Usage:
<orbit_equations g J
computes the ideal J of equations defining the orbit of
a homogeneous polynomial g under the general linear group.
THE CURRENT RING MUST BE A RING WITH AT LEAST AS MANY VARIABLES AS
THE NUMBER OF COEFFICIENTS OF g.
Parameters:
g = 1x1 matrix containing the polynomial (generally not over
the current ring.)
Output values:
J = ideal in the current ring of polynomials
vanishing on the closure of the orbit of g.
The script applies a general change of variables to f and computes
the equations satisfied by the new coefficients.
Caveats:
The polynomial must be homogeneous with all variables of
degree 1. The script runs quite slowly in all but the smallest
cases. Thus it is worth making sure that there are no extra
variables in either the ring of f or the current ring, the ring
representing the coefficients of the general form.