# Difference between revisions of "ApCoCoA-1:NCo.Multiply"

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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>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 ( | + | 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>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 multiplication 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 multiplication 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.SetFp(3); | NCo.SetFp(3); | ||

− | NCo.SetX( | + | NCo.SetX("abc"); |

NCo.RingEnv(); | NCo.RingEnv(); | ||

Coefficient ring : Fp = Z/(3) | Coefficient ring : Fp = Z/(3) | ||

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Ordering : LLEX | Ordering : LLEX | ||

------------------------------- | ------------------------------- | ||

− | F1 := [[2, | + | F1 := [[2,"a"],[1,""]]; |

− | F2 := [[2, | + | F2 := [[2,"b"],[1,"ba"]]; |

NCo.Multiply(F1,F2); -- over F3 | NCo.Multiply(F1,F2); -- over F3 | ||

− | [[2, | + | [[2, "aba"], [1, "ab"], [1, "ba"], [2, "b"]] |

------------------------------- | ------------------------------- | ||

NCo.Multiply(F2,F1); | NCo.Multiply(F2,F1); | ||

− | [[2, | + | [[2, "baa"], [2, "ba"], [2, "b"]] |

------------------------------- | ------------------------------- | ||

NCo.Multiply(F1,[]); | NCo.Multiply(F1,[]); | ||

Line 48: | Line 48: | ||

------------------------------- | ------------------------------- | ||

NCo.Multiply(F1,F2); -- over Q | NCo.Multiply(F1,F2); -- over Q | ||

− | [[2, | + | [[2, "aba"], [4, "ab"], [1, "ba"], [2, "b"]] |

------------------------------- | ------------------------------- | ||

NCo.Multiply(F2,F1); | NCo.Multiply(F2,F1); | ||

− | [[2, | + | [[2, "baa"], [5, "ba"], [2, "b"]] |

------------------------------- | ------------------------------- | ||

</example> | </example> |

## Latest revision as of 13:43, 29 October 2020

This article is about a function from ApCoCoA-1. |

## NCo.Multiply

Multiplication of two polynomials in a free monoid ring.

### Syntax

NCo.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.

Please set ring environment *coefficient field* ` K`, *alphabet* (or set of indeterminates) `X` and *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 multiplication 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.SetFp(3); NCo.SetX("abc"); NCo.RingEnv(); Coefficient ring : Fp = Z/(3) Alphabet : abc Ordering : LLEX ------------------------------- F1 := [[2,"a"],[1,""]]; F2 := [[2,"b"],[1,"ba"]]; NCo.Multiply(F1,F2); -- over F3 [[2, "aba"], [1, "ab"], [1, "ba"], [2, "b"]] ------------------------------- NCo.Multiply(F2,F1); [[2, "baa"], [2, "ba"], [2, "b"]] ------------------------------- NCo.Multiply(F1,[]); [ ] ------------------------------- NCo.Multiply([],F1); [ ] ------------------------------- NCo.Multiply([],[]); [ ] ------------------------------- NCo.UnsetFp(); NCo.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : LLEX ------------------------------- NCo.Multiply(F1,F2); -- over Q [[2, "aba"], [4, "ab"], [1, "ba"], [2, "b"]] ------------------------------- NCo.Multiply(F2,F1); [[2, "baa"], [5, "ba"], [2, "b"]] -------------------------------

### See also