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Question: Why are different solutions of same equation in Maple and Matlab ？

Question: Why are different solutions of same equation in Maple and Matlab ？

lcz 969 Maple 2019
solve
March 13 2020
1

 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)

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) 
%%
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

It is easy to check that  first two in Maple and Matlab are  same.

Who is right? Does Maple miss complex solutions?

 

 

 

 

 

 

 

 
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