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Transformation rules for Floor/Ceiling

  • To: mathgroup at
  • Subject: [mg16953] Transformation rules for Floor/Ceiling
  • From: maharri at
  • Date: Thu, 8 Apr 1999 02:32:48 -0400
  • Organization: Deja News - The Leader in Internet Discussion
  • Sender: owner-wri-mathgroup at

I am trying to come up with a set of transformation rules (in Mathematica) to help
simplify formulas involving Floor and Ceiling. There are a number of
identities for these (e.g. Ceiling[a/b] = Floor[a+b-1/b] if b is an integer).
Since anykind of programming is difficult from scratch, I'd like to see some
examples to see if I'm going about it in the right manner.

1) I've done a web search for something like this and I can't find anything of
the sort. Have you ever seen something like this (and if so, do you have
pointers as to how to do it)?

2) The Mathematica docs give some ideas (when to use :> rather than ->, checking
FullForm to make sure you're matching the appropriate patterns). But I'd
really like to see a large example, like for instance the actual
transformation rules that Mathematica uses for polynomials or trig (i.e. the internal
rules it uses for Simplify, FullSimplify, Reduce, TrigReduce, etc.). Any
ideas? Pointers?

Mitch Harris (UIUC/CS)

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