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MathGroup Archive 2006

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RE: Simple question from a biologist

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67180] RE: [mg67139] Simple question from a biologist
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sun, 11 Jun 2006 02:18:37 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Although it hasn't gotten you into any trouble here, in general it is better
to use symbol names that start with small case letters because then you can
be sure they won't conflict with Mathematica defined symbols. So rewriting
and taking the first (and only) solution...

sol = Solve[{{{-x, 0, z}, {x, -y, 0}, {0, y, -z}} .
       {a, b, c} == 0, a + b + c == 1}, {a, b, c}][[1]]

{a -> (y*z)/(x*y + x*z + y*z), b -> (x*z)/(x*y + x*z + y*z),
  c -> (x*y)/(x*y + x*z + y*z)}

Then we could, for example, calculate all your rates in a list and check
that they are equal. We just write the expression for each rate and then
substitute the solution. You don't have to Solve again.

{a x, b y, c z} /. sol
Equal @@ %

{(x*y*z)/(x*y + x*z + y*z), (x*y*z)/(x*y + x*z + y*z),
  (x*y*z)/(x*y + x*z + y*z)}
True

Or, perhaps more what you want, your could define the rate function as
follows...

rate[x_, y_, z_] = a x /. sol
(x*y*z)/(x*y + x*z + y*z)

Then you could, for example, plot the rate as a function of x and y for
fixed values of z.

Plot3D[rate[x, y, 1], {x, 0.00001, 2}, {y, 0.00001, 2}];

A couple of good books are 'The Beginner's Guide to Mathematica' by Jerry
Glynn & Theodore Gray and 'Mathematica Navigator: Graphics and Methods of
Applied Mathematics' by Heikki Ruskeepaa. But it is very worthwhile going
through Part I of The Mathematica Book. And using Help as much as possible.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/




From: tnad [mailto:terry_najdi at hotmail.com]
To: mathgroup at smc.vnet.net


I'm a bit new to this so please bear with me. I solved this eqation:

Sol = Solve[{{{-x, 0, z}, {x, -y, 0}, {0, y, -z}}.{A, B, C} == 0, A + B + C
== 1}, {A, B, C}]

and got the ouputs of A, B and C interms of x,y, and z each.

Now I want to express a term called "rate" where rate = Ax = By = Cz in
terms of x, y and Z only.

So I tried to do this:
Solve[rate == Ax , rate] /. Sol

but I cannot get the rate in terms of x,y and z.
Is there a better way to do this? Also if someone knows of a better
tuttorial (better than the built-in tuttorial) for mathematica, please let
me know.



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