Hi Greg,
Hope the following code helps you in implementing your function:
from sage.symbolic.function import SymbolicFunction
class real_nth_root_class(SymbolicFunction):
def __init__(self):
SymbolicFunction.__init__(self, 'real_nth_root', nargs=2)
def _evalf_(self, x, n, parent=None):
# Handle python floats which do not have the 'nth_root' method
if isinstance(x, float):
return float(RDF(x).nth_root(n))
return parent(x).nth_root(n)
real_nth_root = real_nth_root_class()
In actual usage:
sage: real_nth_root( x, 3)
real_nth_root(x, 3)
sage: f(x) = real_nth_root( x, 3)
sage: f
x |--> real_nth_root(x, 3)
sage: plot( real_nth_root( x, 3), -5, 5 )
# plots the graph.
Regards,
basu.
On Fri 11 Jul 2014 06:23:21 AM SGT, Gregory Bard wrote:
I think we have a consensus that we should do *something* but unless I
am very much mistaken, the suggestion from Vincent Delecroix and Nils
Bruin that we make a symbolic function has advantages.
I was looking at Nils's code, but I have to confess that I don't
understand that code. Actually, I wasn't able to get the following to
work, but I have a feeling that I am making a minor and stupid mistake
with the syntax.
################
from sage.symbolic.function import SymbolicFunction
class nth_root(SymbolicFunction):
def __init__(self):
SymbolicFunction.__init__(self, 'nth_root', nargs=2)
def _evalf_(self, n, x, parent=None):
return parent(x).nth_root(n)
plot( nth_root( x, 3), -5, 5 )
################
Maybe someone here could explain exactly what the distinction is or
what the pros/cons are for my approach versus Nils's? I have no idea.
I have also posted this on Sage-Edu, but perhaps all future replies
should be restricted to Sage-Devel and not Sage-Edu?
---Greg
On Wednesday, June 25, 2014 1:10:06 AM UTC-4, Gregory Bard wrote:
As Vincent and Niles have brought up, there might be advantages to it
being a symbolic function. How does one actually go about making that
happen? Is this an intrusive change, or an easy one? I really have no
idea...
---Greg
On Sun, Jun 22, 2014 at 5:00 PM, Vincent Delecroix
<20100.delecr...@gmail.com <mailto:20100.delecr...@gmail.com>> wrote:
> As Niles already said it would be better to have it as a
symbolic function
>
> sage: f(x) = real_nth_root(x, 5)
> sage: f
> x |--> real_nth_root(x,5)
>
> 2014-06-22 22:36 UTC+02:00, Gregory Bard
<gregory.bard1...@gmail.com <mailto:gregory.bard1...@gmail.com>>:
>> Yes, that is reasonable. Let us call it "real_nth_root"
instead, as
>> suggested by Nicolas Thiery. Any other requests/comments?
>>
>> It would be superb if this could be resolved by June 30th, when my
>> book goes to the American Mathematical Society for publication...
>> ---Greg
>>
>> On Sun, Jun 22, 2014 at 9:02 AM, William Stein
<wst...@gmail.com <mailto:wst...@gmail.com>> wrote:
>>> On Sun, Jun 22, 2014 at 8:27 AM, Nicolas M. Thiery
>>> <nicolas.thi...@u-psud.fr <mailto:nicolas.thi...@u-psud.fr>>
wrote:
>>>> On Fri, Jun 20, 2014 at 06:33:52PM -0700, Gregory Bard wrote:
>>>>> It seems that the consensus on both Sage-devel and Sage-edu
is to go
>>>>> with some sort of nth_real_root function. I propose the
following,
>>>>> which I have tested for evaluation, plotting,
differentiation, and
>>>>> integration. Sadly, the derivative has a Dirac delta in it,
which is
>>>>> ... perhaps unavoidable because of the vertical tangency of the
>>>>> cuberoot function at x=0. (Naturally, we can remove the
asserts once
>>>>> testing is completed.
>>>>> ---Greg
>>>>>
>>>>> def nth_real_root( x, n ):
>>>>
>>>> Just 2 cents of outsider feedback since I have not followed the
>>>> discussion, and am not knowledgeable on the topic. This names
suggests
>>>> to me that we look at all the real roots of n (for whatever this
>>>> means), and then take the n-th one. So maybe real_nth_root
instead?
>>>
>>> +1
>>>
>>>>
>>>> Cheers,
>>>> Nicolas
>>>> --
>>>> Nicolas M. Thiéry "Isil" <nthi...@users.sf.net
<mailto:nthi...@users.sf.net>>
>>>> http://Nicolas.Thiery.name/
>>>>
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>>>
>>>
>>> --
>>> William Stein
>>> Professor of Mathematics
>>> University of Washington
>>> http://wstein.org
>>>
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