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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