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Re: Testing Mathematica Expressions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106614] Re: Testing Mathematica Expressions?
  • From: Noqsi <jpd at noqsi.com>
  • Date: Mon, 18 Jan 2010 02:36:38 -0500 (EST)
  • References: <hiuusd$92o$1@smc.vnet.net>

On Jan 17, 5:13 am, AES <sieg... at stanford.edu> wrote:

> 5)  Is  ToExpression["exprx"] /. ruleOne  really exactly the same thing
> (or, will it produce exactly the same results) as    exprx /. ruleOne?

That you even ask this question shows that you simply haven't done
your homework. Please study the tutorials listed at:

tutorial/ExpressionsOverview

in the Documentation Center.

Many programming systems (including Mathematica) feature powerful
string pattern and replacement capabilities. The most common approach
is so-called "regular expressions", which after >40 years of
refinement are extremely flexible and powerful for text processing. In
principle, they could be used for computer algebra, but in practice
they are impractical. The amusing http://blog.stevenlevithan.com/archives/algebra-with-regexes
starts out "Regexes suck at math".

In Mathematica, Replace[] is not the same as StringReplace[]. Indeed,
they are very different, and their application areas are almost
disjoint.

Computer algebra is necessarily more formal and mechanical than human
algebra. Wolfram has done a great job of presenting the underlying
structures in a comprehensible way to a human user, but there are
practical limits. And often, as a human user, you need to access that
formal, mechanical level to unambiguously program Mathematica for
particular tasks, so completely hiding it would be a disaster.

The checkered history of generalized functions in Mathematica should
serve as a cautionary example to those who believe that attempting
heuristic decoding of user intentions is a good idea in any but the
shallowest situations. See:

http://forums.wolfram.com/mathgroup/archive/2009/Jun/msg00180.html

for further discussion of this issue.





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