Revision history [back]

This is quite straightforward:

P.<x1,x2,x3,x4> = PolynomialRing(QQ)                                                                                                                                                                                                                    
I = ideal(x1*x3,x2*x4) + ideal(x1+x3,x2+x4)                                                                                                                                                                                                               
R = P.quotient_ring(I)
print( R((x1+x4)*(x2+x3)) / R(x1*x2) )

This is quite straightforward:

P.<x1,x2,x3,x4> A.<x1,x2,x3,x4> = PolynomialRing(QQ)                                                                                                                                                                                                                    
I I12 = ideal(x1*x3,x2*x4) + ideal(x1+x3,x2+x4)                                                                                                                                                                                                               
R = P.quotient_ring(I)
A.quotient_ring(I12)
print( R((x1+x4)*(x2+x3)) / R(x1*x2) )