# Revision history [back]

Since computation of f2 involves division by S((y + 4)^2), you'd need to define S as

S = K.quotient(y^2 - x^3 - 4*x).fraction_field()


Since computation of f2 involves division by S((y + 4)^2), you'd need to define S as

S = K.quotient(y^2 - x^3 - 4*x).fraction_field()


to get S(y - 2*x) in I.

Since computation of f2 involves division by S((y + 4)^2), you'd need to define S as

S = K.quotient(y^2 - x^3 - 4*x).fraction_field()


to get S(y - 2*x) in I.I.

Since First, multivariate ideal machinery in Sage is known to be buggy for non-fields and Integers(11) is not recognized as a field. Replace it with GF(11).

Second, since computation of f2 involves division by S((y + 4)^2), you'd you indeed need to define S asas a fraction field:

S = K.quotient(y^2 - x^3 - 4*x).fraction_field()


to get S(y - 2*x) in I.

First, the multivariate ideal machinery in Sage is known to be buggy for non-fields over non-fields, and Integers(11) is not recognized as a field. Replace it with GF(11).

Second, since computation of f2 involves division by S((y + 4)^2), you indeed need to define S as a fraction field:

K.<x, y> = GF(11)[]
S = K.quotient(y^2 - x^3 - 4*x).fraction_field()


to get S(y - 2*x) in I.