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

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{{Version|1}}
 
<command>
 
<command>
 
   <title>BBSGen.PolDeg</title>
 
   <title>BBSGen.PolDeg</title>
   <short_description>: This function computes the arrow degree of a given homogenous polynomial from the ring K[c].(see <ref>BBSGen.WMat</ref>)
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   <short_description>This function computes the arrow degree of a given homogenous polynomial from the ring K[c](see <ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>).
 
    
 
    
 
              
 
              
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<syntax>
 
<syntax>
  
BBSGen. Poldeg(F,OO,BO,N,W);
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BBSGen.Poldeg(F,OO,BO,N,W);
 
BBSGen.Poldeg(F:POLY,OO:LIST,BO:LIST,N:INT,W:MAT):VECTOR;   
 
BBSGen.Poldeg(F:POLY,OO:LIST,BO:LIST,N:INT,W:MAT):VECTOR;   
 
</syntax>
 
</syntax>
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<itemize>
 
<itemize>
   <item>@param A homogeneous polynomial with respect to the arrow grading from the ring K[c], order ideal OO, border BO,number of indeterminates of the polynomial ring K[x_1,...,x_n] and the weight matrix(<ref>BBSGen.Wmat</ref>).(see <commandref>BB.Border</commandref> from the package borderbasis)
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   <item>@param A homogeneous polynomial with respect to the arrow grading from the ring K[c], order ideal OO, border BO,number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(<ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>).
 
</item>
 
</item>
   <item>@return Degree vector of the given homogenous polynomial wrt. the arrow grading .  </item>
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   <item>@return Degree vector of the given homogenous polynomial wrt. the arrow grading.  </item>
 
</itemize>
 
</itemize>
  
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Use R::=QQ[x[1..2]];
 
Use R::=QQ[x[1..2]];
  
OO:=BB.Box([1,1]);
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OO:= $apcocoa/borderbasis.Box([1,1]);
BO:=BB.Border(OO);
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BO:=$apcocoa/borderbasis.Border(OO);
 
Mu:=Len(OO);
 
Mu:=Len(OO);
 
Nu:=Len(BO);
 
Nu:=Len(BO);
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   <types>
 
   <types>
 
     <type>borderbasis</type>
 
     <type>borderbasis</type>
     <type>ideal</type>
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  <type>bbsmingensys</type>
 +
     <type>Vector</type>
 
     <type>apcocoaserver</type>
 
     <type>apcocoaserver</type>
 
   </types>
 
   </types>
  
  <see>BBSGen.Wmat</see>
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  <see>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</see>
  
<see>BBSGen.NonTriv</see>
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<see>ApCoCoA-1:BBSGen.NonTriv|BBSGen.NonTriv</see>
<see>BBSGen.BBFinder</see>
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<see>ApCoCoA-1:BBSGen.BBFinder|BBSGen.BBFinder</see>
   <key>Wmat</key>
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   <key>Poldeg</key>
   <key>BBSGen.Wmat</key>
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   <key>BBSGen.Poldeg</key>
   <key>bbsmingensys.Wmat</key>
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   <key>bbsmingensys.Poldeg</key>
   <wiki-category>Package_bbsmingensys</wiki-category>
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   <wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:51, 7 October 2020

This article is about a function from ApCoCoA-1.

BBSGen.PolDeg

This function computes the arrow degree of a given homogenous polynomial from the ring K[c](see BBSGen.Wmat).


Syntax

BBSGen.Poldeg(F,OO,BO,N,W);
BBSGen.Poldeg(F:POLY,OO:LIST,BO:LIST,N:INT,W:MAT):VECTOR;  

Description


  • @param A homogeneous polynomial with respect to the arrow grading from the ring K[c], order ideal OO, border BO,number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(BBSGen.Wmat).

  • @return Degree vector of the given homogenous polynomial wrt. the arrow grading.


Example

Use R::=QQ[x[1..2]];

OO:= $apcocoa/borderbasis.Box([1,1]);
BO:=$apcocoa/borderbasis.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);
N:=Len(Indets());
W:=BBSGen.Wmat(OO,BO,N);
Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; 

F:= c[2,4]c[4,1] - c[3,3]c[4,2] - c[2,3] + c[3,4]; 

BBSGen.Poldeg(F,OO,BO,N,W);

R :: Vector(1, 1)




BBSGen.Wmat

BBSGen.NonTriv

BBSGen.BBFinder