# ApCoCoA-1:SB.TermRepr

This article is about a function from ApCoCoA-1. If you are looking for the ApCoCoA-2 version of it, see Package sagbi/SB.FindLTRepr. |

## SB.TermRepr

Computes a representation of a term in other terms if it exists.

### Syntax

SB.TermRepr(Term:POLY,TermList:LIST of POLY):LIST of INT SB.TermRepr(Term:POLY,TermList:LIST of POLY,ReprType:INT):LIST of INT

### Description

This functions tries to compute a term representation of the given term `Term` in terms of the list `TermList`. If it is not possible to get such a representation NULL will be returned. If a representation exists a list of integers will be returned which gives the exponents of the power product of the term in the other terms, e.g. for the term `Term=x^2y` and the list of terms `TermList=[x,y]` the function will return `[2,1]` as the representation.

With the optional parameter `ReprType` it is possible to choose between different ways of getting a possible representation.

@param

*Term*A term in the current ring.@param

*TermList*A list of terms in the current ring.@return A list of integers, which gives the representation, or NULL.

The following parameter is optional:

@param

*ReprType*Either 0,1 or 2. With this parameter it is possible to choose between different ways of getting the representation: By`ReprType=0`a toric ideal is used to compute the representation. This is also the default value. By`ReprType=1`algebra homomorphisms are used, by`ReprType=2`a system of diophantine equations is used to compute the representation.

#### Example

Use R::=QQ[x,y]; SB.TermRepr(x^2y^2,[x,y]); SB.TermRepr(x^2y^2,[xy^2,x,y]); ------------------------------------------------------- -- output: [2, 2] ------------------------------- [1, 1, 0] ------------------------------- -- Done. -------------------------------

#### Example

Use R::=QQ[x,y,z]; L:=[x^2y^4z^8,xy^3,z^5]; SB.TermRepr(xy^4z,L); -- for xy^4z no representation is existing T:=L[1]^3L[3]^2; -- T = (x^2y^4z^8)^3 * (xy^3)^0 * (z^5)^2 T; SB.TermRepr(T,L); ------------------------------------------------------- -- output: NULL ------------------------------- x^6y^12z^34 ------------------------------- [3, 0, 2] ------------------------------- -- Done. -------------------------------