I've found here:
http://mathworld.wolfram.com/InverseErf.html
[image: erf^(-1)(erf(x))][image: =][image: x,]
(2)
with the identity holding for [image: x in R]
Is this a bit of information that can be added (by me?) to sage?
On Saturday, December 28, 2013 11:32:02 AM UTC-8, Buck Golemon wrote:
>
> Yes, I can, but it doesn't have the intended (or any) effect:
>
> sage: assume(x, 'real')
> sage: assume(y, 'real')
> sage: assumptions()
> [x is real, y is real]
> sage: solve(erf(x) == erf(y), x)
> [x == inverse_erf(erf(y))]
>
>
> On Saturday, December 28, 2013 11:27:09 AM UTC-8, Buck Golemon wrote:
>>
>> 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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