# ApCoCoA-1:NCo.BSubtract

## NCo.BSubtract

Subtraction of two polynomials in a free monoid ring over the binary field F_{2}={0,1}.

### Syntax

```NCo.BSubtract(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 alphabet (or set of indeterminates) X and word ordering via the functions NCo.SetX and NCo.SetOrdering, respectively, before calling this function. The default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

• @param F1, F2: two polynomials in the free monoid ring F_{2}<X>, which are left and right operands of subtraction, respectively. Each polynomial is represented as a LIST of words (or terms). Each word is represented as a STRING. For example, xy^2x is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial f=xy-y+1 is represented as F:=["xy", "y", ""]. The zero polynomial 0 is represented as the empty LIST [].

• @return: a LIST which represents the polynomial equal to F1-F2. Note that we have F1-F2=F2+F2 over F_{2}.

#### Example

```NCo.SetX("xX");
NCo.SetOrdering("LLEX");
F1:=["xX",""];
F2:=["Xx",""];
NCo.BSubtract(F1,F2);
["xX", "Xx"]
-------------------------------
NCo.BSubtract(F1,F1);
[ ]
-------------------------------
NCo.BSubtract([],F1);
["xX", ""]
-------------------------------
```