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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

How do you get the first 100 squares with your favorite language?

In J, it's simple:

`(1+i.100)^2`

Range[100]^2 in Mm?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Hi;

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Functional programming is very powerful once we get a hang of it.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

I agree, I am hoping I can convince Agnishom of 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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Anybody will, once they realize how compact the code can get!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Yes, he is a very bright guy and luckily he does not have lots of years of programming in procedural languages to make it difficult.

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

That's right.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Did you see the new problem in Bafflers?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Yes, I was trying a way to use only the formulas for sector and square, could not proceed that way.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Oh okay, you will get it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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bobbym wrote:

How do you get the first 100 squares with your favorite language?

Python Code:

`for i in xrange(1,101): print i**2`

Functional Way (Python):

`map(lambda x: x**2,xrange(1,101))`

Maxima Code:

`for a: 1 thru 100 do display(a^2);`

Functional Way (Maxima):

`makelist(k^2,k,1,100);`

Mathematica Code:

`Function[x,x^2] /@ Range[1,100]`

or

`Map[Function[x,x^2],Range[1,100]]`

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Simpler is Range[100]^2.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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But that is a matrix operation of which I know nothing.

he does not have lots of years of programming in procedural languages to make it difficult.

I've got atleast 7 years of Procedural experience.

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Nope, that is not a matrix operation. You are thinking it is like m x m but it is not.

Range[100] generates a list from1 to 100. Range[100]^2 means square every element of the list. This is why loops are unnecessary. In functional languages commands work on entire lists as if they were single objects. This is more readable and saves the programmer the details of indexing an array.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

Range[100]^2 means Range[100] multiplied with Range[100]. Which is multiplying the matrix [1,2,3,...100] with the matrix [1,2,3,...100]. That is how it works.

'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

**Online**

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

It is not a matrix, it is a list. Let me illustrate.

What do you think Range[10]^(1/2) does?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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If you are thinking that InsertSomeFunction[Range[100]] is the same as InsertSomeFunction /@ Range[100] then you are wrong.

Proof. Assume the contrary.

See this counterexample: there is a difference between Speak[Range[100]] is not the same as Speak /@ Range[100]

It works in the other case because it is a matrix operation.

What do you think Range[10]^(1/2) does?

It multiplies the matrix {1,2,3,4,5,6,7,8,9,10} with the constant 1/2

*Last edited by Agnishom (2014-03-02 01:37:32)*

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

It is not a matrix, it is a list. Let me illustrate.

What do you think Range[10]^(1/2) does?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

What do you think Range[10]^(1/2) does?

It multiplies the matrix {1,2,3,4,5,6,7,8,9,10} with the constant 1/2

A matrix and a list is the same thing

*Last edited by Agnishom (2014-03-02 01:40:22)*

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

That is incorrect.

`Range[10]^(1/2)`

`Range[10]^n`

See how it was mapped to each element. Single brackets are lists.

`Sin[Range[10]]`

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

That is incorrect.

Sorry, I meant that it raises the matrix {1,2,3,4,5,6,7,8,9,10} to the power 0.5

Then why isn't Speak[Range[100]] and Speak /@ Range[100] the same?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Speak does that because it treats the argument as a string. Just reading what it sees. Because for most functions have the attribute called listable. That means that they map themselves over lists.

{1,2,3,4,5,6,7,8,9,10} is not a matrix, it is a list. In M, matrices are lists inside of lists. {{1,2,3},{4,5,6},{7,8,9}} that is a matrix. You see, in M everything is a list just like lisp.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Is it okay to say that for any list L, f[L] does the same thing as f /@ L?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Yes, in all cases that I have seen that will be true. The \@ means map. Just like a mapping in mathematics. It maps the function f onto all the elements of the list.

Please do not get confused here. In M, the list is used to represent vectors, matrices, sets, and arrays. It depends on the context and what commands you are using afterward whether you are speaking of a list or a vector.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

Okay, can we get back to explaining that code?

'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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