Difference between revisions of "Package sagbi/SB.IsInSubalgebra"
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| − | This function takes a polynomials <tt>f</tt> and a list of polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt>. | + | This function takes a polynomials <tt>f</tt> and a list of polynomials <tt>G</tt> and checks whether <tt>F</tt> is in the algebra generated by the polynomials in <tt>G</tt>. |
<itemize> | <itemize> | ||
<item>@param <em>f</em> A polynomial.</item> | <item>@param <em>f</em> A polynomial.</item> | ||
Revision as of 10:49, 27 September 2020
| This article is about a function in ApCoCoA-2.0. If you are looking for the ApCoCoA-1.0 version of it, see ApCoCoA:SB.IsInSubalgebra. |
SB.IsInSubalgebra
Tests whether a polynomial is in a subalgebra.
Syntax
SB.IsInSubalgebra(f:POLY, G:LIST of POLY):BOOL
Description
This function takes a polynomials f and a list of polynomials G and checks whether F is in the algebra generated by the polynomials in G.
@param f A polynomial.
@param G A list of 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(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(y[3]^4, G); ----------------------------------------------------------------------------- false
