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Re: Trig Simplifications
*To*: mathgroup at smc.vnet.net
*Subject*: [mg3707] Re: Trig Simplifications
*From*: ianc (Ian Collier)
*Date*: Wed, 10 Apr 1996 02:11:22 -0400
*Organization*: Wolfram Research, Inc.
*Sender*: owner-wri-mathgroup at wolfram.com
In article <4ka54g$sai at dragonfly.wolfram.com>, Alexander Casti
<arc at carmen.phys.columbia.edu> wrote:
> Basically my question is how to get mathematica to write
>
> Exp[I x] in place of Cos[x] + I Sin[x]
>
> Suppose I have the expression
>
> In[1]: f[x_]= Cos[x] + I Sin[x] - Cos[2 X] + I Sin[2 X]
>
> I would like mathematica to simplify this into
>
> f[x_]= Exp[I X] - Exp[2 I X]
>
> I tried the substitution command
>
> In[2]: % ./ Cos[X]+I Sin[X]-> Exp[I X] and it returned
> Out[2]: E^{I X} - Cos[2 X] + I Sin[2 X]
>
> So, it seems as though this simple minded approach is not
> enough for mathematica to understand the substitution rules
> for powers of complex exponentials other than the one I
> explicitly gave.
> In addition, commands like Simplify[Blah] do not seem to do
> the trick either. I believe I have the trigonometry package
> loaded in (via the command Needs["Algebra`Trigonometry`"]).
> What must I do ?
>
> Thanks for your time.
>
> Alex
You can do this using the function TrigToComplex which
is defined in Algebra`Trigonometry`, one of the standard
packages distributed with Mathematica. Here is an example:
In[1]:=
Needs[ "Algebra`Trigonometry`" ]
In[2]:=
expr = Cos[x] + I Sin[x]
Out[2]=
Cos[x] + I Sin[x]
In[3]:=
TrigToComplex[ expr ]
Out[3]=
-I x I x -I x I x
-E + E E + E
------------- + ------------
2 2
In[4]:=
Simplify[%]
Out[4]=
I x
E
This is documented in more detail on pages 15-17 of "The
Guide to Standard Mathematica Packages" Technical Report.
I hope this helps.
--Ian
-----------------------------------------------------------
Ian Collier
Wolfram Research, Inc.
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tel:(217) 398-0700 fax:(217) 398-0747 ianc at wolfram.com
Wolfram Research Home Page: http://www.wolfram.com/
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