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Solving a set of linear equations

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  • Kermit Rose
    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
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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, 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
      about the
      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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