# Solving equation with algebraic numbers

Hello, SAGE gives me error when I load this: solve(x^2-AA(sqrt(3))==0,x) but it gives no problem when I load solve(x^2-sqrt(3)==0,x) This is a small example of a bigger problem I have in which I must solve a system of equations involving algebraic numbers through AA(.) and QQbar(.). How can I make SAGE solve equations with this type of numbers? or there is no way? Thanks!

You can convert algebraic numbers to symbolic expressions using

`SR(...)`

. Probably you would rather want to define an ideal in a polynomial ring, and compute a Gröbner basis and/or the associated`variety`

(if the system has finitely many solutions). Can you add the system you actually want to solve?Hello rburing, i tried loading solve(x^2-SR(AA(sqrt(3)))==0,x) but it gives error, what do you think?

It seems Maxima can't handle the symbolic wrapper around

`AA`

elements. Try`SR(AA(sqrt(3))).numerical_approx()`

for numerics, or`AA(sqrt(3)).radical_expression()`

for an exact expression. Not all algebraics are expressible in terms of radicals, so this is not a good approach in general. Also`solve`

may return only approximate solutions in more complicated cases. I would instead create an ideal`I`

in a polynomial ring and call`I.variety(AA)`

or`I.variety(QQbar)`

.thanks rburing!