On Friday 9 February 2024 at 08:16:03 UTC-8 Georgi Guninski wrote:
When I try to extract digits of tanh(91) via floor, I still get error
sage: floor(10^4*tanh(91))
ValueError
The sage code doesn't use gp for this. The error you're encountering
happens in
sage.functions.other._eval_floor_ceil
and it happens because the system tries to evaluate the expression using
interval arithmetic. It iteratively increases the precision until it find
an interval that doesn't straddle an integer or it gives up after a set
number of trials. You're hitting that second condition. You don't make it
easier by multiplying by 10^4. In fact, you make it harder: you now need
more digits to get the interval to not include an integer.
Without more information, this code basically has to give up after a fixed
number of tries: it could be evaluating an expression that actually does
evaluate to 1. In that case, no amount of increased precision will result
in an interval that doesn't contain an integer. It's a well-known problem
in numerical approximation: discontinuous functions are basically not
computable in that model.
gp computes it both ways :)
sage: gp.default('realprecision',10^5)
0
sage: gp('floor(tanh(91))')
0
so does sage if you tell it to use the same approach gp uses:
sage: tanh(91).n(30).floor()
1
sage: tanh(91).n(300).floor()
0
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