Difference between revisions of "ApCoCoA-1:NC.Add"
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| − | Addition of two polynomials in a | + | Addition of two polynomials in a non-commutative polynomial ring. |
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<syntax> | <syntax> | ||
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<see>NC.SetOrdering</see> | <see>NC.SetOrdering</see> | ||
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<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
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<type>non_commutative</type> | <type>non_commutative</type> | ||
</types> | </types> | ||
| − | <key> | + | <key>ncpoly.Add</key> |
<key>NC.Add</key> | <key>NC.Add</key> | ||
<key>Add</key> | <key>Add</key> | ||
<wiki-category>Package_ncpoly</wiki-category> | <wiki-category>Package_ncpoly</wiki-category> | ||
</command> | </command> | ||
Revision as of 14:40, 25 April 2013
NC.Add
Addition of two polynomials in a non-commutative polynomial 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. The default coefficient field is Q. The 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 the 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 : ELIE ------------------------------- 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
