ApCoCoA-1:NCo.Multiply: Difference between revisions
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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>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 ( | 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<X></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><X></tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1, | <item>@param <em>F1, F2:</em> two polynomials in <tt>K<X></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><X></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( | 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, | F1 := [[2,"a"],[1,""]]; | ||
F2 := [[2, | F2 := [[2,"b"],[1,"ba"]]; | ||
NCo.Multiply(F1,F2); -- over F3 | NCo.Multiply(F1,F2); -- over F3 | ||
[[2, | [[2, "aba"], [1, "ab"], [1, "ba"], [2, "b"]] | ||
------------------------------- | ------------------------------- | ||
NCo.Multiply(F2,F1); | NCo.Multiply(F2,F1); | ||
[[2, | [[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, | [[2, "aba"], [4, "ab"], [1, "ba"], [2, "b"]] | ||
------------------------------- | ------------------------------- | ||
NCo.Multiply(F2,F1); | NCo.Multiply(F2,F1); | ||
[[2, | [[2, "baa"], [5, "ba"], [2, "b"]] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
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
