Σ & ∏

[yukulele]

I would like to be able to use the sum (Σ) or the product (∏)

like this

 10
  Σ  2⁻ⁿ cos(2ⁿ π x)
 k=0

Unfortunately math.sum() only allow to sum parameters or matrix terms.

I suggest to add a new signature for sum (and prod) if 3rd term is a function:

sum(initVal, endVal, callback)

example:

sum(0, 10, f(n) = 2^-n cos(2^n pi x))

[josdejong]

Thanks for your suggestion, it's an interesting idea.

Maybe it would be better to have the function as first argument:

sum(fn, start, end)

Because that is how you would read it aloud: "The sum of ... for k is 0 to 10".

Note that this function is just eye candy for:

sum(range(initVal, endVal)).map(callback)

So I'm not entirely sure it would add much. It reads very natural though, and with toTex we could output the correct math syntax for this expression.

EDIT: updated the example

[yukulele]

Note that this function is just eye candy for:

range(initVal, endVal).map(callback)

I guess it's more like this:

sum(range(initVal, endVal).map(callback))

It does the job! ...maybe a little verbose?

---

Maybe it would be better to have the function as first argument

not sure...

• visually, bound are place before expression in the Σ notation
• and it must be hard to read if the function is long:

sum(f(x) = 1^n * cos(3^n * pi * x), 0, 10)

a more explicit syntax might be:

sum(start to end, fn)
sum(0 to 10, f(x) = x^2)

[josdejong]

Ah, you're right, I forgot the sum(...) around range(), updated that now.

I guess the order is personal preference, I personally do not find it hard to read but that may be just me (knowing what to expect). It's not a strong preference though. I'm curious to hear what others like best. And maybe we can have a look at other math application to see what syntax they use.