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| − | <command>
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| − | <title>BBSGen.NonStandPoly</title>
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| − | <short_description> Finds the non-standard polynomials of the ring <tt>K[c_{ij}]</tt> with respect to the arrow grading. </short_description>
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| − | <syntax>
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| − | BBSGen.NonStandPoly(OO:LIST,BO:LIST,N:INT,W:MATRIX):LIST
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| − | </syntax>
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| − | <description>
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| − | <itemize>
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| − | <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
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| − | <item>@param <em>BO</em> A list of terms representing the border.</item>
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| − | <item>@param <em>N</em> The number of elements of the Polynomial ring <tt>K[x_1,...x_n]</tt>.</item>
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| − | <item>@param <em>W</em> The weight matrix.</item>
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| − | <item>@return A list of non-standard polynomials from <tt>K[c_{ij}]</tt> with their degree vectors from field <tt>K</tt>.</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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| − | OO:=BB.Box([1,1]);
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| − | BO:=BB.Border(OO);
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| − | Mu:=Len(OO);
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| − | Nu:=Len(BO);
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| − | W:=Wmat(OO,BO,N);
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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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| − | BBSGen.NonStandPoly(OO,BO,N,W);
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| − |
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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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| − | [ 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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| − | [ 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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| − | [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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| − | [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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| − | [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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| − | [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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| − | [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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| − | </example>
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| − | </description>
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| − | <types>
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| − | <type>bbsmingensys</type>
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| − | </types>
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| − | <see>BBSGen.Wmat</see>
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| − | <see>BBSGen.NonStand</see>
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| − | <see>BB.Box</see>
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| − | <see>BB.Border</see>
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| − | <key>Wmat</key>
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| − | <key>BBSGen.NonStandPoly</key>
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| − | <key>bbsmingensys.NonStandPoly</key>
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| − | <wiki-category>Package_bbsmingensys</wiki-category>
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| − | </command>
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