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

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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. | 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 non-commutative polynomials, which are left and right operands of subtraction 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 [[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>@param <em>F1, F2:</em> two non-commutative polynomials, which are left and right operands of subtraction 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> |

## Revision as of 17:52, 25 April 2013

## NC.Sub

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

### Syntax

NC.Sub(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 subtraction 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.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[0,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NC.Subtract(F1,F2); -- over Q (default field) [[-1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : ELIM ------------------------------- NC.SetFp(); -- set default Fp = F2 NC.RingEnv(); Coefficient ring : Fp = Z/(2) Alphabet : abc Ordering : ELIM ------------------------------- NC.Subtract(F1,F2); -- over F2 [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.Subtract(F1,F1); [ ] -------------------------------

### See also