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Establishing rules for Simplify/FullSimplify?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16241] Establishing rules for Simplify/FullSimplify?
  • From: "Kevin Jaffe" <kj0 at mailcity.com>
  • Date: Fri, 5 Mar 1999 00:41:07 -0500
  • Organization: MailCity (http://www.mailcity.lycos.com:80)
  • Sender: owner-wri-mathgroup at wolfram.com

Is there any way to teach Mathematica new manipulation rules for
Simplify or FullSimplify?  For example, I would like Mathematica to
enforce the equality:

Cross[a, b] + Cross[b, a] == 0

(My version, 3.0, does not).

Or, I would like to define a new sqrt function that satisfies the
equality

mySqrt[n^2] == n

Sometimes (though I can't find an example at the moment), I've defined
upvalues of the form

a /: (a < b c) = True;

so that Mathematica will automatically simplify an expression like
If[a < b c, foo, bar], but still it fails to simplify either
If[a < c b, foo, bar], or If[a > b c, foo, bar]; does this mean that
all such inferences must be coded explicitly?

Also, I'm interested in turning off some standard transformation
rules.  For example, I would like Mathematica to leave untouched
expressions such as

x x

i.e., not convert it to x^2.

Is any of this possible?

Thanks for your advice,

KJ



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