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D.2.4.8 PtoCrep
Procedure from library grobcov.lib (see grobcov_lib).
- Usage:
- PtoCrep(L)
Input L: list [ Comp_1, .. , Comp_s ] where
Comp_i=[p_i,[p_i1,..,p_is_i] ], is
the P-representation of a locally closed set V(N) \ V(M)
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)
NOTE: Operates in a ring R=Q[a] (a=parameters)
KEYWORDS: locally closed set, canoncial form
EXAMPLE: PtoCrep; 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;
// (P,Q) represents a locally closed set
ideal P=x^3+x*y^2+x*z^2-25*x;
ideal Q=y-4,x*z,x^2-3*x;
// Now compute the P-representation=
def L=Prep(P,Q);
L;
==> [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
// Now compute the C-representation=
def J=PtoCrep(L);
J;
==> [1]:
==> _[1]=x3+xy2+xz2-25x
==> [2]:
==> _[1]=y-4
==> _[2]=xz
==> _[3]=x2-3x
// Now come back recomputing the P-represetation of the C-representation=
Prep(J[1],J[2]);
==> [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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