Difference between revisions of "Package sagbi/SB.IsInSubalgebra SAGBI"
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<short_description>Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.</short_description> | <short_description>Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.</short_description> | ||
| − | <syntax> | + | <syntax>SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL</syntax> |
| − | SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL | ||
| − | |||
<description> | <description> | ||
This function takes a polynomials <tt>f</tt> and a list of homogeneous polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt> using truncated SAGBI bases. | This function takes a polynomials <tt>f</tt> and a list of homogeneous polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt> using truncated SAGBI bases. | ||
| Line 19: | Line 17: | ||
G := [x[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^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); | SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G); | ||
| − | -- | + | -- true</example> |
| − | true | ||
| − | |||
<example> | <example> | ||
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G := [y[1]^2-y[3]^2, y[1]*y[2]+y[3]^2, y[2]^2-2*y[3]^2]; | 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); | SB.IsInSubalgebra_SAGBI(y[3]^4, G); | ||
| − | -- | + | -- false</example> |
| − | false | ||
| − | |||
</description> | </description> | ||
Revision as of 12:55, 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
