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[sage-support] Re: Simplification Issue Implicates Canonical Form Nils Bruin Mon Feb 20 12:01:11 2012

On Feb 18, 5:24 pm, Mark Rahner <[EMAIL PROTECTED]> wrote:
> converts 1/sqrt(5) to 1/5*sqrt(5) so I suspect that this issue can be
> traced to the GiNaC canonical form.

Yes, it does so for a very good reason: By simplifying expressions
this way, you're sure to recognize equal expressions. Compare 2/
sqrt(6) and sqrt(6)/3, for instance. You'll easily recognize they're
equal if you remove sqrts from the denominator. By sacrificing the
apparent simplicity of 1/sqrt(5) to get 1/5*sqrt(5), one big problem
in deciding if algebraic numbers are equal disappears completely
(there are still other ones, due to the fact that expressions line
sqrt(1+sqrt(2)) are ambiguous). It's a standard convention to deal
with fractions involving roots. It's often taught in schools.

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