Difference between revisions of "ApCoCoA-1:NC.Add"
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(New page: <command> <title>Gbmr.MRAdd</title> <short_description> Addition of two polynomials over a monoid ring. </short_description> <syntax> Gbmr.MRAdd(X:STRING, Ordering:STRING, R:LIST, F1:LIST,...) |
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<command> | <command> | ||
| − | <title> | + | <title>NC.Add</title> |
<short_description> | <short_description> | ||
| − | Addition of two polynomials over a | + | Addition of two polynomials over a free associative K-algebra. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | + | NC.Add(F1:LIST, F2:LIST):LIST | |
</syntax> | </syntax> | ||
<description> | <description> | ||
<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. | ||
<itemize> | <itemize> | ||
| − | <item> | + | <item>Before calling the function, please set ring environment coefficient field (<tt>K</tt>), alphabet (<tt>X</tt>) and ordering through the functions NC.SetFp(P) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.</item> |
| − | + | <item>@param <em>F1</em> left operand of addition operator. It is a polynomial in <tt>K<X></tt>. Each polynomial is represented as a LIST of LISTs, which are pairs of form <tt>[c, w]</tt> where <tt>c</tt> is in <tt>K</tt> and <tt>w</tt> is a word in <tt>X*</tt>. For example, polynomial <tt>F:=xy-y+1</tt> is represented as <tt>F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]</tt>. Zero polynomial is represented as an empty LIST <tt>[]</tt>.</item> | |
| − | <item>@param <em> | + | <item>@param <em>F2</em> right operand of addition operator. It is a polynomial in <tt>K<X></tt>.</item> |
| − | |||
<item>@return: a LIST which represents a polynomial equal to <tt>F1+F2</tt>.</item> | <item>@return: a LIST which represents a polynomial equal to <tt>F1+F2</tt>.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | + | NC.SetX(<quotes>abc</quotes>); | |
| − | + | NC.SetOrdering(<quotes>ELIM</quotes>); | |
| − | + | F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; | |
| − | + | F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; | |
| − | + | NC.Add(F1,F2); | |
| − | + | [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] | |
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------------------------------- | ------------------------------- | ||
| − | + | </example> | |
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</description> | </description> | ||
<seealso> | <seealso> | ||
Revision as of 08:37, 14 July 2010
NC.Add
Addition of two polynomials over a free associative K-algebra.
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.
Before calling the function, please set ring environment coefficient field (K), alphabet (X) and ordering through the functions NC.SetFp(P) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F1 left operand of addition operator. It is a polynomial in K<X>. Each polynomial is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in K and w is a word in X*. For example, polynomial F:=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. Zero polynomial is represented as an empty LIST [].
@param F2 right operand of addition operator. It is a polynomial in K<X>.
@return: a LIST which represents a polynomial equal to F1+F2.
Example
NC.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NC.Add(F1,F2); [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] -------------------------------
See also
