On Tue, 25 Mar 2014 05:09:20 -0700, Rustom Mody wrote:
> Two completely separate questions
>
> 1. Symbols outside of US-104-keyboard/ASCII used for python
> functions/constants
> 2. Non-linear math notation
>
> It goes back not just to the first programming languages but to Turing's
> paper that what a mathematician can do on 2-d paper can be done on a 1-d
> 'tape'. IOW conflating 1 and 2 is not even a poor strawman argument --
> Its only 1 that anyone is talking about.
Not so. Mark Harris said:
[quote]
But what if python had a math symbols extension so that universal
mathematics could be written the way we do it on a black|board,
er, I mean white|board?
I think that's pretty explicit that he's talking about writing
mathematical code the way mathematicians write mathematics.
Antoon Pardon referred to borrowing the symbols used in mathematics. But
the point is that the symbols come with notation: - (minus) can be prefix
unary operator or a infix binary operator. ∑ (summation) is a quaternary
operator, it takes four arguments: a variable name, a lower limit, an
upper limit, and an expression. To be true to the mathematical notation,
we ought to write it the way mathematicians do.
The thing is, we can't just create a ∑ function, because it doesn't work
the way the summation operator works. The problem is that we would want
syntactic support, so we could write something like this:
p = 2
∑(n, 1, 10, n**p)
This cannot be an ordinary function, because if it were, the n**p
expression would be evaluated before passing the result to the function.
We want it to delay evaluation, like a list comp:
[n**p for n in range(1, 11)]
the expression n**p gets evaluated inside the list comp. That cannot be
written as a function either:
list_comp(n**p, n, range(1, 11))
Mark's idea of a maths blackboard is not ridiculous. That's what
Mathematica does. To enter a sum like the above in Mathematica, you can
enter:
ESC sum ESC Ctrl+$ n=1 Ctrl+% 10 Ctrl+Space n^p
to give you the summation
10
∑ n**p
n=1
Obviously this requires a custom editor.
https://reference.wolfram.com/mathematica/tutorial/EnteringTwoDimensionalInput.html
But Mathematica is a specialist system for doing mathematics, not a
general purpose language like Python. Of course one could *write* a
Mathematica-like system in Python, and I expect that Sage may even have
something like this (if it doesn't, it could) but one shouldn't hammer
the specialised round peg of complex mathematical notation into the
square peg of a general purpose programming language.
--
Steven D'Aprano
http://import-that.dreamwidth.org/
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