Difference between revisions of "ApCoCoA-1:NCo.Multiply"
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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 using this function. The default coefficient field is <tt>Q</tt>, and the default ordering is the length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | + | 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 (<quotes>LLEX</quotes>). 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,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | <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,<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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</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>NCo.SetFp</see> | + | <see>ApCoCoA-1:NCo.SetFp|NCo.SetFp</see> |
| − | <see>NCo.SetOrdering</see> | + | <see>ApCoCoA-1:NCo.SetOrdering|NCo.SetOrdering</see> |
| − | <see>NCo.SetX</see> | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
Revision as of 08:32, 7 October 2020
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(<quotes>abc</quotes>); NCo.RingEnv(); Coefficient ring : Fp = Z/(3) Alphabet : abc Ordering : LLEX ------------------------------- F1 := [[2,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[2,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NCo.Multiply(F1,F2); -- over F3 [[2, <quotes>aba</quotes>], [1, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NCo.Multiply(F2,F1); [[2, <quotes>baa</quotes>], [2, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- 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, <quotes>aba</quotes>], [4, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NCo.Multiply(F2,F1); [[2, <quotes>baa</quotes>], [5, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] -------------------------------
See also
