Difference between revisions of "Package sagbi/SB.IsInSA SAGBI"
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{{Version|2}} | {{Version|2}} | ||
<command> | <command> | ||
| − | <title>SB. | + | <title>SB.IsInSA_SAGBI</title> |
<short_description>This function tests whether a polynomial is in a given standard-graded subalgebra.</short_description> | <short_description>This function tests whether a polynomial is in a given standard-graded subalgebra.</short_description> | ||
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</syntax> | </syntax> | ||
<description> | <description> | ||
| − | This function takes a polynomial < | + | This function takes a polynomial <tt>f</tt> and a subalgebra <tt>S</tt> and tests whether <tt>f</tt> is an element of <tt>S</tt> using truncated SAGBI bases. |
<itemize> | <itemize> | ||
| − | <item>@param < | + | <item>@param <tt>f</tt> A polynomial </item> |
| − | <item>@param < | + | <item>@param <tt>S</tt> A standard-graded subalgebra, i.e. of type <tt>TAGGED("$apcocoa/sagbi.Subalgebra")</tt> and the generators of f are homogeneous polynomials with respect to the standard grading.</item> |
| − | <item>@return < | + | <item>@return <tt>true</tt> if <tt>f</tt> is an element of <tt>S</tt> and <tt>false</tt> if not.</item> |
</itemize> | </itemize> | ||
Revision as of 12:04, 26 October 2020
| This article is about a function from ApCoCoA-2. |
SB.IsInSA_SAGBI
This function tests whether a polynomial is in a given standard-graded subalgebra.
Syntax
SB.IsInSA(f: RINGELEM,S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL
Description
This function takes a polynomial f and a subalgebra S and tests whether f is an element of S using truncated SAGBI bases.
@param f A polynomial
@param S A standard-graded subalgebra, i.e. of type TAGGED("$apcocoa/sagbi.Subalgebra") and the generators of f are homogeneous polynomials with respect to the standard grading.
@return true if f is an element of S and false if not.
Example
Use R ::= QQ[x,y,z];
S := SB.Subalgebra(R,[x^2,y+z]);
f := x^4 +2*x^3*y +x^2*y^2 +x^2 +2*x*y +y^2;
SB.IsInSA_SAGBI(f,S); -- true
See also
Package sagbi/SB.IsInSubalgebra
Package sagbi/SB.IsInSubalgebra_SAGBI
