Re: Euclidean Algorithm in Mathematica

Well, thanks!

I need a slighty different example.

I would like to call the first two remainders within
a new function without defining the variables
alpha and beta outside first.

So I don't want to have this line first
{alpha, beta} = myRemainders[12, 7]

but something of the shape
g[a, b] = alpha + beta where
alpha is the first entry of the result of
myRemainders[a, b] and beta the second one.

Many thanks,
Nena

Jean-Marc Gulliet wrote:

Nena wrote:
Excellent! Thanks!

Just one little alternation.
Let alpha and beta be the first two remainders with
the condition that they are both less than the square root
of a. And also alpha > beta.

How can I list alpha and beta separately?
So that I can treat alpha and beta as variables for further
manipulations. For example to calculate
g[alpha_, beta_] := alpha^2 + beta^2

For example

In[1]:=
Remainder[a_, b_] := a - Quotient[a, b]*b
Remainder[a_, 0] := 0
myRemainders[a_, b_] := Module[{lst},
lst = FixedPointList[{Last[#1], Remainder @@ #1} &, {a, b}];
Select[lst, #1[[2]] < Sqrt[a] &, 2][[All, 2]]]

In[4]:=
{alpha, beta} = myRemainders[12, 7]

Out[4]=
{2,1}

In[5]:=
alpha

Out[5]=
2

In[6]:=
beta

Out[6]=
1

In[7]:=
alpha^2 + beta^2

Out[7]=
5

Regards,
Jean-Marc

.

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