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NC.Multiply

Multiplication of two polynomials over a free associative K-algebra.
Syntax
          
NC.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.

Before calling the function, please set ring environment coefficient field K, alphabet X and ordering through the functions NC.SetFp(Prime) (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.

Example
NC.SetFp(3);
NC.SetX("abc")
NC.RingEnv();
Coefficient ring : Fp = Z/(3)
Alphabet : abc
Ordering : LLEX

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F1 := [[2,"a"],[1,""]];
F2 := [[2,"b"],[1,"ba"]];
NC.Multiply(F1,F2); -- over F3
[[2, "aba"], [1, "ab"], [1, "ba"], [2, "b"]]
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NC.Multiply(F2,F1);
[[2, "baa"], [2, "ba"], [2, "b"]]
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NC.Multiply(F1,[]);
[ ]
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NC.Multiply([],F1);
[ ]
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NC.Multiply([],[]);
[ ]
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NC.UnsetFp();
NC.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : LLEX

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NC.Multiply(F1,F2); -- over Q
[[2, "aba"], [4, "ab"], [1, "ba"], [2, "b"]]
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NC.Multiply(F2,F1);
[[2, "baa"], [5, "ba"], [2, "b"]]
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See Also