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D.7.3.11 NullCone
Procedure from library rinvar.lib (see rinvar_lib).
- Usage:
- NullCone(G, action); ideal G, action
- Purpose:
- compute the ideal of the nullcone of the linear action of G on K^n,
given by 'action', by means of Deksen's algorithm
- Assume:
- basering = K[s(1..r),t(1..n)], K = Q or K = Q(a) and minpoly != 0,
G is an ideal of a reductive algebraic group in K[s(1..r)],
'action' is a linear group action of G on K^n (n = ncols(action))
- Return:
- ideal of the nullcone of G.
- Note:
- the generators of the nullcone are homogeneous, but in general not invariant
Example:
| | LIB "rinvar.lib";
ring R = 0, (s(1..2), x, y), dp;
ideal G = -s(1)+s(2)^3, s(1)^4-1;
ideal action = s(1)*x, s(2)*y;
ideal inv = NullCone(G, action);
inv;
==> inv[1]=x^4
==> inv[2]=x^3*y^3
==> inv[3]=x^2*y^6
==> inv[4]=x*y^9
==> inv[5]=y^12
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