Difference between revisions of "Package sagbi/SB.IsInSA SAGBI"
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<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> | ||
| − | <syntax>SB.IsInSA(f: RINGELEM,ref S: TAGGED( | + | <syntax>SB.IsInSA(f: RINGELEM,ref S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL</syntax> |
<description> | <description> | ||
This function takes a polynomial <tt>f</tt> and a subalgebra <tt>S</tt> and tests whether <tt>f</tt> is an element of <tt>S</tt> using truncated SAGBI bases. | This function takes a polynomial <tt>f</tt> and a subalgebra <tt>S</tt> and tests whether <tt>f</tt> is an element of <tt>S</tt> using truncated SAGBI bases. | ||
<itemize> | <itemize> | ||
<item>@param <tt>f</tt> A polynomial </item> | <item>@param <tt>f</tt> A polynomial </item> | ||
| − | <item>@param <tt>S</tt> A standard-graded subalgebra, i.e. of type <tt>TAGGED( | + | <item>@param <tt>S</tt> A standard-graded subalgebra, i.e. of type <tt>TAGGED("$apcocoa/sagbi.Subalgebra")</tt> and the generators of f are homogeneous polynomials with respect to the standard grading.</item> |
<item>@return <tt>true</tt> if <tt>f</tt> is an element of <tt>S</tt> and <tt>false</tt> if not.</item> | <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> | ||
Latest revision as of 13:22, 29 October 2020
| This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.IsInSubalgebra. |
SB.IsInSA_SAGBI
This function tests whether a polynomial is in a given standard-graded subalgebra.
Syntax
SB.IsInSA(f: RINGELEM,ref 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,ref S); -- true
See also
Package sagbi/SB.IsInSubalgebra
Package sagbi/SB.IsInSubalgebra_SAGBI
Package sagbi/SB.IsInToricRing
