Thanks.
If I understand you, the problems lie in the complex domain, where I was
only thinking of the real numbers.
Can I not do something to the effect of assume(x, 'real') ?
On Saturday, December 28, 2013 10:07:41 AM UTC-8, JamesHDavenport wrote:
>
> erf, as a function C->C, is not 1:1 (see 7.13(i) of DLMF), so this
> "simplification" would be incorrect.
> I do not know how to tell Sage that you want real-valued
> functions/variables, when of course it would be correct to do the
> simplification.
>
> On Friday, 27 December 2013 22:40:40 UTC, Buck Golemon wrote:
>>
>> 1) Sage seems unable to reduce `erf(x) == erf(y)` to `x == y`. How can I
>> help this along?
>>
>> solve(erf(x) == erf(y), x)[0].simplify_full()
>>
>> Actual output: x == inverse_erf(erf(y))
>> Expected output: x == y
>>
>> I had expected that sage would trivially reduce `inverse_erf(erf(y))` to
>> `y`.
>>
>> 2) This output references 'inverse_erf', which doesn't seem to be
>> importable t from anywhere in sage. Am I correct?
>>
>> ---
>>
>> My concrete problem is re-deriving the formula for the
>> normal-distribution cdf. I get a good solution from sage, but fail in
>> showing that it's equivalent to a known solution because:
>>
>> var('x sigma mu')
>> assume(sigma > 0)
>> eq3 = (-erf((sqrt(2)*mu - sqrt(2)*x)/(2*sigma)) == -erf((sqrt(2)*(mu -
>> x))/(2*sigma)))
>> bool(eq3)
>>
>> Actual output: False
>> Expected output: True
>>
>>
>> However this quite similar formula works fine:
>>
>> eq3 = (-erf(sqrt(2)*mu - sqrt(2)*x) == -erf(sqrt(2)*(mu - x)))
>> bool(eq3)
>>
>> Output: True
>>
>> ---
>> Include:
>> Platform (CPU) -- x86_64
>> Operating System -- Ubuntu 13.10
>> Exact version of Sage (command: "version()") -- 'Sage Version 5.13,
>> Release Date: 2013-12-15'
>>
>>
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