# graph(RingMap) -- closure of the graph of a rational map

## Synopsis

• Function: graph
• Usage:
graph phi
• Inputs:
• phi, , representing a rational map $\Phi:X \dashrightarrow Y$
• Optional inputs:
• Outputs:
• , representing the projection on the first factor $\mathbf{Graph}(\Phi) \to X$
• , representing the projection on the second factor $\mathbf{Graph}(\Phi) \to Y$

## Description

 i1 : phi = map(QQ[x_0..x_3],QQ[y_0..y_2],{-x_1^2+x_0*x_2,-x_1*x_2+x_0*x_3,-x_2^2+x_1*x_3}) 2 2 o1 = map (QQ[x ..x ], QQ[y ..y ], {- x + x x , - x x + x x , - x + x x }) 0 3 0 2 1 0 2 1 2 0 3 2 1 3 o1 : RingMap QQ[x ..x ] <--- QQ[y ..y ] 0 3 0 2 i2 : graph phi QQ[x ..x , y ..y ] 0 3 0 2 o2 = (map (----------------------------------------, QQ[x ..x ], {x , x , x , (x y - x y + x y , x y - x y + x y ) 0 3 0 1 2 3 0 2 1 1 2 2 0 1 1 0 2 ------------------------------------------------------------------------ QQ[x ..x , y ..y ] 0 3 0 2 x }), map (----------------------------------------, QQ[y ..y ], {y , 3 (x y - x y + x y , x y - x y + x y ) 0 2 0 3 0 2 1 1 2 2 0 1 1 0 2 ------------------------------------------------------------------------ y , y })) 1 2 o2 : Sequence