pattern matching question

• To: mathgroup at smc.vnet.net
• Subject: [mg61827] pattern matching question
• From: Robert Schoefbeck <schoefbeck at hep.itp.tuwien.ac.at>
• Date: Mon, 31 Oct 2005 06:10:04 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```hello everybody,

i'm having the following problem: from time to times within a long
calculation i have to perform a time consuming operation which takes a
structure
{{n1,m1},{n2,m2},{n3,m3},...}
as an argument and returns a lengthy result. however, these list
structures occur repeatedly, in fact, there are only very few (for a
given calculation) and they occur very often. thus, i wrote a routine
which gets all instances of these list and produces the result as a list
of rules to be used within the actual calculation.

my problem is the following:
say, the list
{{n1,m1},{n1,m2},{n1,m3}}
gives
1/(m1-m2) + something
and
{{n1,m1},{n1,m1},{n1,m3}}
gives
1 + something

if the list of rules is now applied within the calculation the FIRST
rule in my example is used also on the SECOND case with m1=m2 producing
a 1/0

Sorting the list of rules would of course do the trick,
but there is no canonical way, because the generic structure of such a
list is quite involved: any multiples of the m-parameters might occor at
any place.

What i think i need is something like

{{n1,m1},{n1,m2},{n1,m3}}/;(m1=!=m2)-> 1/(m1+m2)+something
{{n1,m1},{n1,m1},{n1,m3}}->1+something

which is not mathematica syntax i believe. To put it differently: I need
a pattern {{_,m1_},{_,m2_},{_,m3_}} to be matched only if the parameters
are different.

is there any elegant solution to this?

robert schoefbeck

```

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