Difference between revisions of "Package sagbi/SB.SAGBI"
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{{Version|2|[[ApCoCoA-1:SB.Sagbi]] and [[ApCoCoA-1:SB.ReducedSagbi]]}} | {{Version|2|[[ApCoCoA-1:SB.Sagbi]] and [[ApCoCoA-1:SB.ReducedSagbi]]}} | ||
| − | |||
<command> | <command> | ||
<title>SB.SAGBI</title> | <title>SB.SAGBI</title> | ||
<short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description> | <short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description> | ||
| − | + | ||
| − | <syntax> | + | <syntax> |
SB.SAGBI(G:LIST of POLY):LIST of POLY | SB.SAGBI(G:LIST of POLY):LIST of POLY | ||
| − | </syntax> | + | </syntax> |
<description> | <description> | ||
This function computes a finite SAGBI-basis of a subalgebra <tt>S</tt> generated by the polynomials of the list <tt>G</tt>, if a finite SAGBI-basis of <tt>S</tt> is existing. Then a list of polynomials is returned which form a SAGBI-basis of <tt>S</tt>. Otherwise the computation runs until it is interrupted. | This function computes a finite SAGBI-basis of a subalgebra <tt>S</tt> generated by the polynomials of the list <tt>G</tt>, if a finite SAGBI-basis of <tt>S</tt> is existing. Then a list of polynomials is returned which form a SAGBI-basis of <tt>S</tt>. Otherwise the computation runs until it is interrupted. | ||
| − | <itemize> | + | <itemize> |
| − | + | <item>@param <em>G</em> A list of polynomials which generates a subalgebra.</item> | |
| − | + | <item>@return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by <tt>G</tt>.</item> | |
| − | </itemize> | + | </itemize> |
| − | <example> | + | <example> |
Use QQ[x,y,z], DegRevLex; | Use QQ[x,y,z], DegRevLex; | ||
S := SB.SAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2]); | S := SB.SAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2]); | ||
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-- x^2 -z^2, | -- x^2 -z^2, | ||
-- x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4 | -- x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4 | ||
| − | -- ] | + | -- ]</example> |
| − | </example> | ||
</description> | </description> | ||
| + | |||
<seealso> | <seealso> | ||
<see>Package sagbi/SB.TruncSAGBI</see> | <see>Package sagbi/SB.TruncSAGBI</see> | ||
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<see>Package sagbi/SB.GetTruncSAGBI</see> | <see>Package sagbi/SB.GetTruncSAGBI</see> | ||
</seealso> | </seealso> | ||
| + | |||
<types> | <types> | ||
<type>sagbi</type> | <type>sagbi</type> | ||
<type>poly</type> | <type>poly</type> | ||
</types> | </types> | ||
| + | |||
<key>SAGBI</key> | <key>SAGBI</key> | ||
<key>SB.SAGBI</key> | <key>SB.SAGBI</key> | ||
<key>apcocoa/sagbi.SAGBI</key> | <key>apcocoa/sagbi.SAGBI</key> | ||
| + | |||
<wiki-category>Package sagbi</wiki-category> | <wiki-category>Package sagbi</wiki-category> | ||
</command> | </command> | ||
Revision as of 08:49, 28 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.Sagbi and ApCoCoA-1:SB.ReducedSagbi. |
SB.SAGBI
Computes a finite SAGBI-basis of a subalgebra if existing.
Syntax
SB.SAGBI(G:LIST of POLY):LIST of POLY
Description
This function computes a finite SAGBI-basis of a subalgebra S generated by the polynomials of the list G, if a finite SAGBI-basis of S is existing. Then a list of polynomials is returned which form a SAGBI-basis of S. Otherwise the computation runs until it is interrupted.
@param G A list of polynomials which generates a subalgebra.
@return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by G.
Example
Use QQ[x,y,z], DegRevLex; S := SB.SAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2]); indent(S); -- [ -- y^2 -2*z^2, -- x*y +z^2, -- x^2 -z^2, -- x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4 -- ]
See also
Package sagbi/SB.GetTruncSAGBI
