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D.2.4.6 Prep
Procedure from library grobcov.lib (see grobcov_lib).
- Usage:
- Prep(N,M);
Input: ideal N (null ideal) (not necessarily radical nor maximal)
ideal M (hole ideal) (not necessarily containing N)
RETURN: The canonical P-representation of the locally closed set V(N) \ V(M)
Output: [ Comp_1, .. , Comp_s ] where
Comp_i=[p_i,[p_i1,..,p_is_i]]
NOTE: Operates in a ring R=Q[a] (a=parameters)
KEYWORDS: Locally closed set, Canoncial form
EXAMPLE: Prep; shows an example
Example:
| | LIB "grobcov.lib";
if(defined(Grobcov::@P)){kill Grobcov::@R; kill Grobcov::@P; kill Grobcov::@RP;}
short=0;
ring R=0,(x,y,z),lp;
ideal E=x*(x^2+y^2+z^2-25);
ideal N=x*(x-3),y-4;
Prep(E,N);
==> [1]:
==> [1]:
==> _[1]=x2+y2+z2-25
==> [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
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