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Re: Displaying Equations Symbolically and Numerically

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  • Subject: [mg114757] Re: Displaying Equations Symbolically and Numerically
  • From: David Bailey <dave at>
  • Date: Thu, 16 Dec 2010 05:47:49 -0500 (EST)
  • References: <ieadkv$r9h$>

On 15/12/10 12:51, Gregory Lypny wrote:
> Hello everyone,
> I would like to be able to display equations for my students in symbolic
> form on the left side and with the numbers plugged in on the right side
> but am not quite sure how to do it programmatically.  Suppose my
> equation in "symbolic" form is
> 	sqrt(x^(a+b)) + c ln(d/e)
> I know I can make it look like real math by having it displayed as
> TraditionalForm.  However, I also want to display the solution with
> particular values for the variable x and the parameters a, b, c, d, and
> e slotted in, something like
> 	sqrt(x^(a+b)) + c ln(d/e) = sqrt(9^(2+1)) + 4 ln(32/8) = answer
> to recognize that some students may be a little rusty at simplifying on
> the fly.   Wrapping the whole package in Manipulate would put the icing
> on the cake.
> Any tips on how apply the appropriate styles would be most appreciated.
> Regards,
> Gregory
Your question is a little vague (I don't see where Manipulate might come 
in), but presumably it is the middle expression that you have difficulty 
with - because it is partially evaluated. The easiest way to obtain it, 
is to perform the substitutions on the expression wrapped in HoldForm.

HoldForm[sqrt (x^(a + b)) + c ln (d/e)] /. {9 -> 9, a -> 2, b -> 1,
   c -> 4, d -> 32, e -> 8}

You can then remove the HoldForm, with for example expr/.HoldForm->Identity

The general problem of making Mathematica follow the steps that a person 
might have used in a hand calculation, is much more difficult, however. 
Mathematica often uses quite exotic methods to solve (for example) 
integrals, and anyway these intermediate steps are not displayed.

David Bailey

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