Difference between revisions of "ApCoCoA-1:NCo.Multiply"

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(New page: <command> <title>NCo.Multiply</title> <short_description> Multiplication of two polynomials in a free monoid ring. </short_description> <syntax> NCo.Multiply(F1:LIST, F2:LIST):LIST </synta...)
 
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{{Version|1}}
 
<command>
 
<command>
 
<title>NCo.Multiply</title>
 
<title>NCo.Multiply</title>
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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.
 
<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.
 
<par/>
 
<par/>
Please set ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before calling the function. The default coefficient field is <tt>Q</tt>. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.
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Please set ring environment <em>coefficient field</em> <tt> K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>ApCoCoA-1:NCo.SetFp|NCo.SetFp</ref>, <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> and <ref>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</ref>, respectively, before using this function. The default coefficient field is <tt>Q</tt>, and the default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
 
<itemize>
 
<itemize>
<item>@param <em>F1, F2:</em> two polynomials in <tt>K&lt;X&gt;</tt>, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item>
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<item>@param <em>F1, F2:</em> two polynomials in <tt>K&lt;X&gt;</tt>, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item>
 
<item>@return: a LIST which represents the polynomial equal to <tt>F1*F2</tt>.</item>
 
<item>@return: a LIST which represents the polynomial equal to <tt>F1*F2</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
 
NCo.SetFp(3);
 
NCo.SetFp(3);
NCo.SetX(<quotes>abc</quotes>);
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NCo.SetX("abc");
 
NCo.RingEnv();
 
NCo.RingEnv();
 
Coefficient ring : Fp = Z/(3)
 
Coefficient ring : Fp = Z/(3)
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Ordering : LLEX
 
Ordering : LLEX
 
-------------------------------
 
-------------------------------
F1 := [[2,<quotes>a</quotes>],[1,<quotes></quotes>]];
+
F1 := [[2,"a"],[1,""]];
F2 := [[2,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
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F2 := [[2,"b"],[1,"ba"]];
 
NCo.Multiply(F1,F2); -- over F3
 
NCo.Multiply(F1,F2); -- over F3
[[2, <quotes>aba</quotes>], [1, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
+
[[2, "aba"], [1, "ab"], [1, "ba"], [2, "b"]]
 
-------------------------------
 
-------------------------------
 
NCo.Multiply(F2,F1);
 
NCo.Multiply(F2,F1);
[[2, <quotes>baa</quotes>], [2, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
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[[2, "baa"], [2, "ba"], [2, "b"]]
 
-------------------------------
 
-------------------------------
 
NCo.Multiply(F1,[]);
 
NCo.Multiply(F1,[]);
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-------------------------------
 
-------------------------------
 
NCo.Multiply(F1,F2); -- over Q
 
NCo.Multiply(F1,F2); -- over Q
[[2, <quotes>aba</quotes>], [4, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
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[[2, "aba"], [4, "ab"], [1, "ba"], [2, "b"]]
 
-------------------------------
 
-------------------------------
 
NCo.Multiply(F2,F1);
 
NCo.Multiply(F2,F1);
[[2, <quotes>baa</quotes>], [5, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
+
[[2, "baa"], [5, "ba"], [2, "b"]]
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
 
</description>
 
</description>
 
<seealso>
 
<seealso>
<see>NCo.SetFp</see>
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<see>ApCoCoA-1:NCo.SetFp|NCo.SetFp</see>
<see>NCo.SetX</see>
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<see>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</see>
<see>Introduction to CoCoAServer</see>
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<see>ApCoCoA-1:NCo.SetX|NCo.SetX</see>
 +
<see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
 
</seealso>
 
</seealso>
 
<types>
 
<types>
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<key>NCo.Multiply</key>
 
<key>NCo.Multiply</key>
 
<key>Multiply</key>
 
<key>Multiply</key>
<wiki-category>Package_gbmr</wiki-category>
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<wiki-category>ApCoCoA-1:Package_gbmr</wiki-category>
 
</command>
 
</command>

Latest revision as of 13:43, 29 October 2020

This article is about a function from ApCoCoA-1.

NCo.Multiply

Multiplication of two polynomials in a free monoid ring.

Syntax

NCo.Multiply(F1:LIST, F2:LIST):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Please set ring environment coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NCo.SetFp, NCo.SetX and NCo.SetOrdering, respectively, before using this function. The default coefficient field is Q, and the default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

  • @param F1, F2: two polynomials in K<X>, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the polynomial f=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].

  • @return: a LIST which represents the polynomial equal to F1*F2.

Example

NCo.SetFp(3);
NCo.SetX("abc");
NCo.RingEnv();
Coefficient ring : Fp = Z/(3)
Alphabet : abc
Ordering : LLEX
-------------------------------
F1 := [[2,"a"],[1,""]];
F2 := [[2,"b"],[1,"ba"]];
NCo.Multiply(F1,F2); -- over F3
[[2, "aba"], [1, "ab"], [1, "ba"], [2, "b"]]
-------------------------------
NCo.Multiply(F2,F1);
[[2, "baa"], [2, "ba"], [2, "b"]]
-------------------------------
NCo.Multiply(F1,[]);
[ ]
-------------------------------
NCo.Multiply([],F1);
[ ]
-------------------------------
NCo.Multiply([],[]);
[ ]
-------------------------------
NCo.UnsetFp();
NCo.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : LLEX
-------------------------------
NCo.Multiply(F1,F2); -- over Q
[[2, "aba"], [4, "ab"], [1, "ba"], [2, "b"]]
-------------------------------
NCo.Multiply(F2,F1);
[[2, "baa"], [5, "ba"], [2, "b"]]
-------------------------------

See also

NCo.SetFp

NCo.SetOrdering

NCo.SetX

Introduction to CoCoAServer