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Piecewise and multiple values

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89980] Piecewise and multiple values
  • From: Giacomo Ciani <jackspam79 at gmail.com>
  • Date: Wed, 25 Jun 2008 06:31:08 -0400 (EDT)

Hi all,

in brief my problem: I'm using mathematica to create the solutions for
problems that actually came in few different versions (meaning that
the problem in the same, but the initial data change). Suppose I ave
version 1 in which m=3,k=1,..., version 2 in which m=5,k=2,... and so
on... Typically, I use an approach like:

data={m->{3,5,6},k->{1,2,7},...}

Then I write and solve the general symbolic equations, and the replace
the values with the above rule, like:

sol = Solve[...]
sol/.data

obtaining a list of numerical solutions corresponding to the different
set of data contained in the "data" list, like:

{(num sol corresponding to m=3,k=5,...),(num sol corresponding to
m=5,k=2,...)}

This works very well for me, because it allows me to solve the problem
once and check the numerical solution for all the different versions
at a glance.

The problem arises in the case I have to use a Piecewise function. In
this case I define:

      | f   x<z
h = |
      | g   x>z

but when I evaluate

f/.data

I obtain something like:

      | {f1,f2,...}     x<{z1,z2,...}
h = |
      | {g1,g2,...}   x>{z1,z2,...}

that I don't know how to plot or "disentagle", i.e. obtain expressions
like:

        | f1     x<z1
h1 = |
        | g1    x>z1


        | f2     x<z2
h2 = |
        | g2    x>z2

and so on...

Do you have any suggestion? I would prefer to retain my data
replacement scheme, and just understand how to create "disentangled"
piecewise functions...

Thaks

Giacomo


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