Programming is about mathematics and not coding.

Problem:

Any rational number a/b (in lowest terms) can be expressed either
as a terminating decimal or a repeating decimal.

We consider here only repeating decimals.

Given, a and b, which are intergers with any number of digits,
find the repeating portion in the decimal expansion.

That is, the decimal expansion will be:

a1, a2, a3, ... an, [r1, r2, r3 ... rn]

where [... ri ...] is the repeating portion.

Example:

1/28 = 0.03 571428 571428...

The non-repeating, leading portion can be very long and so too can
the repeating portion.

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On Fri, 08 Mar 2024 14:20:12 +0000, Nuxxie wrote:

But it fails for 1/28:

zn_order(10,28);
false

I found out the problem here.

The denominator, d, has to be factored as 2^i * 5^j * d', where
possibly i=1 and j=1.

In this case, 28 = 2^2 * 7 (i.e. i=2, j=0)

Now, zn_order(10,7) = 6

Thus 1/28 has a repeating portion of length 6 which is preceeded
by max(i,j) = 2 digits:

1/28 = 0.03571428571428...

This is fantastic stuff!

My main source, so far, is this link:

https://math.stackexchange.com/questions/377683/length-of-period-of- decimal-expansion-of-a-fraction

Maxima uses multi-precision, based on GMP, and can handle extremely
large decimal expansions.

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On Thu, 07 Mar 2024 21:25:16 -0600, Physfitfreak wrote:

I don't think the dorks here know such stuff. And the good ones believe
it's waste of time but what they do (i.e. "fart") is not waste of time.

Project Euler, a well respected forum for programmers, doesn't think
that it's a waste of time:

https://projecteuler.net/problem=26

So I'll go ahead and ruin it for them all :)

(method of nines)

I don't know. Being a scientist/engineer, I have little background
in number theory.

But, after some research, it is related to the "multiplicative order"
of the denominator.

In Maxima CAS, there is a function that determines the multiplicative
order: zn_order(a, d), where a is the base and d the denominator.

Example:

zn_order(10,31);
15

Thus, 1/31 should have a repeating length of 15, and it does.

zn_order(10,79832137);
516846

1/79832137 should have a repeating length of 516846; I haven't checked.

But it fails for 1/28:

zn_order(10,28);
false

So the method is not totally general.

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On Fri, 08 Mar 2024 15:43:54 +0000, Nuxxie wrote:

1/37252902384619140625

The decimal expansion will begin with 11 digits followed by a repeating porion of length 54,494,498,496.

This number would need 64 GiB of memory, but we could write it out to a
file using Maxima or bc or GMP.

Someone please write out this number to a file. As 1 byte per character
it should be about 55 GiB in size.

Then verify that the decimals start with 11 digits and then repeat
after 54,494,498,496 + 11 digits. Just verify that the first 100 or
so digits are the same.

Y'all have big, fat mouths. Let's see if that can translate into
serious computing action.

The first to do it will receive a BIG PRIZE.

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On Fri, 08 Mar 2024 14:54:29 +0000, Nuxxie wrote:

1/28 = 0.03571428571428...

This is fantastic stuff!

Let's now do a big one.

1/37252902384619140625

First find the prime factorization:

ifactors(37252902384619140625);
[[5,11],[7,1],[47297,1],[2304403,1]]

Thus, we need to express this as:

5^11 * 762939440837

Now find the multiplicative order:

zn_order(10, 762939440837);

54494498496

The result:

The decimal expansion will begin with 11 digits followed
by a repeating porion of length 54,494,498,496.

This number would need 64 GiB of memory, but we could
write it out to a file using Maxima or bc or GMP.

I won't try but maybe someone else will.

This kind of stuff is what a computer is for. No fucking Netflix.
No fucking Gmail. Just this.

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On 3/8/2024 2:56 PM, rbowman wrote:

On Thu, 7 Mar 2024 21:25:16 -0600, Physfitfreak wrote:

(method of nines)

Ah, nines. When I was in elementary school I got pretty good with the Trachtenberg system. I would check the answer by casting out the nines.

https://en.wikipedia.org/wiki/Trachtenberg_system https://en.wikipedia.org/wiki/Casting_out_nines

That really pissed off my teachers. "Show your work!"

elementary school? wtf?

I figured you were some kind of Young Sheldon-ish savant.

I got very close to perfect scores in high school geometry. It's all
downhill since.

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On Thu, 7 Mar 2024 21:25:16 -0600, Physfitfreak wrote:

(method of nines)

Ah, nines. When I was in elementary school I got pretty good with the Trachtenberg system. I would check the answer by casting out the nines.

https://en.wikipedia.org/wiki/Trachtenberg_system https://en.wikipedia.org/wiki/Casting_out_nines

That really pissed off my teachers. "Show your work!"

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On 3/7/2024 10:25 PM, Physfitfreak wrote:

On 3/7/2024 12:11 PM, Nuxxie wrote:

Programming is about mathematics and not coding.

Problem:

Any rational number a/b (in lowest terms) can be expressed either
as a terminating decimal or a repeating decimal.

We consider here only repeating decimals.

Given, a and b, which are intergers with any number of digits,
find the repeating portion in the decimal expansion.

That is, the decimal expansion will be:

a1, a2, a3, ... an, [r1, r2, r3 ... rn]

where [... ri ...] is the repeating portion.

Example:

1/28 = 0.03 571428 571428...

The non-repeating, leading portion can be very long and so too can
the repeating portion.

I don't think the dorks here know such stuff. And the good ones believe
it's waste of time but what they do (i.e. "fart") is not waste of time.

So I'll go ahead and ruin it for them all :)

(method of nines)

Ruin away, Sandy. You 2 neurotics are the only ones who care about such nonsense anyway.

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On 3/8/2024 9:20 AM, Lameass Larry Piet wrote:

On Thu, 07 Mar 2024 21:25:16 -0600, Physfitfreak wrote:

I don't think the dorks here know such stuff. And the good ones believe
it's waste of time but what they do (i.e. "fart") is not waste of time.

Project Euler, a well respected forum for programmers, doesn't think
that it's a waste of time:

https://projecteuler.net/problem=26

Remember when you said the exact opposite?


"That entire "Project Euler" web site is pure baloney." Feeb July 2021


"What a totally lame project [Project Euler]. It's where all the string manipulators congregate." Feeb July 2021


phony twat.

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On Fri, 8 Mar 2024 15:16:29 -0600, Physfitfreak wrote:

At one of my jobs, a printing clerk astonished me with calculating large multiplications in his mind, very fast. I kept asking him how he did it,
and he always only smiled at me Every time we were bored we would begin
a race getting the result of some multiplication in mind. Every single
time he won of course. It was fun.

I used to be good at it but it's a definite use it or lose it skill.

I'm a Yankee by birth and even had a great something grandfather that
fought in that war under Miles but I think it was a raw deal. Leaving the
whole slavery red herring aside I am not comfortable with the Roach Motel theory of government.

https://www.youtube.com/watch?v=jKhGHxO-woc

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On Fri, 8 Mar 2024 15:12:18 -0500, DFS wrote:

I got very close to perfect scores in high school geometry. It's all downhill since.

I never got into that QED stuff. Being a code monkey I'll take some old
Greek's word for it an cut to the chase.

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On 3/8/2024 10:43 AM, Larry 'Nuxxie' Piet wrote:

The result:

The decimal expansion will begin with 11 digits followed
by a repeating porion of length 54,494,498,496.

This number would need 64 GiB of memory, but we could
write it out to a file using Maxima or bc or GMP.

I won't try but maybe someone else will.

This kind of stuff is what a computer is for. No fucking Netflix.
No fucking Gmail. Just this.

no gmail? idiot.

no online sports or videos? idiot.

Screw that useless, boring math twaddle. The popular trend today is
Usenet databases:

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