Four Squares Reborn

bobbym · 2014-03-02 02:08:12

Do you understand what a pure function is?

Agnishom · 2014-03-02 02:19:51

Do LISP programmers call it a lambda function? It is an anonymous function

bobbym · 2014-03-02 02:21:35

Yes, that is exactly correct. It is borrowed from the Lambda Calculus.

M uses a slot # and a & to make one.

Agnishom · 2014-03-02 02:29:28

Lambda Calculus?

I do not understand the # and & part, it looks very creepy. Please illustrate

bobbym · 2014-03-02 02:31:52

It is used right here:

FindInstance[a^2 + b^2 + c^2 + d^2 == n, {a, b, c, d}, 
      Integers, RandomSeed -> #]& /@ Range[20];

But there is one more thing before we get to it...

Agnishom · 2014-03-02 02:38:09

yes?

bobbym · 2014-03-02 02:39:33

M uses options to enhance the commands. They are put in like this

(Name of the option) -> value, usually at the end of the command.

Agnishom · 2014-03-02 02:47:12

Yes, I have seen that. There are a lot of options in the commands that do Interactive things

bobbym · 2014-03-02 02:49:49

FindInstance[a^2 + b^2 + c^2 + d^2 == n, {a, b, c, d}, 
      Integers, RandomSeed -> #]& /@ Range[20];

FindInstance uses random methods to arrive at answers as well as all known math methods. Because it sometimes has to use random numbers it requires a seed. Do you know what a random seed?

Agnishom · 2014-03-02 03:17:09

I think it is a number which is used to intiatalise a PRNG

bobbym · 2014-03-02 03:23:18

That is correct so instead of doing

FindInstance[a^2 + b^2 + c^2 + d^2 == n, {a, b, c, d},Integers, RandomSeed -> 1]

FindInstance[a^2 + b^2 + c^2 + d^2 == n, {a, b, c, d},Integers, RandomSeed -> 2]

FindInstance[a^2 + b^2 + c^2 + d^2 == n, {a, b, c, d},Integers, RandomSeed -> 3]
.
.
.
FindInstance[a^2 + b^2 + c^2 + d^2 == n, {a, b, c, d},Integers, RandomSeed -> 20]

to get 20 different seeds ( remember we want 20 different answers and hope that if he starts from different seeds he will get a different answer). We map the slot operator # to {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} which does the above but without all the work of writing that.

Agnishom · 2014-03-02 03:29:53

Why do you have to supply the seed manually?

bobbym · 2014-03-02 03:33:55

Because the seed could be anything, how can M know which one I want?

Agnishom · 2014-03-02 04:34:45

What is this?

ans = Union[Flatten[ans, 1]];

bobbym · 2014-03-02 14:35:23

Flatten removes all dimensionality and returns a list. Union is the same as the mathematical set command.

Agnishom · 2014-03-02 15:17:13

What would the output look like without that command?

bobbym · 2014-03-02 15:20:43

Quite confusing. Generally the Flatten command does this,

Flatten[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}]

{1, 2, 3, 4, 5, 6, 7, 8, 9}

notice all list brackets were destroyed and the matrix is flattened into a list.

Agnishom · 2014-03-02 15:37:20

WHy did you use it in that code?

bobbym · 2014-03-02 15:39:49

I wanted to make sure the Union command and the Length command would work correctly.

Agnishom · 2014-03-02 15:46:28

Can we do this instead?

square4[n_] := 
 Block[{ans}, 
  ans = FindInstance[a^2 + b^2 + c^2 + d^2 == n, {a, b, c, d}, 
      Integers, RandomSeed -> #]& /@ Range[200,220];
  ans = Union[Flatten[ans, 1]];
  If[Length[ans] == 20, {a, b, c, d} /. ans]]

bobbym · 2014-03-02 15:48:47

We sure could but is it anymore correct then what I have done? I mean, we are still gambling that 20 different seeds will coax FindInstance to get the 20 different answers we require.

Agnishom · 2014-03-02 15:51:29

I was just asking.

bobbym · 2014-03-02 15:54:27

It will run if that is what you mean and get the correct answer.

Agnishom · 2014-03-02 16:08:28

Okay, May I ask you a question that you'll not enjoy answering?

bobbym · 2014-03-02 16:11:02

Hmmm, I am afraid to ask. What is the question?

Math Is Fun Forum

#51 2014-03-02 02:08:12

Re: Four Squares Reborn

#52 2014-03-02 02:19:51

Re: Four Squares Reborn

#53 2014-03-02 02:21:35

Re: Four Squares Reborn

#54 2014-03-02 02:29:28

Re: Four Squares Reborn

#55 2014-03-02 02:31:52

Re: Four Squares Reborn

#56 2014-03-02 02:38:09

Re: Four Squares Reborn

#57 2014-03-02 02:39:33

Re: Four Squares Reborn

#58 2014-03-02 02:47:12

Re: Four Squares Reborn

#59 2014-03-02 02:49:49

Re: Four Squares Reborn

#60 2014-03-02 03:17:09

Re: Four Squares Reborn

#61 2014-03-02 03:23:18

Re: Four Squares Reborn

#62 2014-03-02 03:29:53

Re: Four Squares Reborn

#63 2014-03-02 03:33:55

Re: Four Squares Reborn

#64 2014-03-02 04:34:45

Re: Four Squares Reborn

#65 2014-03-02 14:35:23

Re: Four Squares Reborn

#66 2014-03-02 15:17:13

Re: Four Squares Reborn

#67 2014-03-02 15:20:43

Re: Four Squares Reborn

#68 2014-03-02 15:37:20

Re: Four Squares Reborn

#69 2014-03-02 15:39:49

Re: Four Squares Reborn

#70 2014-03-02 15:46:28

Re: Four Squares Reborn

#71 2014-03-02 15:48:47

Re: Four Squares Reborn

#72 2014-03-02 15:51:29

Re: Four Squares Reborn

#73 2014-03-02 15:54:27

Re: Four Squares Reborn

#74 2014-03-02 16:08:28

Re: Four Squares Reborn

#75 2014-03-02 16:11:02

Re: Four Squares Reborn

Board footer