# CoCoA:EvalBinExp

## EvalBinExp

binomial expansion functions

### Description

The function <ttref>BinExp</ttref> computes the K-binomial

expansion of N, i.e., the unique expression

<verbatim>

``` N = Bin(N(K),K) + Bin(N(K-1),K-1) + ... + Bin(N(I),I)
```

</verbatim> where <formula>N(K) > ... > N(I) >= 1</formula>, for some I.

This function computes the sum of the binomial coefficients

appearing in the K-binomial expansion of N after replacing each

summand Bin(N(J),J) by Bin(N(J)+Up,J+Down). It is useful in generalizations of Macaulay's theorem characterizing Hilbert functions.

It is the same as <ttref>BinExp</ttref> with 4 arguments except it

takes a precomputed binomial expansion as an argument rather than N and K.

#### Example

```  BE := BinExp(13,4);
BE;
Bin(5,4) + Bin(4,3) + Bin(3,2) + Bin(1,1)
-------------------------------
EvalBinExp(BE,1,1);
16
-------------------------------
BinExp(13,4,1,1);
16
-------------------------------
```

### Syntax

```EvalBinExp(B:TAGGED(<quotes>\$binrepr.BinExp</quotes>),Up:INT,Down:INT):INT

where N and K are positive integers, and Up and Down are integers.
```

```   <type>integer</type>
```