ApCoCoA-1:FGLM.FGLM: Difference between revisions

From ApCoCoAWiki
Stadler (talk | contribs)
No edit summary
Skaspar (talk | contribs)
Description update.
Line 1: Line 1:
  <command>
<command>
    <title>FGLM.FGLM</title>
  <title>FGLM.FGLM</title>
    <short_description>Perform a FGLM Groebner Basis conversion using ApCoCoAServer.</short_description>
  <short_description>Perform a FGLM Groebner Basis conversion using ApCoCoAServer.</short_description>
<syntax>
  <syntax>FGLM(GBOld:LIST, M:MAT):LIST
FGLM(GBOld:LIST, M:MAT):LIST
FGLM(GBOld:LIST):LIST</syntax>
FGLM(GBOld:LIST):LIST
  <description>
</syntax>
    <description>
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
<par/>
<par/>
Line 13: Line 11:
the given Groebner Basis must be zero-dimensional. The Groebner
the given Groebner Basis must be zero-dimensional. The Groebner
Basis contained in list GBOld will be converted into a Groebner
Basis contained in list GBOld will be converted into a Groebner
Basis with respect to term ordering Ord(M), i.e. M must be a matrix
Basis with respect to term ordering <ref>Ord</ref>(M), i.e. M must be a matrix
specifying a term ordering. If the parameter M is not specified, CoCoA
specifying a term ordering. If the parameter M is not specified, ApCoCoA
will assume M = Ord(). Please note that the resulting polynomials belong
will assume M = <ref>Ord</ref>(). Please note that the resulting polynomials belong
to a different ring than the ones in GBOld.
to a different ring than the ones in GBOld.
 
<par/>
Ther return value will be the transformed Groebner basis polynomials.
The return value will be the transformed Groebner basis polynomials.
<itemize>
<itemize>
   <item>@param <em>GBOld</em> A Groebner basis of a zero-dimensional ideal.</item>
   <item>@param <em>GBOld</em> A Groebner basis of a zero-dimensional ideal.</item>
Line 33: Line 31:
BringIn(GBNew);
BringIn(GBNew);
</example>
</example>
</description>
  </description>
<seealso>
   <see>GBasis5, and more</see>
   <see>GBasis5, and more</see>
</seealso>
  <types>
<types>
    <type>groebner</type>
  <type>groebner</type>
    <type>matrix</type>
  <type>matrix</type>
    <type>list</type>
  <type>list</type>
    <type>apcocoaserver</type>
  <type>apcocoaserver</type>
  </types>
</types>
  <key>FGLM</key>
<key>FGLM</key>
  <key>FGLM.FGLM</key>
<key>FGLM.FGLM</key>
  <key>fglm.FGLM</key>
<key>fglm.FGLM</key>
  <key>groebner basis conversion</key>
<key>groebner basis conversion</key>
  <wiki-category>Package_fglm</wiki-category>
<wiki-category>Package_fglm</wiki-category>
</command>
</command>

Revision as of 11:43, 24 April 2009

FGLM.FGLM

Perform a FGLM Groebner Basis conversion using ApCoCoAServer.

Syntax

FGLM(GBOld:LIST, M:MAT):LIST
FGLM(GBOld:LIST):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

The function FGLM calls the ApCoCoAServer to perform a

FGLM Groebner Basis conversion. Please note that the ideal generated by

the given Groebner Basis must be zero-dimensional. The Groebner Basis contained in list GBOld will be converted into a Groebner Basis with respect to term ordering Ord(M), i.e. M must be a matrix specifying a term ordering. If the parameter M is not specified, ApCoCoA will assume M = Ord(). Please note that the resulting polynomials belong to a different ring than the ones in GBOld.

The return value will be the transformed Groebner basis polynomials.

  • @param GBOld A Groebner basis of a zero-dimensional ideal.

  • @param M A matrix representing a term ordering.

  • @return A Groebner basis of the ideal generated by the polynomials of GBOld. The polynomials of the new Groebner basis will belong to the polynomial ring with term ordering specified by M or Ord() in case M is not given.

Example

Use QQ[x, y, z], DegRevLex;
GBOld := [z^4 -3z^3 - 4yz + 2z^2 - y + 2z - 2, yz^2 + 2yz - 2z^2 + 1, y^2 - 2yz + z^2 - z, x + y - z];
M := LexMat(3);
GBNew := FGLM(GBOld, M);
Use QQ[x, y, z], Ord(M);
-- New basis (Lex)
BringIn(GBNew);

GBasis5, and more