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MathGroup Archive 1998

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Re: Conditions on patterns in Flat functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13394] Re: Conditions on patterns in Flat functions
  • From: "Allan Hayes" <hay at haystack.demon.cc.uk>
  • Date: Thu, 23 Jul 1998 03:32:38 -0400
  • References: <6oup6q$j1o@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Tobias Oed wrote in message <6oup6q$j1o at smc.vnet.net>...
>Hi all, I have a problem with conditions on patterns in flat functins,
>here is an example:
>
>
>In[1]:= CosPlusISin[expr_]:= expr //. {
>                ((a_. Cos[th_] + b_. Sin[th_] /; b === I a ) :> a E^(I
>th)),
>                ((a_. Cos[th_] + b_. Sin[th_] /; b === - I a ) :> a
>E^(-I th))
>        }
>
>In[2]:= 4 Cos[x]+4 I Sin[x]
>
>Out[2]= 4 Cos[x] + 4 I Sin[x]
>
>In[3]:= CosPlusISin[%]
>
>           I x
>Out[3]= 4 E
>
>In[4]:= test=4 Cos[x]+4 I Sin[x] + something
>
>Out[4]= something + 4 Cos[x] + 4 I Sin[x]
>
>In[5]:= CosPlusISin[test]
>
>Out[5]= something + 4 Cos[x] + 4 I Sin[x]
>
>
>The solutions I found:
>
>In[10]:= CosPlusISin1[expr_]:= expr //. {
>                ((a_. Cos[th_] + b_. Sin[th_] +c___ /; b === I a ) :> a
>E^(I th)+c),
>                ((a_. Cos[th_] + b_. Sin[th_] +c___ /; b === - I a ) :>
>a E^(-I th)+c)
>         }
>
>In[11]:= CosPlusISin2[expr_]:= expr //. {
>                ((a_. Cos[th_] + b_. Sin[th_] +c_. /; b === I a ) :> a
>E^(I th)+c),
>                ((a_. Cos[th_] + b_. Sin[th_] +c_. /; b === - I a ) :> a
>E^(-I th)+c)
>         }
>
>In[12]:= CosPlusISin1[test]
>
>            I x
>Out[12]= 4 E    + something
>
>In[13]:= CosPlusISin2[test]
>
>            I x
>Out[13]= 4 E    + something
>
>The questions:
>
>Which solution of the two is better, and why does the original idea not
>work since Plus is Flat ?
>
>Tobias
>

Tobias,
I don't have the answers, but here are two more puzzling variants

In[1]:=
CosPlusISin2[expr_]:= expr //.
{(a_. Cos[th_] + b_. Sin[th_]) :> a E^(I th)/; b === I a ,
 (a_. Cos[th_] + b_. Sin[th_]) :> a E^(-I th) /; b === - I a }

In[2]:=
CosPlusISin2[4 Cos[x]+4 I Sin[x] + something]

Out[2]=
4*E^(I*x) + something

Although:

In[3]:=
ReplaceList[
4 Cos[x]+4 I Sin[x] + something,
{(a_. Cos[th_] + b_. Sin[th_]) :> a E^(I th)/; b === I a ,
 (a_. Cos[th_] + b_. Sin[th_]) :> a E^(-I th) /; b === - I a }]

Out[3]=
{}

------------------------------------------------------------- 
Allan Hayes
Training and Consulting
Leicester UK
http://www.haystack.demon.co.uk
hay at haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44(0)116 271 8642



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