D.2.9.6 redspec

Usage:

redspec(N,W);
N: null conditions ideal
W: set of non-null polynomials (ideal)

Return:

a list (N1,W1,L1) containing a red-specification of the segment (N,W). N1 is the radical reduced ideal characterizing the segment. V(N1) is the Zarisky closure of the segment (N,W).
The segment S=V(N1) \ V(h), where h=prod(w in W1)
N1 is uniquely determined and no prime component of N1 contains none of the polynomials in W1. The polynomials in W1 are prime and reduced w.r.t. N1, and are considered non-null on the segment. L1 contains the list of prime components of N1.

Note:

can be called from ring @R but it works in ring @P.

LIB "redcgs.lib";
ring r=(0,a,b,c),(x,y),dp;
setglobalrings();
ideal N=(ab-c)*(a-b),(a-bc)*(a-b);
ideal W=a^2-b^2,bc;
redspec(N,W);
==> [1]:
==>    _[1]=(b2-1)
==>    _[2]=(a-bc)
==> [2]:
==>    _[1]=(b)
==>    _[2]=(c-1)
==>    _[3]=(c+1)
==>    _[4]=(c)
==> [3]:
==>    [1]:
==>       _[1]=(b+1)
==>       _[2]=(a+c)
==>    [2]:
==>       _[1]=(b-1)
==>       _[2]=(a-c)