Hi there.
I'm kind of new to Maple and i'm trying to solve a Linear Algebra problem for my class of Linear Algebra of the course of Physics. Also, my first language is portuguese so forgive for my not-so-perfect english.
I have a (solved) linear system of 7 equations and 12 variables (A, B, C, D, E, F, G, H, I, J, K, L) that is the following:
- A = 33 - K - L
- B = 1 + F - J
- C = -15 - F + J + K + L
- D = 15 + H - K
- E = 16 - F - H + J + K
- G = 34 - H - J - L
- I = 18 - J - K
Note: I'm using letters (A, B, ..., L) instead of X_{1}, X_{2}, ..., X_{12} because it's easier to write it like this here and because I don't know if the X_{n} notation is allowed on Maple (i don't think so).
So, the system is possible but undetermined (with 5 degrees of freedom), being F, H, J, K and L the free variables.
Until here, everything's fine. The problem arises when the professor asks us for every solution of the system that satisfies the condition that all the variables (form A to L) are positive integers (A, B, C, D, E, F, G, H, I, J, K, L ϵ IN → natural numbers).
From my understanding, that gives rise to a system of linear inequalities with 12 variables and the following inequalities:
- A = 33 - K - L > 0
- B = 1 + F - J > 0
- C = -15 - F + J + K + L > 0
- D = 15 + H - K > 0
- E = 16 - F - H + J + K > 0
- G = 34 - H - J - L > 0
- I = 18 - J - K > 0
- F > 0
- H > 0
- J > 0
- K > 0
- L > 0 (and A,B,C,D,E,F,G,H,I,J,K,L ϵ IN)
After some research, i found that a possible way to solve this type of system of linear inequalities is trough a method of elimination (analog to Gauss-Jordan's elimination method for systems of linear equations) named Fourier-Motzkin. But it's hardwork and i wanted to do it on the computer. After some research, i came across with the following Maple command:
SolveTools[Inequality][LinearMultivariateSystem]
http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools%2fInequality%2fLinearMultivariateSystem
So, I tried to use that command to solve my system, with the following result (or non-result):
with(SolveTools[Inequality]);
LinearMultivariateSystem({F > 0, H > 0, J > 0, K > 0, L > 0, 1+F-J > 0, 15+H-K > 0, 18-J-K > 0, 33-K-L > 0, 34-H-J-L > 0, -15-F+J+K+L > 0, 16-F-H+J+K > 0}, [F, H, J, K, L]);
Error, (in SolveTools:-Inequality:-Piecewise) piecewise takes at least 2 parameters
So, i really need help solving this as the professor told us that the first one to solve would win a book, eheh. I don't know what I'm doing wrong. Maybe this Maple command is not made for 12 variables? Or maybe i'm just writing something on a wrong form. I've never used Maple before so i can be doing something really stupid without knowing it.
I would really apreciate an answer, as my only goal as a future physicist is to unveil the secrets of the Cosmos to us all.
Thank you again.
Miguel Jesus