## Solving a set of linear equations

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• I have a set of 16 linear equations in 16 variables , for which the coefficients are expressions in parametric variables, which may be considered constant,
Message 1 of 1 , Mar 8, 2008
I have a set of 16 linear equations in 16 variables , for which the
coefficients are expressions in
parametric variables, which may be considered constant, with respect to
the 16 variables.

e1 = (u1/v1) e3 +(u2/v2) g4
-f1 = -(u1/v1) f3 +(u2/v2) e4
g2 = (u3/v3) e3 +(u4/v4) g4
e2 = -(u3/v3) f3 +(u4/v4) e4

g1 = (u5/v5) g3 + (u6/v6) g4
h1 = -(u5/v5) h3 + (u6/v6) e4
h2 = (u7/v7) g3 + (u8/v8) g4
f2 = -(u7/v7) h3 + (u8/v8) e4

e1 = (u9/v9)d e3+(u10/v10)h4
-f1 = -(u9/v9)d f3+(u10/v10) f4
h2 = (u11/v11)d e3+(u12/v12)h4
f2 = -(u11/v11)d f3+(u12/v12)f4

g1 = (u13/v13)g3+(u14/v14)h4
-h1 = -(u13/v13)h3+(u14/v14)f4
g2 = (u15/v15)g3+(u16/v16)h4
e2 = -(u15/v15)h3+(u16/v16)f4

I believe that if I can solve these 16 equations for

e1,e2,e3,e4, f1,f2,f3,f4, g1,g2,g3,g4, h1,h2,h3,h4

in terms of the u1, u2, . . .,u16, v1,v2,. . .,v16
that I will have an algorithm for polynomial time factoring of positive
integers.

I have worked on this, and have reduced it to 6 equations, but
because the equations have become highly non-symmetric, I have doubts
correctness of what I've done.

What I'm asking for here is help in verifying, at each step of solving a
set of linear equations,
that no error has been made.

I'm not asking that anyone solve these for me.
I'm asking for advice on how to prevent making mistakes in the
mechanical application
of the standard algorithm for solving a set of linear equations.

One solution to this problem would be a computer program that can solve
sets of linear equations
in which the constant coefficients are algebraic expressions.

If such a program package has not yet been written, I suppose I would
have to write it myself.

Kermit Rose < kermit@... >
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