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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.
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