# ApCoCoA-1:NCo.SetRelations

## NCo.SetRelations

Set relations for a finitely presented monoid ring.

### Syntax

```NCo.SetRelations(R:LIST)
```

### Description

Before calling the function, please set ring environment alphabet (or set of indeterminates) X through the functions NCo.SetX. For more information, please check the relevant functions.

• @param R: a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in <X>. Each word is represented as a STRING. For example, the word xy^2x is represented as "xyyx", and the identity is represented as the empty string "". Thus, the relation (yx, xy) is represented as ["yx", "xy"], and the set of relations {(yx, xy),(zx,xz),(zy,yz)} is represented as [["yx", "xy"],["zx", "xz"],["zy", "yz"]].

#### Example

```NCo.RingEnv();
Coefficient ring : Q
Ordering : LLEX
-------------------------------
NCo.SetX("abc");
R:=[["ba","ab"], ["ca","ac"], ["cb","bc"]]; --ba=ab, ca=ac, cb=bc
NCo.SetRelations(R);
NCo.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : LLEX
Relations : [["ba", "ab"], ["ca", "ac"], ["cb", "bc"]] -- relations generated by {ba=ab, ca=ac, cb=bc}
-------------------------------
```