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Re: smart change of variables?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87698] Re: smart change of variables?
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Wed, 16 Apr 2008 04:58:17 -0400 (EDT)
  • Organization: University of Bergen
  • References: <fu21bk$rb6$1@smc.vnet.net>

Barrow wrote:
> Dear all,
> 
> I have a arithmetic problem.
> I have an expression expr = (p1 + 2*p2)*(k1 + 2*k2)
> where p1 + p2 = k1 + k2
> I wanna make the following change of variables,
> s = (p1 + p2)^2
> t = (p1 - k1)^2
> u = (p1 - k2)^2
> 
> Is it possible to tell Mathematica to express expr
> in terms of s, t, and u automatically?

Use Eliminate to get rid of variables:

In[1]:= Eliminate[{expr == (p1 + 2*p2)*(k1 + 2*k2),
   p1 + p2 == k1 + k2, s == (p1 + p2)^2, t == (p1 - k1)^2,
   u == (p1 - k2)^2}, {p1, k1, p2, k2}]

Out[1]= -81 s^2 + 18 s t - t^2 + 18 s u + 2 t u - u^2 ==
  16 expr^2 + expr (-72 s + 8 t - 8 u)

In[2]:= Reduce[%, expr]

Out[2]= expr == 1/4 (9 s - t - 6 Sqrt[s] Sqrt[u] + u) ||
  expr == 1/4 (9 s - t + 6 Sqrt[s] Sqrt[u] + u)


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