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| − | <command>
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| − | <title>BBSGen.BBTau</title>
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| − | <short_description>
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| − | Let Tau^kl_ij :=t[k,l,i,j] be the (i,j) ^th entry of matrix the operation [A_k,A_l]. For every k,l from {1,..,n} and i,j from {1,...,\mu}, this function finds the polynomial and its degree which corresponds to Tau^kl_ij.
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| − | </short_description>
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| − |
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| − | <syntax>
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| − | BBTau(OO,BO,W,N);
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| − | BBTau(OO:LIST,BO:LIST,W:MATRIX,N:INT):LIST
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| − | </syntax>
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| − | <description>
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| − |
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| − | <itemize>
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| − | <item>@param The order ideal OO, border BO, the number of Indeterminates of the Polynomial Ring and the Weight Matrix.
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| − | </item>
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| − | <item>@return List of generators of the vanishing ideal of the border basis, their position in the matrix [A_k,A_l] and their degree wrt. arrow grading. </item>
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| − | </itemize>
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| − | <example>
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| − | Use R::=QQ[x[1..2]];
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| − |
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| − | OO:=BB.Box([1,1]);
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| − | BO:=BB.Border(OO);
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| − | W:=BBSGen.Wmat(OO,BO,N);
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| − | Mu:=Len(OO);
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| − | Nu:=Len(BO);
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| − | N:=Len(Indets());
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| − | Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]];
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| − |
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| − | Set Indentation;
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| − |
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| − | BBSGen.BBTau(OO,BO,W,N);
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| − |
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| − | [ [t[1,2,1,1], 0,0],
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| − | [ t[1,2,1,2],
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| − | c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3],
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| − | R :: Vector(1, 2)],
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| − | [t[1,2,1,3],
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| − | -c[1,1]c[2,2] - c[1,3]c[4,2] + c[1,4],
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| − | R :: Vector(2, 1)],
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| − | [t[1,2,1,4],
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| − | -c[1,1]c[2,4] + c[1,2]c[3,3] + c[1,4]c[4,3] - c[1,3]c[4,4],
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| − | R :: Vector(2, 2)],
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| − | [ t[1,2,2,1],0,0],
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| − | [ t[1,2,2,2],
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| − | c[2,2]c[3,1] + c[2,4]c[4,1] - c[2,3],
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| − | R :: Vector(1, 1)],
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| − | [ t[1,2,2,3],
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| − | -c[2,1]c[2,2] - c[2,3]c[4,2] - c[1,2] + c[2,4],
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| − | R :: Vector(2, 0)],
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| − | [t[1,2,2,4],
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| − | -c[2,1]c[2,4] + c[2,2]c[3,3] + c[2,4]c[4,3] - c[2,3]c[4,4] - c[1,4],
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| − | R :: Vector(2, 1)],
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| − | [t[1,2,3,1], 0,0],
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| − | [t[1,2,3,2],
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| − | c[3,1]c[3,2] + c[3,4]c[4,1] + c[1,1] - c[3,3],
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| − | R :: Vector(0, 2)],
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| − | [ t[1,2,3,3],
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| − | -c[2,2]c[3,1] - c[3,3]c[4,2] + c[3,4],
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| − | R :: Vector(1, 1)],
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| − | [ t[1,2,3,4],
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| − | -c[2,4]c[3,1] + c[3,2]c[3,3] + c[3,4]c[4,3] - c[3,3]c[4,4] + c[1,3],
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| − | R :: Vector(1, 2)],
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| − | [t[1,2,4,1], 0,0],
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| − | [t[1,2,4,2],
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| − | c[3,1]c[4,2] + c[4,1]c[4,4] + c[2,1] - c[4,3],
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| − | R :: Vector(0, 1)],
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| − | [ t[1,2,4,3],
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| − | -c[2,2]c[4,1] - c[4,2]c[4,3] - c[3,2] + c[4,4],
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| − | R :: Vector(1, 0)],
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| − | [t[1,2,4,4],
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| − | -c[2,4]c[4,1] + c[3,3]c[4,2] + c[2,3] - c[3,4],
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| − | R :: Vector(1, 1)]]
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| − | -------------------------------
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| − |
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| − |
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| − | </example>
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| − |
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| − | </description>
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| − | <types>
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| − | <type>borderbasis</type>
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| − | <type>ideal</type>
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| − | <type>apcocoaserver</type>
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| − | </types>
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| − | <see>BB.Border</see>
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| − | <see>BB.Box</see>
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| − | <see>BBSGen.Wmat</see>
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| − | <key>Wmat</key>
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| − | <key>BBSGen.Wmat</key>
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| − | <key>bbsmingensys.Wmat</key>
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| − | <wiki-category>Package_bbsmingensys</wiki-category>
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| − | </command>
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