Package sagbi/SB.TruncSAGBI
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| This article is about a function in ApCoCoA-2.0. |
SB.TruncSAGBI
Computes a truncated SAGBI-basis of a standard-graded subalgebra.
Syntax
SB.SAGBI(G:LIST of POLY,d:RAT):LIST of POLY
Description
This function computes a d-truncated SAGBI-basis of the subalgebra S generated by the polynomials in the list G, i.e. a set of polynomials F such that any term appearing as the leading term of a polynomial in S of degree smaller than or equal to d is a product of terms appearing as leading term of a polynomial in F.
@param G A list of homogeneous polynomials which generates a subalgebra.
@param d An integer specifying the truncation degree.
@return A tuple [L,b] where L is a list of polynomials which form a d-truncated finite SAGBI-basis of the subalgebra generated by G. b is a boolean value which is true if L is already a complete SAGBI basis.
Example
Use QQ[x[1..3]];
S := SB.TruncSAGBI([x[1]^2-x[3]^2,x[1]*x[2]+x[3]^2,x[2]^2-2*x[3]^2],2);
indent(S,2);
-----------------------------------------------------------------------------
[
[
x[2]^2 -2*x[3]^2,
x[1]*x[2] +x[3]^2,
x[1]^2 -x[3]^2,
x[1]^2*x[3]^2 +x[1]*x[2]*x[3]^2 +(1/2)*x[2]^2*x[3]^2 +(-1/2)*x[3]^4
],
true
]
Example
Use QQ[x,y];
S := SB.TruncSAGBI([x+y,x*y,x*y^2],10); -- K[x+y,xy,xy^2] doesn't have a finite SAGBI basis
indent(S,2);
-----------------------------------------------------------------------------
[
[
x +y,
x*y,
x*y^2,
x*y^3,
x*y^4
],
false
]
