Usage:
<adjoin_fractions a J S K
Compute S/K = R[J/a], where R is the base ring of J, a is a nonzero-
divisor of R, and S is a polynomial ring over R supplied by the user.
Parameters:
a = 1x1 matrix over R
J = an ideal of R
S = a polynomial ring over R, whose extra variables y[i] correspond to the
generators, J[i] of J, and have deg y[i] = deg J[i] - deg a.
Output values:
K = an ideal of S.
The ideal K = ((ay[i] - J[i], all i) : a*). This is correct because
upon inverting the element a, the desired ideal is obviously
(ay[i] - J[i], all i).
The ring R may be a quotient ring.
An alternate method would be to compute the ring R[(J,a)t] using
the script "blowup", and then set a := 1. In effect this computes
the ring of an affine open set of the blowup.
Caveats:
The degree of a MUST BE < the degrees of the given generators of J.