One approach would be to have three inputs to continued_fraction() function
corresponding to the general form of a quadratic irrational fraction (a +
sqrt(b)) / c
We can set b = 0 for other cases. But I think it is not a good approach.
Another approach would be to keep the current interface of
continued_fraction()
unchanged and pattern match to identify sqrt() s involved in the numerator.
def continued_fraction(a, b):
p = Wild('p')
q = Wild('q')
match = a.match(p + sqrt(q))
# and do the processing according to whether
# q = 0 or not
On Fri, Jun 28, 2013 at 8:23 PM, Thilina Rathnayake
<[email protected]>wrote:
> Yes, that is where it should go. I don't think it will be that hard to
> combine.
> There is a Java code <http://www.alpertron.com.ar/CONTFRAC.HTM> that is
> used in Dario Alpern's website.
>
> I need the continued_fraction representation of quadratic irrational
> numbers
> in the Diophantine equation module. I can implement it in diophantine
> module
> but I think that does not belong there. We should implement it in ntheory
> and then use it in Diophantine module. Shall I start on this?
>
>
>
> On Fri, Jun 28, 2013 at 8:49 AM, Stephen Loo <[email protected]> wrote:
>
>> I have considered this, in quantum module, the continued_fraction
>> function is only work for rational number a/b = continued_fraction(a, b),
>> but my function above is work for float and depending on the precision. I
>> don't know how to combine into single function, and it is not suggested to
>> place in quantum module, it should be in ntheory.
>>
>> Stephen
>>
>> Thilina Rathnayake於 2013年6月28日星期五UTC+8上午10時58分36秒寫道：
>>>
>>>
>>> Thanks guys for the help. Shouldn't we add this functionality to the
>>> current continued_fraction or
>>> add a new function to SymPy so user can use it directly?
>>>
>>>
>>>
>>> On Fri, Jun 28, 2013 at 7:45 AM, Stephen Loo <[email protected]> wrote:
>>>
>>>> def continued_fraction(r):
>>>> while True:
>>>> i = int(r)
>>>> yield i
>>>> if i == r:
>>>> break
>>>> r = 1 / (r - i)
>>>>
>>>>
>>>> Thilina Rathnayake於 2013年6月28日星期五UTC+**8上午4時16分34秒寫道：
>>>>
>>>>> Hi all,
>>>>>
>>>>> Is there a function in sympy which gives the continued fraction
>>>>> representation
>>>>> of quadratic irrationalities like, (sqrt(17) + 5 ) / 4?
>>>>>
>>>>> I found an implementation of a continued fraction function in Shor's
>>>>> algorithm:
>>>>> http://docs.sympy.org/dev/**modu**les/physics/quantum/shor.**html<http://docs.sympy.org/dev/modules/physics/quantum/shor.html>
>>>>>
>>>>> But it doesn't seem to give correct results when irrationalities are
>>>>> involved.
>>>>>
>>>>> >>> from sympy.physics.quantum.shor import continued_fraction
>>>>>> >>> continued_fraction(sqrt(17)+5, 4)
>>>>>> [2, 4]
>>>>>>
>>>>>
>>>>> Actual answer should be 2, [3, 1, 1] with the numbers inside []
>>>>> repeating forever.
>>>>> Any help would be appreciated.
>>>>>
>>>>> Regards,
>>>>> Thilina.
>>>>> .
>>>>>
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