# Difference between revisions of "ApCoCoA-1:NC.Mul"

(New page: <command> <title>NC.Multiply</title> <short_description> Multiplication of two polynomials in a non-commutative polynomial ring. </short_description> <syntax> NC.Mul(F1:LIST, F2:LIST):LIST...) |
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<command> | <command> | ||

− | <title>NC. | + | <title>NC.Mul</title> |

<short_description> | <short_description> | ||

Multiplication of two polynomials in a non-commutative polynomial ring. | Multiplication of two polynomials in a non-commutative polynomial ring. | ||

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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 | + | Please set non-commutative polynomial ring (via the command <ref>Use</ref>) and word ordering (via the function <ref>NC.SetOrdering</ref>) before calling this function. The default word ordering is the length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant commands and functions. |

<itemize> | <itemize> | ||

− | <item>@param <em>F1, F2:</em> two polynomials | + | <item>@param <em>F1, F2:</em> two non-commutative polynomials, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. 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> | ||

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</description> | </description> | ||

<seealso> | <seealso> | ||

+ | <see>Use</see> | ||

+ | <see>NC.SetOrdering</see> | ||

<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||

</seealso> | </seealso> |

## Revision as of 17:50, 25 April 2013

## NC.Mul

Multiplication of two polynomials in a non-commutative polynomial ring.

### Syntax

NC.Mul(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 non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.

@param

*F1, F2:*two non-commutative polynomials, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial`f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5`is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial`0`is represented as the empty LIST [].@return: a LIST which represents the polynomial equal to

`F1*F2`.

#### Example

NC.SetFp(3); NC.SetX(<quotes>abc</quotes>); NC.RingEnv(); Coefficient ring : Fp = Z/(3) Alphabet : abc Ordering : LLEX ------------------------------- F1 := [[2,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[2,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NC.Multiply(F1,F2); -- over F3 [[2, <quotes>aba</quotes>], [1, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NC.Multiply(F2,F1); [[2, <quotes>baa</quotes>], [2, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NC.Multiply(F1,[]); [ ] ------------------------------- NC.Multiply([],F1); [ ] ------------------------------- NC.Multiply([],[]); [ ] ------------------------------- NC.UnsetFp(); NC.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : LLEX ------------------------------- NC.Multiply(F1,F2); -- over Q [[2, <quotes>aba</quotes>], [4, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NC.Multiply(F2,F1); [[2, <quotes>baa</quotes>], [5, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] -------------------------------

### See also