Top
Back: rel_orbit_variety
Forward: image_of_variety
FastBack:
FastForward:
Up: finvar_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.7.1.35 relative_orbit_variety

Procedure from library finvar.lib (see finvar_lib).

Usage:
relative_orbit_variety(I,F,s);
I: an <ideal> invariant under the action of a group,
F: a 1xm <matrix> defining the invariant ring of this group,
Finvar::newring: the new ring

Return:
The procedure ends with a new ring named newring.
It contains a Groebner basis
(type <ideal>, named G) for the ideal defining the
relative orbit variety with respect to I in the new ring.

Theory:
A Groebner basis of the ideal of algebraic relations of the invariant ring generators is calculated, then one of the basis elements plus the ideal generators. The variables of the original ring are eliminated and the polynomials that are left define the relative orbit variety with respect to I.

Note:
This procedure is now replaced by rel_orbit_variety (see rel_orbit_variety), which uses a different elemination order that should usually allow faster computations.

Example:
 
LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix F[1][3]=x+y+z,xy+xz+yz,xyz;
ideal I=x2+y2+z2-1,x2y+y2z+z2x-2x-2y-2z,xy2+yz2+zx2-2x-2y-2z;
string newring="E";
relative_orbit_variety(I,F,newring);
print(G);
==> 27*y(3)^6-513*y(3)^4+33849*y(3)^2-784,
==> 1475*y(2)+9*y(3)^4-264*y(3)^2+736,
==> 8260*y(1)+9*y(3)^5-87*y(3)^3+5515*y(3)
basering;
==> // coefficients: QQ
==> // number of vars : 3
==> //        block   1 : ordering lp
==> //                  : names    y(1) y(2) y(3)
==> //        block   2 : ordering C
See also: rel_orbit_variety.


Top Back: rel_orbit_variety Forward: image_of_variety FastBack: FastForward: Up: finvar_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.3.1, 2022, generated by texi2html.