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Is there a formal way of representing "currency denominations?" by Augustus Himmlewick - Sun, 20 May 2018 16:15:17 EST ID:KdxuUdQ5 No.15657 Ignore Report Quick Reply
File: 1526847317954.gif -(772771B / 754.66KB, 380x285) Thumbnail displayed, click image for full size. 772771
I've recently been trying to write a tail-recursive program which counts how many different ways `x` amount of money can be made using `y` denominations of currency.

I started making progress when I noticed that my denominations didn't need to have different values. They could all be worth the same amount, and the program would still work correctly. It seemed a little odd to me, that I was generating unique combinations of things that all had the same integral value. On my computer I just see:

f( 1 ) = 1
f( 2 ) = 1
f( 1 ) =/= f( 2 )

^and that makes me a little uncomfortable. Now, because these kinds of rules are actually really useful inside of my computer, I was wondering if they've been rigorously studied by mathematicians. Is there a name for these things? Are there papers I can read?
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Charles Bellertune - Tue, 22 May 2018 02:52:07 EST ID:KdxuUdQ5 No.15659 Ignore Report Quick Reply
I found these things called "Diophantine equations" and I think they're related to my problem.
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Sophie Dicklestone - Tue, 29 May 2018 18:00:34 EST ID:sR7kJ2DP No.15662 Ignore Report Quick Reply
Are you talking about representing it in terms of something else? What constitutes the currency’s price? I don’t know if this is so much a math question as an economics/monetary system question.
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Archie Pockfoot - Thu, 31 May 2018 00:02:42 EST ID:drSlH/C1 No.15663 Ignore Report Quick Reply
>>15657

Sounds like you're trying to find solutions to polynomials with multiple independent variables.

For instance finding ways to add up to a dollar with pennies, nickels, and dimes is a solution to the polynomial 0.01x + 0.05y + 0.1z =1. Diophantine equations are a special type of this, with 2 variables.

The 3 equations you listed there are inconsistent with each other, so I'm not sure what you mean by that part.

Since we are trying to find different ways to add up to a certain amount of money, the total degree of your polynomial is always going to be 1. In general, if we have a linear polynomial with 3 variables there are going to be infinitely many solutions. But since we want our solutions to be triples of natural numbers there are going to be finitely many.

This field of math is called algebraic geometry, and it's a really deep topic even if it seems like you are starting with a simple problem. If you are interested I'm sure you can search around and find good introductory books on it, but I can't provide a suggestion as I don't know much abot it myself and don't know your background.

The number of ways to add up to a dollar doesn't depend on the value of a dollar, just in the number of smaller parts you can break it down in to. In other words the dollar being worth 1 yen or 1million yen makes no difference.
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Samuel Cranningsack - Thu, 31 May 2018 00:05:29 EST ID:rcbFGyVC No.15664 Ignore Report Quick Reply
>>15663
Sounds like you're trying to find solutions to polynomials with multiple independent variables.

For instance finding ways to add up to a dollar with pennies, nickels, and dimes is a solution to the polynomial 0.01x + 0.05y + 0.1z =1. Diophantine equations are a special type of this, with 2 variables.

The 3 equations you listed there are inconsistent with each other, so I'm not sure what you mean by that part.

Since we are trying to find different ways to add up to a certain amount of money, the total degree of your polynomial is always going to be 1. In general, if we have a linear polynomial with 3 variables there are going to be infinitely many solutions. But since we want our solutions to be triples of natural numbers there are going to be finitely many.

This field of math is called algebraic geometry, and it's a really deep topic even if it seems like you are starting with a simple problem. If you are interested I'm sure you can search around and find good introductory books on it, but I can't provide a suggestion as I don't know much abot it myself and don't know your background.

The number of ways to add up to a dollar doesn't depend on the value of a dollar, just in the number of smaller parts you can break it down in to. In other words the dollar being worth 1 yen or 1million yen makes no difference.
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Fanny Fupperford - Sun, 03 Jun 2018 02:26:17 EST ID:3oORF0f9 No.15667 Ignore Report Quick Reply
1528007177643.gif -(1560B / 1.52KB, 174x14) Thumbnail displayed, click image for full size.
>>15664
Wolfram alpha says the thing what I am dealing with is called a "frobenius equation" which is a kind of diophantine equation where the coefficients and solutions must be non-negative integers.

I do have a textbook on discrete mathematics, but unfortunately the words "diophantine" and "frobenius" appear nowhere in the index.
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Fanny Fupperford - Sun, 03 Jun 2018 02:28:09 EST ID:3oORF0f9 No.15668 Ignore Report Quick Reply
>>15667
Oh shit, I didn't think that would happen. The .gif I uploaded displays properly on wolfram alpha's website:

http://mathworld.wolfram.com/FrobeniusEquation.html

nb
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Fuck Sickledodge - Mon, 18 Jun 2018 16:39:08 EST ID:DSHkuT0l No.15671 Ignore Report Quick Reply
>>15668

If you want to solve these with a computer you could try one of the various math suites. Some of them support calls from other languages, so if you want to write your Python program and then call something else to solve your equation and give back some solutions as a list it shouldn't be a problem.


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