A programming language for mathematical calculations?

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What do you think, what programming language is best to implement complex calculations (financial and actuarial mathematics, statistics).

I understand that for these purposes, collected super computers and HPC clusters, but all the same, which language to use is preferable in terms of the relatively weak processing power?

I think that the language should be functional, as this paradigm is the closest to pure mathematics, just as important, the possibility of clustering.


In General, anyone have any thoughts on this?

If anyone has experience writing such application I would be very grateful, if describe at least three words as you did.


Thank you!
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First, the paradigm of functional programming, just-just talking about how to write programs. The purpose of this paradigm is to formalize programs as mathematical functions.
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Of course, these are some big goals, someone thinks that is the only true way of programming, someone worships the paradigm as God. But these people, excuse me for such a rude statement — fools. The truth is "between". In other words, functional programming allows to make the code more compact, beautiful, fast, but using only this paradigm, ignoring the rest — only harm.

It is important to understand what is required of the language. As I see it, the only requirement is high speed with small resources will not grow(am I right?).
If it's so critical(the 100 and 1 time, rate task!), the choice is not great: C, C++.
If you want to partake of the functional paradigm, you can try Haskell, CL(Common Lisp). But I repeat, if the problem is the word "function", it does not mean that you need to use "functional programming".
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For statistics there is a special language of R. Cross-platform, open, with a bunch of libraries.
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Haskell.
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>>high speed with small resources
>>Yes, it is, but something I would like to get is the speed of development and elegance of code output (Yes, I like pretty things)
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C# + F# ?)
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I think that the language should be functional, as this paradigm is the closest to pure mathematics

I'd say if you want to do this mathematical calculations, it is necessary to think about the mathematical package such as Matlab. If You want to get concise code, with this there should be no problems. A huge number of standard functions of mathematics and statistics. With tolboxane Financial Derivatives Toolbox Financial Toolbox is not familiar, but the features list looks impressive.
The speed of computing with the right programming, according to my observations below, not more than 2 times (compared with C#, for example). You can use the compilers and to call functions in the Matlab from any language. However in this case, a significant disadvantage is the slow start the Matlab environment.
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