Singular

D.2.4.6 Crep

Procedure from library `grobcov.lib` (see grobcov_lib).

Usage:
Crep(N,M);
Input: ideal N (null ideal) (not necessarily radical nor maximal) ideal M (hole ideal) (not necessarily containing N)
RETURN: The canonical C-representation of the locally closed set. [ P,Q ], a pair of radical ideals with P included in Q, representing the set V(P) \ V(Q) = V(N) \ V(M)
NOTE: Operates in a ring R=Q[a] (a=parameters)
KEYWORDS: locally closed set, canoncial form
EXAMPLE: Crep; shows an example

Example:
 ```LIB "grobcov.lib"; if(defined(Grobcov::@P)){kill Grobcov::@R; kill Grobcov::@P; kill Grobcov::@RP;} ring R=0,(x,y,z),lp; short=0; ideal E=x*(x^2+y^2+z^2-25); ideal N=x*(x-3),y-4; def Cr=Crep(E,N); Cr; ==> [1]: ==> _[1]=x^3+x*y^2+x*z^2-25*x ==> [2]: ==> _[1]=y-4 ==> _[2]=x*z ==> _[3]=x^2-3*x def L=Prep(E,N); L; ==> [1]: ==> [1]: ==> _[1]=x^2+y^2+z^2-25 ==> [2]: ==> [1]: ==> _[1]=z ==> _[2]=y-4 ==> _[3]=x-3 ==> [2]: ==> _[1]=z+3 ==> _[2]=y-4 ==> _[3]=x ==> [3]: ==> _[1]=z-3 ==> _[2]=y-4 ==> _[3]=x ==> [2]: ==> [1]: ==> _[1]=x ==> [2]: ==> [1]: ==> _[1]=y-4 ==> _[2]=x def Cr1=PtoCrep(L); Cr1; ==> [1]: ==> _[1]=x^3+x*y^2+x*z^2-25*x ==> [2]: ==> _[1]=y-4 ==> _[2]=x*z ==> _[3]=x^2-3*x ```