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D.2.4.7 PtoCrep
Procedure from library grobcov.lib (see grobcov_lib).
- Usage:
- PtoCrep(list L)
list L= [ Comp_1, .. , Comp_s ] where
list Comp_i=[p_i,[p_i1,..,p_is_i] ], is the
P-representation of a locally closed set
V(N) \ V(M). To be called in a ring Q[a][x]
or a ring Q[a]. But the ideals can contain
only the parameters in Q[a].
- Return:
- The canonical C-representation [P,Q] of the
locally closed set. A pair of radical ideals with
P included in Q, representing the
set V(P) \ V(Q)
Example:
| | LIB "grobcov.lib";
//EXAMPLE:
if(defined(R)){kill R;}
ring R=0,(a,b,c),lp;
short=0;
ideal p=a*(a^2+b^2+c^2-25);
ideal q=a*(a-3),b-4;
// C-representaion of V(p) \ V(q)
def Cr=Crep(p,q);
Cr;
==> [1]:
==> _[1]=a^3+a*b^2+a*c^2-25*a
==> [2]:
==> _[1]=b-4
==> _[2]=a*c
==> _[3]=a^2-3*a
// P-representation of V(p) \ V(q)
def L=Prep(p,q);
L;
==> [1]:
==> [1]:
==> _[1]=a^2+b^2+c^2-25
==> [2]:
==> [1]:
==> _[1]=c-3
==> _[2]=b-4
==> _[3]=a
==> [2]:
==> _[1]=c+3
==> _[2]=b-4
==> _[3]=a
==> [3]:
==> _[1]=c
==> _[2]=b-4
==> _[3]=a-3
==> [2]:
==> [1]:
==> _[1]=a
==> [2]:
==> [1]:
==> _[1]=b-4
==> _[2]=a
PtoCrep(L);
==> [1]:
==> _[1]=a^3+a*b^2+a*c^2-25*a
==> [2]:
==> _[1]=b-4
==> _[2]=a*c
==> _[3]=a^2-3*a
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