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#76 2014-03-02 16:23:30

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
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Re: Four Squares Reborn

How do you do this using non-mathematical languages or without the FindInstance command?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#77 2014-03-02 16:29:51

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

There is a program on the net in C++. You could use the greedy algorithm.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#78 2014-03-02 16:36:58

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
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Re: Four Squares Reborn

C++? I have no idea how to do big integer arithmetic with it


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#79 2014-03-02 16:39:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

I was not aware that it supported anything bigger than a long double?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#80 2014-03-02 16:45:53

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

There might be some way to do that. I do not want to do it again, I already did it last year.

Can we do it in M without the FindInstance command ?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#81 2014-03-02 16:47:40

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

You could use procedural commands just like you did in C++. But unless that is faster, I would stick with FI.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#82 2014-03-02 16:51:38

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

When did I do anything in C++? FindInstance did not help me learn anything new


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#83 2014-03-02 16:56:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

Whatever language you programmed it in before. M has the procedural paradigm too.

FindInstance did not help me learn anything new

You saw how to use a very powerful command, that is nothing? What are you trying to learn?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#84 2014-03-02 16:57:18

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

I am trying to learn how such algorithms work.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#85 2014-03-02 17:01:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

There is no known algorithm that specifically does that job. I think they just use the greedy algorithm.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#86 2014-03-02 17:11:18

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

Okay teach me the greedy algorithm


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#87 2014-03-02 17:12:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

Take the biggest square you can, subtract it from the number, repeat this process with the new number.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#88 2014-03-02 17:26:28

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

Probably a good idea, but there can be faster algorithms for this problem


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#89 2014-03-02 17:28:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

What are they?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#90 2014-03-02 17:42:50

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

How am I supposed to know? I am only a bumpkin


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#91 2014-03-02 17:43:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

What is that?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#92 2014-03-02 17:51:29

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

ask bobbym


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#93 2014-03-02 17:53:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

He went downstairs.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#94 2014-03-02 18:16:02

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

Call him on his mobile phone.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#95 2014-03-02 18:17:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

He does not have a mobile phone, I am starting to get worried about him.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#96 2014-03-02 18:26:03

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

Call him up on his Mathematica


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#97 2014-03-02 18:28:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

Oh, he is back. He said they did not care for the name question but they told him there are a few math tricks but no known algorithm to do it.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#98 2014-03-04 02:10:47

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

Why is this not working:

FindInstance[7==a+b && PrimeQ[a] && PrimeQ[b],{a,b}, Integers]

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#99 2014-03-04 02:32:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Four Squares Reborn

Perhaps you should bound the problem a little better.

FindInstance[{a > 0, b > 0, a \[Element] Primes, b \[Element] Primes, 
  a + b == 7}, {a, b}, Integers, 3]

{{a -> 2, b -> 5}, {a -> 5, b -> 2}}


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#100 2014-03-04 04:04:19

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,228
Website

Re: Four Squares Reborn

Why is my code wrong?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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