Difference between revisions of "ApCoCoA-1:NCo.Add"
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<command> | <command> | ||
<title>NCo.Add</title> | <title>NCo.Add</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 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 the <em>word 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 addition 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 addition 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.SetX( | + | NCo.SetX("abc"); |
| − | NCo.SetOrdering( | + | NCo.SetOrdering("ELIM"); |
NCo.RingEnv(); | NCo.RingEnv(); | ||
Coefficient ring : Q | Coefficient ring : Q | ||
| Line 23: | Line 24: | ||
Ordering : ELIE | Ordering : ELIE | ||
------------------------------- | ------------------------------- | ||
| − | F1 := [[1, | + | F1 := [[1,"a"],[1,""]]; |
| − | F2 := [[1, | + | F2 := [[1,"b"],[1,"ba"]]; |
NCo.Add(F1,F2); -- over Q | NCo.Add(F1,F2); -- over Q | ||
| − | [[1, | + | [[1, "ba"], [1, "a"], [1, "b"], [1, ""]] |
------------------------------- | ------------------------------- | ||
NCo.SetFp(); -- set default Fp = F2 | NCo.SetFp(); -- set default Fp = F2 | ||
| Line 35: | Line 36: | ||
------------------------------- | ------------------------------- | ||
NCo.Add(F1,F2); -- over F2 | NCo.Add(F1,F2); -- over F2 | ||
| − | [[1, | + | [[1, "ba"], [1, "a"], [1, "b"], [1, ""]] |
------------------------------- | ------------------------------- | ||
NCo.Add(F1,F1); -- over F2 | NCo.Add(F1,F1); -- over F2 | ||
| Line 43: | Line 44: | ||
</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> | ||
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<key>NCo.Add</key> | <key>NCo.Add</key> | ||
<key>Add</key> | <key>Add</key> | ||
| − | <wiki-category>Package_gbmr</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_gbmr</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:36, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NCo.Add
Addition of two polynomials in a free monoid ring.
Syntax
NCo.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 the word 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 addition 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.SetX("abc");
NCo.SetOrdering("ELIM");
NCo.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : ELIE
-------------------------------
F1 := [[1,"a"],[1,""]];
F2 := [[1,"b"],[1,"ba"]];
NCo.Add(F1,F2); -- over Q
[[1, "ba"], [1, "a"], [1, "b"], [1, ""]]
-------------------------------
NCo.SetFp(); -- set default Fp = F2
NCo.RingEnv();
Coefficient ring : Fp = Z/(2)
Alphabet : abc
Ordering : ELIM
-------------------------------
NCo.Add(F1,F2); -- over F2
[[1, "ba"], [1, "a"], [1, "b"], [1, ""]]
-------------------------------
NCo.Add(F1,F1); -- over F2
[ ]
-------------------------------
See also
