Difference between revisions of "ApCoCoA-1:SB.Sagbi"
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(New page: <command> <title>SB.Sagbi</title> <short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description> <syntax> SB.Sagbi(G:LIST of POLY):LIST of POLY </...) |
Andraschko (talk | contribs) (added version info) |
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| + | {{Version|1|[[Package sagbi/SB.SAGBI]]}} | ||
<command> | <command> | ||
<title>SB.Sagbi</title> | <title>SB.Sagbi</title> | ||
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-- indeed a SAGBI-basis. | -- indeed a SAGBI-basis. | ||
TRUE | TRUE | ||
| + | ------------------------------- | ||
| + | -- Done. | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | <example> | ||
| + | Use R::=QQ[x,y]; | ||
| + | |||
| + | G:=[x+y, xy, xy^2]; | ||
| + | SB.Sagbi(G); | ||
| + | |||
| + | ------------------------------------------------------- | ||
| + | -- output: | ||
| + | |||
| + | --- Computation was interrupted --- | ||
| + | NULL | ||
------------------------------- | ------------------------------- | ||
-- Done. | -- Done. | ||
| Line 64: | Line 80: | ||
</example> | </example> | ||
</description> | </description> | ||
| − | <see>SB.IsSagbi</see> | + | <seealso> |
| − | <see>SB.IsSagbiOf</see> | + | <see>ApCoCoA-1:SB.IsSagbi|SB.IsSagbi</see> |
| + | <see>ApCoCoA-1:SB.IsSagbiOf|SB.IsSagbiOf</see> | ||
| + | </seealso> | ||
<types> | <types> | ||
<type>sagbi</type> | <type>sagbi</type> | ||
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<key>sb.sagbi</key> | <key>sb.sagbi</key> | ||
<key>sagbi.sagbi</key> | <key>sagbi.sagbi</key> | ||
| − | <wiki-category>Package_sagbi</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_sagbi</wiki-category> |
</command> | </command> | ||
Latest revision as of 18:06, 27 October 2020
| This article is about a function from ApCoCoA-1. If you are looking for the ApCoCoA-2 version of it, see Package sagbi/SB.SAGBI. |
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 will be interrupted after a reasonable time, i.e. it seems that there is no finite SAGBI-basis, and NULL will be returned.
@param G A list of polynomials which generates a subalgebra.
@return Either a list of polynomials which form a finite SAGBI-basis of the subalgebra generated by G or NULL, if no finite SAGBI-basis is existing.
Example
Use R::=QQ[x,y]; G:=[x-y,x+y]; SB.IsSagbi(G); SB.Sagbi(G); ------------------------------------------------------- -- output: FALSE ------------------------------- -- The result is correct, because a SAGBI-basis of G is the following: [ x - y, x + y, y] ------------------------------- -- Done. -------------------------------
Example
Use R::=QQ[x[1..6]];
Generators:=[-x[4] - x[6], -x[1], x[2]^2 + x[3]^2,
-4x[4]^2 - 5/2x[5]^2 + 2x[4]x[6] - 4x[6]^2,
-2x[2]x[3]x[4] + x[2]^2x[5] - x[3]^2x[5] + 2x[2]x[3]x[6],
-x[2]^2x[4] + x[3]^2x[4] - 2x[2]x[3]x[5] + x[2]^2x[6] - x[3]^2x[6]];
SB.IsSagbi(Generators);
-- Computation of a SAGBI-basis
Basis:=SB.Sagbi(Generators);
SB.IsSagbi(Basis);
-------------------------------------------------------
-- output:
FALSE
-------------------------------
-- Of course the test passes now because the computed SAGBI-basis is
-- indeed a SAGBI-basis.
TRUE
-------------------------------
-- Done.
-------------------------------
Example
Use R::=QQ[x,y]; G:=[x+y, xy, xy^2]; SB.Sagbi(G); ------------------------------------------------------- -- output: --- Computation was interrupted --- NULL ------------------------------- -- Done. -------------------------------
See also
