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| <command>
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| <title>Gbmr.PRGB</title>
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| <short_description>
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| Compute reduced Groebner basis of right ideal.
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| </short_description>
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| <syntax>
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| Gbmr.PRGB(Alphabet:STRING, Rules:LIST, Order:STRING, F:LIST):LIST
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| </syntax>
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| <description>
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| <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.
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| <itemize>
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| <item>@param <em>Alphabet</em>: Alphabet of the rewriting system.</item>
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| <item>@param <em>Rules</em>: Rewriting rules of the rewriting system.</item>
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| <item>@param <em>Order</em>: Ordering of monoids.</item>
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| <item>@param <em>F</em>: List of generators.</item>
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| <item>@return A list of polynomials which forms a reduced Groebner basis of right ideal generated by F.</item>
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| </itemize>
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| <example>
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| Alphabet := "abc";
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| Rules := [["aa",""], ["bb",""], ["ab","c"], ["ac", "b"], ["cb", "a"]];
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| Order := "LLEX";
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| F1 := [[1,"a"], [1,"b"], [1,"c"]];
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| F := [F1];
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| Gbmr.PRGB(Alphabet, Rules, Order, F);
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| -------------------------------
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| [1+-1b,
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| 1+1c+1a,
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| 1c+1b+1c,
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| 1c+1b+1cc,
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| 1+1a+1ca,
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| 1b+1cc+1bc,
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| 1+1ca+1ba]
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| </example>
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| </description>
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| <seealso>
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| <see>Introduction to CoCoAServer</see>
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| </seealso>
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| <types>
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| <type>apcocoaserver</type>
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| <type>groebner</type>
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| </types>
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| <key>gbmr.PRGB</key>
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| <key>PRGB</key>
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| <wiki-category>Package_gbmr</wiki-category>
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| </command>
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