Difference between revisions of "Package invarFC0/InvFC0.SAGBI"
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<item>@param <tt>G</tt> A list of matrices of size <tt>n</tt> over a ring <tt>P</tt> with <tt>n</tt> indeterminates.</item> | <item>@param <tt>G</tt> A list of matrices of size <tt>n</tt> over a ring <tt>P</tt> with <tt>n</tt> indeterminates.</item> | ||
<item>@param <tt>d</tt> (optional) An integer describing the truncation degree.</item> | <item>@param <tt>d</tt> (optional) An integer describing the truncation degree.</item> | ||
| − | <item>@return A list of polynomials that form a (<tt>d</tt> | + | <item>@return A list of polynomials that form a (<tt>d</tt>-truncated) SAGBI basis.</item> |
</itemize> | </itemize> | ||
Latest revision as of 16:06, 9 February 2021
| This article is about a function from ApCoCoA-2. |
InvFC0.SAGBI
This function computes a SAGBI basis of an invariant ring.
Syntax
InvFC0.SAGBI(G:LIST of MAT, opt d:INT):LIST of POLY
Description
This function computes a (d-truncated) SAGBI basis of the invariant ring P^G.
WARNING: May not terminate if P^G does not have a finite SAGBI basis.
@param G A list of matrices of size n over a ring P with n indeterminates.
@param d (optional) An integer describing the truncation degree.
@return A list of polynomials that form a (d-truncated) SAGBI basis.
Example
Use P ::= QQ[x,y,z];
T := matrix(P, [[0,1,0],
[1,0,0],
[0,0,1]]);
C := matrix(P, [[0,1,0],
[0,0,1],
[1,0,0]]);
S3 := [T*T,T,C,T*C,T*C*C,T*C*T];
InvFC0.SAGBI(S3);
Example
A := Mat(P, [[0,1,0],
[0,0,1],
[1,0,0]]);
G := [A,A^2,A^3]; // cyclic group generated by A
TruncG := InvFC0.SAGBI(G,7); // has no finite DegRevLex-SAGBI basis
See also
Package invarFC0/InvFC0.MinGens
