function: coefficients
• Usage:
coefficients phi
• Inputs:
• phi,
• Optional inputs:
• Outputs:
• , 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