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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
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