Difference between revisions of "Package sagbi/SB.IsInSA SAGBI"
From ApCoCoAWiki
Andraschko (talk | contribs) (Created page with "{{Version|2}} <command> <title>SB.IsInSA</title> <short_description>This function tests whether a polynomial is in a given standard-graded subalgebra.</short_description>...") |
m (replaced <quotes> tags by real quotes) |
||
| (7 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
| − | {{Version|2}} | + | {{Version|2|[[ApCoCoA-1:SB.IsInSubalgebra]]}} |
<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> | ||
| − | <syntax> | + | <syntax>SB.IsInSA(f: RINGELEM,ref S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL</syntax> |
| − | SB.IsInSA(f: RINGELEM,S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL | ||
| − | |||
<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("$apcocoa/sagbi.Subalgebra")</tt> and the generators of f are homogeneous polynomials with respect to the standard grading.</item> |
| − | <item>@return < | + | <item>@return <tt>true</tt> if <tt>f</tt> is an element of <tt>S</tt> and <tt>false</tt> if not.</item> |
</itemize> | </itemize> | ||
| Line 19: | Line 17: | ||
S := SB.Subalgebra(R,[x^2,y+z]); | S := SB.Subalgebra(R,[x^2,y+z]); | ||
f := x^4 +2*x^3*y +x^2*y^2 +x^2 +2*x*y +y^2; | f := x^4 +2*x^3*y +x^2*y^2 +x^2 +2*x*y +y^2; | ||
| − | SB.IsInSA_SAGBI(f,S); -- true | + | SB.IsInSA_SAGBI(f,ref S); -- true</example> |
| − | |||
</description> | </description> | ||
<seealso> | <seealso> | ||
| + | <see>Package sagbi/SB.Subalgebra</see> | ||
<see>Package sagbi/SB.IsInSA</see> | <see>Package sagbi/SB.IsInSA</see> | ||
<see>Package sagbi/SB.IsInSubalgebra</see> | <see>Package sagbi/SB.IsInSubalgebra</see> | ||
<see>Package sagbi/SB.IsInSubalgebra_SAGBI</see> | <see>Package sagbi/SB.IsInSubalgebra_SAGBI</see> | ||
| + | <see>Package sagbi/SB.IsInToricRing</see> | ||
</seealso> | </seealso> | ||
Latest revision as of 13:22, 29 October 2020
| This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.IsInSubalgebra. |
SB.IsInSA_SAGBI
This function tests whether a polynomial is in a given standard-graded subalgebra.
Syntax
SB.IsInSA(f: RINGELEM,ref S: TAGGED("$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
