Re: Numerical approximation of ceiling functions?

[P Purkayastha]

On 04/21/2013 09:50 AM, Kenneth Lin wrote:
> Hi Sage,
>
> I'm not sure if it's that I'm not doing this right, but I have this
> function that has a ceiling in it. I defined it like so:
>
> |
> botrk(h0_prime,a0,s0,c0)=h0_prime /ceil(log(20*(a0 +25)/(h0_prime
> +20*(a0 +25)),0.95))*(s0 +0.4)*(1+c0)
> |
>
> But it won't do approximations of the ceiling, only returning another
> symbolic expression that can't be approximated.
>
> |
> sage: botrk(3000, 10, 1, 0.1)
> 4620.00000000000/ceil(-19.4957257462237*log(7/37))
> sage: botrk(3000, 10, 1, 0.1).n()
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call last)
> <ipython-input-63-503406e1b435> in <module>()
> ----> 1 botrk(Integer(3000), Integer(10), Integer(1), RealNumber('0.1')).n()
>
> /usr/lib/sagemath/local/lib/python2.7/site-packages/sage/symbolic/expression.so
> in sage.symbolic.expression.Expression._numerical_approx
> (sage/symbolic/expression.cpp:21011)()
>
> TypeError: cannot evaluate symbolic expression numerically
>
> |
>
> Does anyone know how to approximate ceilings? For my purpose, I could
> just plug this in again and get a result, but I was hoping for a better,
> cleaner way of doing it.

Don't know why it stumbles on the ceiling. A function works on the other
hand, since it avoids symbolics.

sage: def botrk(h0_prime, a0, s0, c0): return h0_prime / ceil(log(20 *
(a0 + 25) / (h0_prime + 20 * (a0 + 25)), 0.95)) * (s0 + 0.4) * (1 + c0)
....:
sage: botrk(3000, 10, 1, 0.1)
140.000000000000