How to operate 'solve(...)'

I want to know how to operate 'solve()'.

I have to solve the equation of 5th degree.

So, i use the solve function.

I also read the help of solve but, i do not know the principle of the solve function.

In the 'help', the document does not have the principle.

I trace the 'help'.

solve() - vpa() - root() - Symbolic Math Toolbox™

Finally, i reach Symbolic Math Toolbox™.

The help of Symbolic Math Toolbox™ just explain "this provide mathematical function..."

But, there are not any detailed explain.

Is it secret??

Answer 1

[Steven Lord]

Do you want to know how to use the solve function (which is described in the documentation) or do you want to know how the solve function works (which is not described in the documentation?) How the solve function works is quite complicated and we do not document the steps it takes in solving equations.

If you're trying to solve the general 5th degree polynomial in radicals and are wondering why solve doesn't work on that general polynomial, see Abel and Ruffini.

Answer 2

[John D'Errico]

As Steve said, solve is a complicated thing. It also probably changes with time. So if someone did spend the days or weeks or longer to fully document that tool for you to read, at least something would probably have changed by the time you get around to reading it all.

If you really want to understand how computer algebra systems work, you might be best off learning about them in general. There are surely lots of books and courses out there. But fully understanding a tool like solve will require some serious effort, that cannot possibly be covered here.

It sounds like you tried to use solve on a 5th degree polynomial,andit failed, so you wanted to understand how solve works. The problem is, no matter what you did with some general 5th degree polynomial, you can never solve it to gain an analytical solution. So reading about solve will not help you here.

At best, you can find a numerical solution to such a problem. But ... if you have ANY symbolic (unknown) coefficients for that polynomial, it is not possible to solve in general using a tool like vpasolve (or fsolve).