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MathGroup Archive 1989

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Need help Solv[]ing equations

  • To: mathgroup
  • Subject: Need help Solv[]ing equations
  • From: sdoyle at fed.frb.gov
  • Date: Fri, 24 Mar 89 15:48:08 CST

Hi:
	I am trying to solve a system of four equations using Mathematica,
and Solve[] (and/or Reduce[]) are running out of memory. It is possible
that the equations have no solution. I'm using SunMathematica (sun3.68881) 
1.1 on a Sun 3/60.  I'd like to understand why Mathematica has difficulty
with this problem (it probably isn't Mathematica's fault.)  

	This set of equations is from two economists that don't have
access to Mathematica. They would like a solution, but I'm more interested
in how the algorithms work. Any hints/solutions/truth&beauty appreciated.

Part 1:How to create the out-of-memory error:

	I've attached the file SolveProblem.m below. After you
read the file in (e.g. <<SolveProblem.m) try either of the following:
	
This takes about half an hour
	> In[2]:= Solve[eqns,{w,x,y,z}]
	> Out of memory.

Also about half an hour (different session)
	> In[2]:= Reduce[Share[eqns], {w,x,y,z}]
	> Out of memory.

Share seems to simply to delay out-of-memory message. As an aside, Mathematica
doesn't seem to respond to Control-C after either Solve[] or Reduce[]
has been running a while (I did wait a few minutes to respond before 
killing the process). 


(******************* File SolveProblem.m  ************************)
(* 
	Small model that Solve[] has problems solving.
	
	Solve[eqns, {w,x,y,z}]
*)

eqns = {
	w x y z == 1/b^2,

	w x (y + z) + y z (w + x) ==
		- (c a + f g)/(a q  b^2 (f c + p d)),
	
	w (x + z)  +  y (w + x)   +   z (x + y)  ==
		(1 + 2 b a q (f c + p d))/ (a q b^2 (f c + p d)),

	w + x + y + z == -(f q + c a)/(b q a (f c + p d))
	}



(****************** End of file SolveProblem.m ************************)

Part 2: Various questions:

1. Why is this problem hard? 

2. Solve[] and Reduce[] are (to me) black boxes. If this were *my* problem
   I'd start by reducing the dimensions to three, and create some plots. Can
   others suggest a better search procedure? 

3. Are there ways of posing problems to Solve[] and Reduce[] that are 
   easier for them to solve? Since I don't know what the algorithms are
   doing internally, I don't know if the failure to find a solution is
   because
	a) The problem has no solution
	b) The algorithm doesn't deal with this class of problems, so
   	   I'm abusing the software
	c) I haven't RTFM closely enough


Thanks! 


 Sean Doyle    
 Board of Governors of the Federal Reserve System 
 20 and Constitution, NW
 Mail Stop 76
 Washington, DC 20551
 (202) 452-2352            
 uucp: uunet!fed!m1swd00 , internet: sdoyle at fed.frb.gov




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