# 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