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Re: "Reduce" wierdness (or too slow?)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89095] Re: "Reduce" wierdness (or too slow?)
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 25 May 2008 06:26:50 -0400 (EDT)
  • References: <200805250602.CAA15503@smc.vnet.net>

The problem is that using Reduce[...,Reals] in this context amounts to  
adding lots of inequalities. To see this, just take a couple of the  
equations:

Reduce[{t7*z1 + t3*z2 + z3 + z4 == H + (t3^2 + t7^2)/k,
   t7*z1 + z3 + z4 == 2*H + (t7^2)/k}, {H, t1, t2, t3, t4, t5, t6, t7,  
v2, w1,
   w2, z1, z2, z3, z4}, Reals, Backsubstitution -> True]

You will see all the inequalites that had to be added by Reduce to  
make all expressions that appear in Reduce real. This is actually  
harder rather thans simpler than your original formulation.

Andrzej Kozlowski


On 25 May 2008, at 15:02, TuesdayShopping wrote:

> Re: Reduce" wierdness (or too slow?).
> Thanks for the input from Andrzej Kozlowski, Daniel Lichtblau, Adam  
> Strzebonski and others. OK; No inequations. Below is problem similar  
> (not same) to the earlier one, that does not have any inequations  
> but still Reduce will not solve it in 600 seconds. Even FindInstance  
> will not find a (even partial) solution in 600 seconds. I should  
> have got the solution for H, z2, w1, w2, t1, t2, t3, v2 as below. My  
> goal is that I would like to solve a class of problems (like the one  
> below) for as many variables as I can.
>
> Problem:
> Reduce[{1000 + t2 == t3, 1200 + w1 == w2, 125 + t1 == t2,
> 125 + t5 == t6, k*t3 == 2*(v2 + z2),
> t7*z1 + t2*z2 + z3 + z4 == H + (t2^2)/k + (t7^2)/k + w1,
> t7*z1 + t3*z2 + z3 + z4 == H + (t3^2 + t7^2)/k,
> t7*z1 + z3 + z4 == 2*H + (t7^2)/k,
> w1 + t6*z1 + z3 == (t6^2)/k + w1 + w2,
> w1 == w2 + ((t1 - t2)*(t1 + t2 - k*z2))/k,
> w2 + t5*z1 + z3 == (t5^2)/k + w1 + w2,
> w2 == (-t1^2)/k + t1*z2 + z4, z1 == 2*t4/k + v2, z2 == 0}, {H, t1,  
> t2, t3, t4, t5, t6, t7, v2, w1,
> w2, z1, z2, z3, z4}, Reals, Backsubstitution -> True]
>
> (For trying with FindInstance, add variable "k" to list of  
> variables, and of course, remove "Backsubstitution -> True" option)
>
> Solutions that must have been found:
> t1 = ((48 * k - 625)/10),
> t2 = ((48 * k + 625)/10),
> t3 = ((48 * k + 10625)/10),
> v2 = ((48 * k^2 + 10625 * k)/20),
> w1 = ((9600 * k + 1125000)/k),
> w2 = ((10800 * k + 1125000)/k),
> z2 = 0,
> H= z4 = ((2304 * k^2 + 1020000 * k + 112890625)/(100 * k))
>



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