# MultiprojectiveVariety \\ MultiprojectiveVariety -- difference of multi-projective varieties

## Synopsis

• Operator: \\
• Usage:
X \\ Y
• Inputs:
• Outputs:
• , the variety defined by the saturation ideal saturate(ideal X,ideal Y)

## Description

 i1 : R = ZZ/101[x_0,x_1,x_2,y_0,y_1,Degrees=>{3:{1,0},2:{0,1}}]; i2 : X = projectiveVariety ideal(x_0^3*y_0^2+2*x_0^2*x_1*y_0^2+2*x_0*x_1^2*y_0^2+x_1^3*y_0^2+2*x_0^2*x_2*y_0^2+3*x_0*x_1*x_2*y_0^2+2*x_1^2*x_2*y_0^2+2*x_0*x_2^2*y_0^2+2*x_1*x_2^2*y_0^2+x_2^3*y_0^2+2*x_0^3*y_0*y_1+4*x_0^2*x_1*y_0*y_1+4*x_0*x_1^2*y_0*y_1+2*x_1^3*y_0*y_1+4*x_0^2*x_2*y_0*y_1+6*x_0*x_1*x_2*y_0*y_1+4*x_1^2*x_2*y_0*y_1+4*x_0*x_2^2*y_0*y_1+4*x_1*x_2^2*y_0*y_1+2*x_2^3*y_0*y_1+x_0^3*y_1^2+2*x_0^2*x_1*y_1^2+2*x_0*x_1^2*y_1^2+x_1^3*y_1^2+2*x_0^2*x_2*y_1^2+3*x_0*x_1*x_2*y_1^2+2*x_1^2*x_2*y_1^2+2*x_0*x_2^2*y_1^2+2*x_1*x_2^2*y_1^2+x_2^3*y_1^2); o2 : ProjectiveVariety, surface in PP^2 x PP^1 i3 : Y = projectiveVariety ideal(x_0*y_0+x_1*y_0+x_2*y_0+x_0*y_1+x_1*y_1+x_2*y_1); o3 : ProjectiveVariety, surface in PP^2 x PP^1 i4 : Z = X \\ Y; o4 : ProjectiveVariety, surface in PP^2 x PP^1 i5 : assert(Z == (X \ Y) \ Y)