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Re: Continued Fractions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg75098] Re: Continued Fractions
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Mon, 16 Apr 2007 20:21:42 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <evvbni$b5u$1@smc.vnet.net>
Wu Weidong wrote:
> Hi,
> I'm working on a function which takes 2 integer values as input, a and b an=
> d outputs a list of integers corresponding to the continued fraction repres=
> entation of the rational number a/b.
>
> My function is as follows:
>
> build[a_Integer,b_Integer, l_List] :== Module[{r==1,q,temp},
> While[r!==0,
> If[a>==b,
> q==Quotient[a,b];
> l==Append[l,q];
> r == a-b*q;
> a == r,
>
> temp == a;
> a == b;
> b == temp;
> ];
> ];
> l
> ];
>
> Essentially, if the fraction given is less than 1, the first number in the =
> list is 0. The function then proceeds to find the quotient of the numerator=
> and denominator (and add that to the list) and the remainder. If the remai=
> nder is less than one, it takes the reciprocal and splits it into a whole-n=
> umber part plus another fraction which will be less than 1 and repeat. It s=
> tops when the remainder is 0.
>
> When I tried to run the program, I get the following error messages:
>
> Set::shape: Lists {} and {2} are not the same shape.
>
> Set::setraw: Cannot assign to raw object 45.
>
> Set::shape: Lists {} and {2} are not the same shape.
>
> Set::setraw: Cannot assign to raw object 45.
>
> Set::shape: Lists {} and {2} are not the same shape.
>
> General::stop: Further output of Set::shape
> will be suppressed during this calculation.
>
> Set::setraw: Cannot assign to raw object 45.
>
> General::stop: Further output of Set::setraw
> will be suppressed during this calculation.
>
>
> However, if I just run the While part of the function with a==45, b==16, l=
> =={}, r==1 (so I can enter the while loop), I can find the right result (2,=
> 1,4,3), so I believe my algorithm should be correct. The errors only appear=
> when I put the while loop under the Module structure.
>
> What is wrong with my program?
>
> Thank you.
>
> Regards,
> Rayne
>
Hi Rayne,
Contrary to conventional programming language, the list of arguments to
a function (a, b, and l, in your case) does declare neither some local
variables nor some references to global variables. The list of arguments
is a list of patterns, indeed; patterns that are going to be replaced in
the right-hand side of the expression before evaluation.
Say you ask Mathematica to evaluate build[45, 16, {}]. First,
Mathematica replaces any occurrence of the pattern a by 45, b by 16, and
l by {}. Only then it enters the Module and evaluates (executes) the
While loop. So everything is fine until Mathematica reaches the line "l
= Append[l, q]" in your code, which is now {} = Append[{}, 2]. This
means that you have lost the name l and it has been replaced by its
value (the empty list). (It is like to attempt to evaluate 1 = 2.)
You can see what is going on by using, among many others, the *Trace*
command, as in
build[45, 16, {}]//Trace
Now, you will find below a fixed version of the code you posted. Note
that I have renamed the original arguments m and n and created two local
variables a and b within the Module. Also, it seems that it is not
necessary to give the list l as argument: you can just defined and
initialize it inside the Module.
In[1]:=
build[m_Integer, n_Integer] :=
Module[{a = m, b = n, r = 1, q, temp, lst = {}},
While[r != 0,
If[a >= b,
q = Quotient[a, b];
lst = Append[lst, q];
r = a - b*q;
a = r,
temp = a;
a = b;
b = temp;
];
];
lst
];
In[2]:=
build[45,16]
Out[2]=
{2,1,4,3}
From here, of course, you have to test your code to check if the
results are consistent.
Regards,
Jean-Marc
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