Calculating exact roots of 6th degree polynomial

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Deepayan Bhadra 2017-10-18

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https://ww2.mathworks.cn/matlabcentral/answers/362039-calculating-exact-roots-of-6th-degree-polynomial

编辑： Walter Roberson 2017-10-19

I've a fat 6x6 matrix E with symbolic variables. I'm trying to compute sqrt(eig(E'E)), ie, the singular values. The answer begins with 'root( ) etc. How do I get MATLAB to solve this 6th degree polynomial and show me more pleasing answers? Thanks a lot.

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Answer 1

Image Analyst 2017-10-19

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https://ww2.mathworks.cn/matlabcentral/answers/362039-calculating-exact-roots-of-6th-degree-polynomial#answer_286540

Use roots(), not root().

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Walter Roberson 2017-10-19

root() is the placeholder that replaced RootOf() a couple of releases ago in the Symbolic Toolbox.

Walter Roberson 2017-10-19

编辑：Walter Roberson 2017-10-19

Which Galois group does it belong to? Because it is not generally possible to solve for exact algebraic roots.

https://en.wikipedia.org/wiki/Sextic_equation

By the way, have you ever looked at how long the roots are just for quartics? About 12500 characters per solution when using bare symbols for the coefficients; much much longer if the coefficients are expressions as you imply is happening for you.

Suppose you managed to find a (say) million character closed form for one of your eigenvalues: realistically, what would you do with it?

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