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Re: solve - integer solution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34156] Re: [mg34145] solve - integer solution
  • From: BobHanlon at aol.com
  • Date: Tue, 7 May 2002 03:53:50 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 5/6/02 6:11:49 AM, c.krook at student.tue.nl writes:

>I need to find an instance from the integers that satisfies the following
>equation:
>
>{12 c[1, 0] + 12 c[2, 0] + 25 c[3, 0] - 50 c[3, 1] + 25 c[4, 0] - 50 c[4,
>1],
>  12 c[1, 1] + 12 c[2, 1] + 10 c[3, 0] + 15 c[3, 1] + 10 c[4, 0] + 15 c[4,
>1],
>   c[1, 0] + 2 c[2, 0], c[1, 1] + 2 c[2, 1], c[3, 0] - 5 c[4, 1],
>  c[3, 1] + c[4, 0] - c[4, 1]}=={0,0,0,0,0,0}
>
>Using Solve doesn't give (explicit) integer solutions; Furthermore, since
>I
>only need an arbitrary integer-instance is there an easier way to obtain
>one? (if not, how can I adjust solve?)
>(this is small example; my actual problem involves much larger lists)
>

eqns = {
        12 c[1,0]+12 c[2,0]+25 c[3,0]-50 c[3,1]+
          25 c[4,0]-50 c[4,1],
        12 c[1,1]+12 c[2,1]+10 c[3,0]+15 c[3,1]+
          10 c[4,0]+15 c[4,1],
        c[1,0]+2 c[2,0],
        c[1,1]+2 c[2,1],
        c[3,0]-5 c[4,1],
        c[3,1]+c[4,0]-c[4,1]}==
      {0,0,0,0,0,0};

vars = Cases[eqns, c[_,_], Infinity]//Union;

Reduce[eqns, vars]

Off[Solve::svars]

This will give nine solution sets

Flatten[
    Table[
      Join[
        Solve[eqns /. (t={c[4,0]->12*m, c[4,1]->12*n}),
 
            vars][[1]],
 
        t],
 
      {m,-1,1}, {n,-1,1}],
    1]//ColumnForm


Bob Hanlon
Chantilly, VA  USA


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