Re: "Programming" in mathematica

Jean-Marc, it's me again.

Maybe you can have a look on my new post ;-)
http://groups.google.com/group/sci.math.symbolic/browse_frm/thread/855bd2d000483ac1/e246a989e6a32c0f?lnk=raot&hl=de#e246a989e6a32c0f

Nena


Nena wrote:

Ups, it seems I'm writing rubbish all day long.

The expected answer to f[19] is 5.

Sorry, ignore what I've just posted.
I guess I'm too tired.

Nena

Nena wrote:

Hi Jean-Marc,

Thanks once again!

My formula is wrong!

It should be

Mod[p, c]

instead of

Mod[c, p].

But the function

f[p_Integer /; p > 3] :=
NestWhile[#1 + 1 &, 4, Mod[(Mod[p, #1]^((#1 - 1)/2)), #1] != 1 &]

still doesn't give me my expected answer.

Now I obtain

f[19] = 5

which is +1 too much! I suspect that c has been increased while
c = 4 passed the test Mod[(Mod[p, #1]^((#1 - 1)/2)), #1] != 1

Any ideas to fix that?

Many thanks,
Nena


Jean-Marc Gulliet wrote:

Nena wrote:
Hi Jean-Marc,

Thanks for your answer!

Actually the condition I have it's a bit more
complicated then I first posted.

Instead of checking

Mod[c, p] == 1

I would like the program to check
Mod[Mod[c, p]^((c - 1)/2), c] == 1

So my change of your program would be
f[p_] := NestWhile[#1 + 1 & , 4, Mod[Mod[#1, p]^((#1 - 1)/2), 1#] != 1
----------------------------------------------------------------^^
Beware: slot numbers must be written the other way around, that is #1
(but this is not an issue here since Mathematica interpret it as one
times the first variable, 1*#1)

& ]

Then testing the program I get
f[19] = 20

The answer should be 4.

Where is my fault in changing your program?

I do not see anything wrong in the changes you made to the original
code. However, I suspect either the formula you use as stooping
criterion is not the correct one or your expected value for f[19] is
erroneous.

In[1]:=
f[p_Integer /; p > 3] :=
NestWhile[#1 + 1 & , 4, Mod[Mod[#1, p]^((#1 - 1)/2), #1] != 1 & ]

In[2]:=
f[19]

Out[2]=
20

The result above is in agreement with your formula

In[3]:=
Mod[Mod[c, p]^((c - 1)/2), c] == 1 /. {c -> 20, p -> 19}

Out[3]=
True

While the expected value of 4 for c failed the test

In[4]:=
Mod[Mod[c, p]^((c - 1)/2), c] == 1 /. {c -> 4, p -> 19}

Out[4]=
False

We can follow the process step by step,

In[5]:=
Mod[4, 19]

Out[5]=
4

In[6]:=
Mod[4, 19]^((4 - 1)/2)

Out[6]=
8

In[7]:=
Mod[Mod[4, 19]^((4 - 1)/2), 4]

Out[7]=
0

Regards,
Jean-Marc

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