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Re: Naming pieces of patterns
*To*: mathgroup at smc.vnet.net
*Subject*: [mg29826] Re: Naming pieces of patterns
*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
*Date*: Fri, 13 Jul 2001 04:19:10 -0400 (EDT)
*Organization*: Universitaet Leipzig
*References*: <9ijhj3$rhj$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
pattern matching work with the internal representation
of the equation. In such cases it is better to
replace a single symbol.
Cyril Fischer wrote:
>
> How can I as simply as possible use "substitutions"
> 1.
> -(I/(2 a)) /. I/(2 a) -> A
It cant' work because -I ic Complex[0,-1] and I is Complex[0,1]
and the pattern can't match !
It is better to "solve"
I/(2a)==A for a and replace
-(I/(2 a)) /. a -> I/(2A)
> 2.
> {(a + b), -(a + b)}/. a + b -> e
> gives
> {e, -a - b}
The same reason because
In[]:={(a + b), -(a + b)} // FullForm
Out[]= List[Plus[a, b], Plus[Times[-1, a], Times[-1, b]]]
and -a-b match not a+b but
if you solve a+b==e for a the replacment
{(a + b), -(a + b)} /. a -> e - b
work as expected.
> instead of {e,-e}
>
> 3.
> {-Sqrt[a + b], 1/Sqrt[a + b]} /. Sqrt[a + b] -> e
> gives
> {-e,1/Sqrt[a + b]}
Can't work because Sqrt[a] is internal Power[a,Rational[1,2]]
and 1/Sqrt[a] is internal Power[a,Rational[-1,2]] but you give
only the pattern for Rational[1,2]. But
{-Sqrt[a + b], 1/Sqrt[a + b]} /. (a + b)^n_ :> e^(2n)
work as expected.
>
> 4.
> {I, 2 I, -I} /. I -> J
> gives
> {J, 2 \[ImaginaryI], -\[ImaginaryI]}
Here:
{I, 2 I, -I} /. Complex[a_, b_] :> a + J*b
will work.
>
> I know _why_ these cases do not work, but I would like to know, if there
> is a possibilty to use a common pattern rule to substitute all
> occurences of an expression.
a) use the most general pattern, i.e., a^n_ for Sqrt[a]
b) use Solve[] to replace only a single symbol of your
expression and let Mathematicas algebraic simplifications do
the rest.
Regards
Jens
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