Hello everyone!
I want to find all solutions of following equations :
I used Maple 2019:
solutions:=solve([abs(1+1/3*lambda+1/18*lambda^2-1/324*lambda^3+1/1944*lambda^4)-1=0],[lambda]);
evalf(solutions)
evalf(solutions)
The output is:
So we have two solutions. But when I use Matlab 2018,
four solutions are returned.
syms lambda
eqn =abs(1+1/3*lambda+1/18*lambda^2-1/324*lambda^3+1/1944*lambda^4)-1==0;
solx1=solve(eqn, lambda)
eqn =abs(1+1/3*lambda+1/18*lambda^2-1/324*lambda^3+1/1944*lambda^4)-1==0;
solx1=solve(eqn, lambda)
%%
solx1 =
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 1)
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 2)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 3)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 4)
solx1 =
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 1)
root (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 2)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 3)
roots (z1 ^ 4-6 * z1 ^ 3 + 108 * z1 ^ 2 + 648 * z1, z1, 4)
solx3=solve(eqn, lambda, 'MaxDegree', 4)
double(solx3)
%%The solution is:
-4.2681 + 0.0000i
0.0000 + 0.0000i
5.1340 -11.2012i
5.1340 + 11.2012i
-4.2681 + 0.0000i
0.0000 + 0.0000i
5.1340 -11.2012i
5.1340 + 11.2012i
It is easy to check that first two in Maple and Matlab are same.
Who is right? Does Maple miss complex solutions?