On 05/06/2016 09:50 PM, Marc Tardif wrote:
> Hi folks,
>
> When comparing the product of two square roots to the square root of
> the product using two scalars, I get True:
>
> sage: bool(sqrt(pi)*sqrt(2) == sqrt(pi*2))
> True
>
> But when using a variable instead of one of the scalars, I get False:
>
> sage: n = var('n')
> sage: assume(n>=0)
> sage: bool(sqrt(pi)*sqrt(n) == sqrt(pi*n))
> False
>
The identity isn't true in general. Take,
i * i = sqrt(-1) * sqrt(-1) = -1
and apply the identity:
sqrt(-1 * -1) = sqrt(1) = 1.
In Sage, variables are complex by default, so we can't use that
identity. In a perfect world, your assumption that n >= 0 would fix
that, but the "safe" simplification routines involved with
bool(<expression>) aren't smart enough to use it.
Instead, you can try,
sage: (sqrt(pi)*sqrt(n) - sqrt(pi*n)).simplify_real()
0
The simplify_real() method can be a little more extreme since you're
making it clear that you want to treat the expression as real.
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