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D.2.4.16 stdlocus

Procedure from library grobcov.lib (see grobcov_lib).

stdlocus(ideal F)
The input ideal must be the set equations defining the locus. Calling sequence: locus(F);
The input ring must be a parametrical ideal in Q[x][u], (x=tracer variables, u=remaining variables).
(Inverts the concept of parameters and variables of the ring). Special routine for determining the locus of points of a geometrical construction. Given a parametric ideal F representing the system determining the locus of points (x) which verify certain properties, the call to stdlocus(F) determines the different irreducible components of the locus. This is a simple routine, using only standard Groebner basis computation, elimination and prime decomposition instead of using grobcov. It does not determine the taxonomy, nor the holes of the components

The output is a list of the tops of the components [C_1, .. , C_n] of the locus. Each component is given its top ideal p_i.

The input must be the locus system.

LIB "grobcov.lib";
if(defined(R)){kill R;}
ring R=(0,x,y),(x1,y1),dp;
// Concoid
ideal S96=x1 ^2+y1 ^2-4,(x-2)*x1 -x*y1 +2*x,(x-x1 )^2+(y-y1 )^2-1;
==> [1]:
==>    _[1]=(x^4+2*x^3+x^2*y^2-3*x^2-2*x*y^2-8*x*y-6*x+2*y^2+8*y+6)
==> [2]:
==>    _[1]=(x^2+y^2-4*y+3)