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MathGroup Archive 1996

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Q: System of 2 Eqs w/ 2 Unknowns (Higher Degree).

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4148] Q: System of 2 Eqs w/ 2 Unknowns (Higher Degree).
  • From: domokos at chaph.usc.edu (Marius)
  • Date: Fri, 7 Jun 1996 02:08:54 -0400
  • Organization: University of Southern California, Los Angeles, CA
  • Sender: owner-wri-mathgroup at wolfram.com

Hello!

I don't want anybody to waste time with this, but I wonder what your
opinions are. I have a system of 2 equations with 2 unknowns. The
2 unknowns are A and B. The rest of the variables are all known.

In the initial form, the equations are extremely complicated, with
all variables consisting of long expressions. For example, T contains
a long sum of constants and trigonometric functions, all of them
given.

After substitutions, the equations can be simplified to the ones bellow:

Eq1 := K^2(1-A^2 B^2) - K^2 T^2 - d^2(1-f A)^2 T^2 +
	2 K d A B (1-f A) T^2;

Eq2 := S^2 - A^2 B^2 S^2 - A^2 T^2 + A^2 B^2 T^2 -
	T^2 S^2 + A^2 T^2 S^2;

If I try to solve the original system with the long equations,
the kernel eventually runs out of memory. This happens after
about 10 hours. I am working on a PowerMac 7500, with 16M RAM,
doubled to 32M using RAMDoubler. The kernel memory meter shows
how the memory is progressively filled up, and as it reaches
the upper edge, the kernel indeed generates the "out of memory"
message. The kernel is allocated about 23M RAM.

Working with the simplified equations, though, confuses me.

If I try

Solve[{Eq1 == 0, Eq2 ==0}, {A, B}]

the computer starts working normally. The memory meter
of the kernel starts to fill up as expected, BUT:

After about 15 minutes, as the meter shows less than 20%
of the kernel memory being used, the "out of memory" message
unexpectedly occurs. The meter shows more than 80% of the
memory available, but... everything dies.

It has never happened to me to have the kernel quit this
way, when the meter disagrees with the warning. Also, if
the long equations take over 10 hours to fill up the memory,
I don't think that the short versions do that in 15 minutes.

I am using system 7.5.2 (not updated to 7.5.3), with no Cache.

I would really appreciate your opinions.

Thank you.

Marius Domokos








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