Difference between revisions of "ApCoCoA-1:BBSGen.LinIndepGen"

From ApCoCoAWiki
Line 1: Line 1:
 
<command>
 
<command>
 
   <title>BBSGen.LinIndepGen</title>
 
   <title>BBSGen.LinIndepGen</title>
   <short_description>This function computes the equivalent indeterminates modulo m^2 of BBS where m is the maximal ideal generated by the indeterminates {c_11,...,c_\mu \nu} .</short_description>
+
   <short_description>This function computes the equivalent indeterminates from K[c] modulo m^2 of BBS, where m is the maximal ideal generated by the indeterminates {c_11,...,c_\mu \nu}. As out-put, it gives every equivalence class as a list.</short_description>
 
    
 
    
 
<syntax>
 
<syntax>
Line 8: Line 8:
 
</syntax>
 
</syntax>
 
   <description>
 
   <description>
This function computes the equivalent indeterminates in the cotangent space m\m^2 of BBS and gives these equivalent indeterminates in one list(if they are not equivalent to 0) and additionally the K-linearly independent ones. The base ring can be K[x_1,..,x_n].
+
 
 
<itemize>
 
<itemize>
 
   <item>@param  The order ideal OO.</item>
 
   <item>@param  The order ideal OO.</item>
Line 45: Line 45:
  
  
<see> BBSGen.InFinder</see>
+
 
  
 
<see> BBSGen.PurPow</see>
 
<see> BBSGen.PurPow</see>

Revision as of 09:33, 8 June 2012

BBSGen.LinIndepGen

This function computes the equivalent indeterminates from K[c] modulo m^2 of BBS, where m is the maximal ideal generated by the indeterminates {c_11,...,c_\mu \nu}. As out-put, it gives every equivalence class as a list.

Syntax

BBSGen.LinIndepGen(OO):
BBSGen.LinIndepGen(OO:LIST):LIST

Description


  • @param The order ideal OO.

  • @return The list of classes of indeterminates modulo m^2.


Example

Use R::=QQ[x,y];
OO:=[1,x,y,xy];
BO:=BB.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);

BBSGen.LinIndepGen(OO); 


[[[3, 3], [1, 1]], [[1, 2], [2, 4]], [[4, 3], [2, 1]], [[2, 2]], [[3, 1]], [[4, 4], [3, 2]], [4, 2], [4, 1]]

Class:=BBSGen.LinIndepGen(OO); 

Use BBS::=CoeffRing[c[1..Mu,1..Nu]]; 

BBSGen.IndFinder(Class,Mu,Nu);

[[c[3,3], c[1,1]], [c[1,2], c[2,4]], [c[4,3], c[2,1]], c[2,2], c[3,1], [c[4,4], c[3,2]], c[4,1], c[4,2]]
-------------------------------
-------------------------------




BBSGen.PurPow