Difference between revisions of "Package sagbi/SB.IsInSubalgebra SAGBI"
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| − | <see>SB.IsInSubalgebra</see> | + | <see>Package sagbi/SB.IsInSubalgebra</see> |
| − | <see>SB.IsInSA</see> | + | <see>Package sagbi/SB.IsInSA</see> |
| − | <see>SB.IsInSA_SAGBI</see> | + | <see>Package sagbi/SB.IsInSA_SAGBI</see> |
| − | <see>SB.IsInToricRing</see> | + | <see>Package sagbi/SB.IsInToricRing</see> |
</seealso> | </seealso> | ||
Revision as of 12:23, 26 October 2020
| This article is about a function from ApCoCoA-2. |
SB.IsInSubalgebra_SAGBI
Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.
Syntax
SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL
Description
This function takes a polynomials f and a list of homogeneous polynomials G and checks whether F is in the algebra generated by the polynomials in G using truncated SAGBI bases.
@param f A polynomial.
@param G A list of homogeneous polynomials which generate a subalgebra.
@return true if f is in the subalgebra generated by G, false elsewise.
Example
Use QQ[x[1..2]];
G := [x[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^2];
SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G);
-----------------------------------------------------------------------------
true
Example
Use QQ[y[1..3]];
G := [y[1]^2-y[3]^2, y[1]*y[2]+y[3]^2, y[2]^2-2*y[3]^2];
SB.IsInSubalgebra_SAGBI(y[3]^4, G);
-----------------------------------------------------------------------------
false
See also
Package sagbi/SB.IsInSubalgebra
Package sagbi/SB.IsInToricRing
