MaplePrimes - answers and comments on Question, how to solve these equations ?

No real solutions

Robert Israel — Thu, 18 Mar 2010 04:47:02 Z

These three equations (with m=1) have no real solutions, so it's not surprising that fsolve can't find any. However, you might try m = 1.9.

>   fsolve(eval(eqs,m=1.9), {x1 = 0 .. 1, x2 = 0 .. 1, x3 = 0 .. 1});

{x1 = .1320826971, x2 = .9721759684, x3 = .7957413345}

This doesn't have x1,x2 and x3 in the right order, but by symmetry you can permute the values so that x3 <= x2 <= x1.

For the plot, you could try something like this (but it won't give you the interval of m values you mentioned):

> pts:= NULL: 
  for X3 from 0 to 1 by 0.01 do
    R:= fsolve({-3*x1+4*x1^3-3*x2+4*x2^3-3*X3+4*X3^3 = 0, 
         5*x1-20*x1^3+16*x1^5+5*x2-20*x2^3+16*x2^5+5*X3-20*X3^3+16*X3^5 = 0},
        {x1=X3..1,x2=X3..1});
    if type(R,set) then 
      X2:= min(map(rhs,R));
      X1:= max(map(rhs,R));   
      M1:= X1 + X2 + X3;
      pts:= pts, [X1,M1],[X2,M1],[X3,M1];
    end if
  end do:
  plots[pointplot]([pts]);

SMALL Question

Jean Jacques — Sun, 28 Mar 2010 12:43:45 Z

To refresh my knowledge of MAPLE I was trying to reproduce the examples explained in this query.

But , I cant. With which versions of MAPLE should work those examples? I have the old Maple10.

Regards,

intersectplot

Robert Israel — Thu, 18 Mar 2010 06:17:09 Z

A better way:

> plottools[transform]((x,y,z) -> [x,x+y+z])
   (plots[intersectplot](-3*x1+4*x1^3-3*x2+4*x2^3-3*x3+4*x3^3,
           5*x1-20*x1^3+16*x1^5+5*x2-20*x2^3+16*x2^5+5*x3-20*x3^3+16*x3^5,
    x1=0..1, x2=0..1, x3=0..1));

fsolve and intersectplot

Robert Israel — Sun, 28 Mar 2010 23:55:05 Z

The fsolve examples should work just as well with Maple 10. However, intersectplot was introduced in Maple 11.