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MathGroup Archive 1997

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Re: Help! Sin[n Pi] (n Integer)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8984] Re: [mg8942] Help! Sin[n Pi] (n Integer)
  • From: Mark Evans <evans at gte.net>
  • Date: Tue, 7 Oct 1997 03:35:30 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Greg,

Yes, it is exactly the same type of problem.  In Mathematica, there is
one and only one type of undefined symbol, and that is the complex
number type.  An undefined symbol cannot be declared real, matrix,
integer, or anything else.  This is a *big* problem with Mathematica.

The closest approach to a type declaration is ComplexExpand.  There is
no equivalent IntegerExpand.  You might also look at upvalues, but I
have the feeling they are somewhat unreliable.  In your case you might
try something like IntegerQ[n] ^= True (but check with the book).  I
attempted this with your expressions and they did not simplify.  Of
course, you might want to try putting your equations in exponential
form.

My sense is that sooner or later, the company will have to undertake a
fundamental redesign of much of the software in order to allow what we
would call in other languages "types."  For example, try to write out
and solve any matrix equations of your choice where the matrices are
identified by symbols.  It can't be done.  You have to spell out your
matrix element-by-element, which means you can't use Mathematica to
perform algebra on theoretical matrix systems with arbitrary
dimensions.  The Sqrt[a] problem is another classic that keeps
reappearing on the newsgroup.

So the best course of action is to pay close attention to your equations
and simplify them by hand, or get another program that can do the job.

Best regards,

Mark Evans


> 
> Does anyone know if there's a way to specify that a variable is an
> integer?
> 
> I'm taking a conduction class (with *lots* of separation of variables
> problems) and the quantities Sin[n Pi] or Cos[(2n+1)/2 Pi] come
> up constantly.  I can dispose of them with replacement rules, but I was
> wondering if there's a way to "tag" n as an integer so that Mma will
> automatically kill the Sin and Cos terms later in the derivations.
> 
> It seems like the "specify that a is real so that Sqrt[a^2] automatically
> reduces to a without using PowerExpand" problem from way back and I don't
> remember the solution (if there was one)
> 
> Thanks!
> 
> Greg Anderson
> dwarf at wam.umd.edu




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