Difference between revisions of "ApCoCoA-1:NC.Add"
From ApCoCoAWiki
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<title>NC.Add</title> | <title>NC.Add</title> | ||
<short_description> | <short_description> | ||
| − | Addition of two polynomials over a free | + | Addition of two polynomials over a free monoid ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
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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 coefficient field <tt>K</tt>, alphabet (or indeterminates) <tt>X</tt> and 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>NC.SetFp</ref>, <ref>NC.SetX</ref> and <ref>NC.SetOrdering</ref>, respectively, before calling the function. Default coefficient field is <tt>Q</tt>. Default ordering is 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 addition respectively. Each polynomial is represented as a LIST of | + | <item>@param <em>F1, F2:</em> two polynomials in <tt>K<X></tt>, which are left and right operands of addition 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><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 an empty LIST [].</item> |
| − | <item>@return: a LIST which represents | + | <item>@return: a LIST which represents the polynomial equal to <tt>F1+F2</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
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Ordering : ELIM | Ordering : ELIM | ||
| − | ------------------------------- | + | ------------------------------- |
| + | |||
F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; | F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; | ||
F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; | F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; | ||
| Line 29: | Line 30: | ||
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] | [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] | ||
------------------------------- | ------------------------------- | ||
| + | |||
NC.SetFp(); -- set default Fp = F2 | NC.SetFp(); -- set default Fp = F2 | ||
NC.RingEnv(); | NC.RingEnv(); | ||
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------------------------------- | ------------------------------- | ||
| + | |||
NC.Add(F1,F2); -- over F2 | NC.Add(F1,F2); -- over F2 | ||
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] | [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] | ||
------------------------------- | ------------------------------- | ||
| + | |||
NC.Add(F1,F1); -- over F2 | NC.Add(F1,F1); -- over F2 | ||
[ ] | [ ] | ||
Revision as of 11:21, 7 June 2012
NC.Add
Addition of two polynomials over a free monoid ring.
Syntax
NC.Add(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 NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. Default coefficient field is Q. Default ordering is 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 addition respectively. Each polynomial is represented as a LIST of monomials, which are pairs 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 an empty LIST [].
@return: a LIST which represents the polynomial equal to F1+F2.
Example
NC.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); NC.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : ELIM ------------------------------- F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NC.Add(F1,F2); -- over Q [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.SetFp(); -- set default Fp = F2 NC.RingEnv(); Coefficient ring : Fp = Z/(2) Alphabet : abc Ordering : ELIM ------------------------------- NC.Add(F1,F2); -- over F2 [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.Add(F1,F1); -- over F2 [ ] -------------------------------
See also
