# RationalMap == RationalMap -- equality of rational maps

## Synopsis

• Operator: ==
• Usage:
phi == psi
• Inputs:
• phi,
• psi,
• Outputs:
• , whether phi and psi are the same rational map

## Description

 i1 : QQ[x_0..x_5] o1 = QQ[x ..x ] 0 5 o1 : PolynomialRing i2 : phi = rationalMap {x_0*x_4^2-x_0*x_3*x_5,x_0*x_2*x_4-x_0*x_1*x_5,x_0*x_2*x_3-x_0*x_1*x_4,x_0*x_2^2-x_0^2*x_5,x_0*x_1*x_2-x_0^2*x_4,x_0*x_1^2-x_0^2*x_3} o2 = -- rational map -- source: Proj(QQ[x , x , x , x , x , x ]) 0 1 2 3 4 5 target: Proj(QQ[x , x , x , x , x , x ]) 0 1 2 3 4 5 defining forms: { 2 x x - x x x , 0 4 0 3 5 x x x - x x x , 0 2 4 0 1 5 x x x - x x x , 0 2 3 0 1 4 2 2 x x - x x , 0 2 0 5 2 x x x - x x , 0 1 2 0 4 2 2 x x - x x 0 1 0 3 } o2 : RationalMap (cubic rational map from PP^5 to PP^5) i3 : psi = rationalMap {x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3} o3 = -- rational map -- source: Proj(QQ[x , x , x , x , x , x ]) 0 1 2 3 4 5 target: Proj(QQ[x , x , x , x , x , x ]) 0 1 2 3 4 5 defining forms: { 2 x - x x , 4 3 5 x x - x x , 2 4 1 5 x x - x x , 2 3 1 4 2 x - x x , 2 0 5 x x - x x , 1 2 0 4 2 x - x x 1 0 3 } o3 : RationalMap (quadratic rational map from PP^5 to PP^5) i4 : phi == psi o4 = true