In fact you don't really need MathWorld: erf is continuous monotone
R-(-1,1), so must have an inverse function (-1,1)-R.
How you tell Sage this needs a Sage expert.
On Saturday, 28 December 2013 19:46:49 UTC, Buck Golemon wrote:
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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