Dario Alpern comments

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                                            Dario Alpern

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Yes, you are correct. I have a factorization calculator that runs several minutes in the Web browsers (some people are running it for more than a day), but it has...

Add optional primality certificate using ECPP to factorizations

Complex multiplication requires floating-point operations with arbitrary precision, so this issue depends on #19.

Add N-1/N+1 primality testing and P-1/P+1 integer factoring to the integer factorization calculator

With respect to your last post, I've just implemented it for exponents up to 18. Please refresh the web page and try it.

Add N-1/N+1 primality testing and P-1/P+1 integer factoring to the integer factorization calculator

I've just uploaded a new version that includes the other algebraic factorizations for exponents up to 18. Please refresh the page and try again.

Add N-1/N+1 primality testing and P-1/P+1 integer factoring to the integer factorization calculator

That is a very specific factorization. I do not see how the calculator can detect that the number has the form `8*18^2*x^3+12` where `x = 18^99`. In general, I think...

The polynomial factorization calculator can write a representation of the roots of polynomials (classic, i.e. not mod any number) using only integers and i and the operations of addition, subtraction, multiplication, division, and the extraction of roots (not trigonometric functions or pi)

The problem is that you have to compute roots of complex numbers, so this is equivalent to use trigonometric functions. You cannot find the 6 seventh non-real roots of 1...

The polynomial factorization calculator can write a representation of the roots of polynomials (classic, i.e. not mod any number) using only integers and i and the operations of addition, subtraction, multiplication, division, and the extraction of roots (not trigonometric functions or pi)

The expressions in that PDF are interesting. I do not know if those expressions can be optimized. Of course, cube roots of non-real numbers are required for angles that are...

The polynomial factorization calculator can write a representation of the roots of polynomials (classic, i.e. not mod any number) using only integers and i and the operations of addition, subtraction, multiplication, division, and the extraction of roots (not trigonometric functions or pi)

I've just read the methods found by Gauss and Vandermonde to express the roots of unity using radicals and it appears that the results would be a lot of pages...

The polynomial factorization calculator can write a representation of the roots of polynomials (classic, i.e. not mod any number) using only integers and i and the operations of addition, subtraction, multiplication, division, and the extraction of roots (not trigonometric functions or pi)

The calculator knows how to compute the algebraic roots of 1^(1/2^n), 1^(1/3), 1^(1/5) and 1^(1/17). If you want to compute the algebraic roots of the numbers you mention, for example...

The polynomial factorization calculator can write a representation of the roots of polynomials (classic, i.e. not mod any number) using only integers and i and the operations of addition, subtraction, multiplication, division, and the extraction of roots (not trigonometric functions or pi)

In https://ericbinnendyk.net/roots_of_unity.pdf (not accessible at this moment but you can use archive.org to download it), Eric R. Binnendyk developed an optimized version of Gauss' method to find the radical expressions...