factorials and binomials simplification - nusum less verbose

matchdeclare([a,b],true);

 

defrule(h,binomial(a,b),(a+b)!/a!/b!);

 

apply1(., h);

 

minfactorial(%);

 

will simplify the example you give, but might not always be what you want,
if you want to retain binomial coefs sometimes.

 

The message you see is from the solver for linear equations. I don't know if
there is some way to neatly turn off the messages, but you can definitely
look at the code and disable the printout.

 

RJF

 

  _____  

From: maxima-admin at math.utexas.edu [mailto:maxima-admin at math.utexas.edu] On
Behalf Of giovanni gherdovich
Sent: Tuesday, July 11, 2006 9:07 AM
To: maxima at math.utexas.edu
Subject: factorials and binomials simplification - nusum less
verbose

 

Hallo.

I would like to simplify expression involving binomial coefficients and
factorials. 

binomial(n+1,k) / binomial(n,k)      ------->       (n+1) / (n+1-k)
(n+1)! / n!        -------->        n+1

How can I tell the Maxima Simplifier to do that?

I'm using Maxima within the theorem prover Hol Light, through an interface
written by John Harrison.
There is a Maxima command that is particularly useful for me, nusum, that
makes hypergeometric sequences telescopic (if it's possible).
In order to parse its output from inside Hol, I need to make this command
less verbose. Do you know how can I do?

Example
(%i1) display2d:false;
(%o1) false
(%i2) a(k):=1/2^(n+1) * binomial(n,k) * (2*k-n-1) / (n+1-k);
(%o2) a(k):=1/2^(n+1)*binomial(n,k)*(2*k-n-1)/(n+1-k)
(%i3) nusum(a(k), k, 0, k);
Dependent equations eliminated:  (1)
(%o3) -(k+1)*binomial(n,k+1)/(2*(n-k)*2^n)

I'd like to avoid the string "Dependent equations eliminated:  (1)".

Thank you.

Giovanni Gherdovich

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