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 EvalBinExp

binomial expansion functions
 Syntax
 ``` EvalBinExp(B:TAGGED("\$binrepr.BinExp"), Up:INT, Down:INT):INT where N and K are positive integers, and Up and Down are integers. ```

 Description
The function BinExp computes the K-binomial expansion of N, i.e., the unique expression
```  N = Bin(N(K),K) + Bin(N(K-1),K-1) + ... + Bin(N(I),I)
```
where N(K) > ... > N(I) >= 1, 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 BinExp 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 ------------------------------- ```