Simplifying symbolic expression with radicals

[Emily G]

Hello,

I am trying to find out whether I can get Sage to simplify expressions such as these (and other radicals that are not square root):

(2 + sqrt(2))/(1 + sqrt(2))

The above example should simplify to sqrt(2), but simplify_full() and canonicalize_radical() don't work. Is there a way that I can get Sage to simplify such expressions?

Note: a work-around would be to replace the symbolic expression with a real number by writing 2^0.5, but that's not ideal.

Thank you

[Michael Orlitzky]

On 10/16/2017 04:21 PM, Emily G wrote:
>
> (*2* + sqrt(*2*))/(*1* + sqrt(*2*))

>
> The above example should simplify to sqrt(2),
> but simplify_full() and canonicalize_radical() don't work. Is there a
> way that I can get Sage to simplify such expressions?
>

This gets the result that you want,

sage: f = (2 + sqrt(2))/(1 + sqrt(2))
sage: f._sympy_().simplify()
sqrt(2)

by using SymPy's simplification routine instead of the default Maxima
one. I'm not sure how safe that is in general (e.g. it might do weird
things with complex numbers), so I'd read through the SymPy docs before
using it on anything important.

[slelievre]

Mon 2017-09-16 20:22:25 UTC, Emily G:

You could convert your symbolic expression involving radicals

to an element of the field of algebraic numbers.

    sage: a = (2 + sqrt(2))/(1 + sqrt(2))

    sage: QQbar(a)

    1.414213562373095?

    sage: QQbar(a).radical_expression()

    sqrt(2)