Taylor Series[HELP]

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Taylor Series[HELP]

Postby GabrielSilva » Fri May 24, 2013 1:50 am

blablablablablabla... (So... you know cos(x) = 1 - x^2/2! + x^4/4! - x^6/6!....; with this I'm trying to write a code to do this for me with a good nivel of precision...)

Here is my code!
Code: Select all
def juice(x):
    x = float(x)
    k = (-1.0)*x**2/d
    np = input("Nivel of precision: ")
    np = float(np)
    while d < (np):
        if d % 2 == 0:
            d = d*(d-1)   
        y = k*y + y            # I'm just feeling that my error is here!; I want to take the last sum to multiply it by the constant k...
        d = d + 1
    return y   

Could you give me some advice about this code? Please, don't post your code here, if you do this the fun is over..., I'm just seaching the way of think to solve this code.
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Joined: Mon May 20, 2013 12:20 am

Re: Taylor Series[HELP]

Postby casevh » Fri May 24, 2013 4:55 am

I'll offer a couple of suggestions.

I assume that "nivel" means the number of terms that you want to evaluate. I would prompt for "Nivel of precision" outside the function call and pass it as an argument.

Let's assume you are calculating the first four terms and that we are using ^ to mean exponentiation. Other than just using brute-force evaluation, you can re-write the polynomial as:

Code: Select all
Let k = -(x^2), then
cos(x) = 1 + k/2! + k^2/4! + k^3/6!
       = 1 + k/(2*1) + k^2/((4*3)*(2*1)) + k^3/((6*5)*(4*3)*(2*1))
       = 1 + k/(2*1) + k/(2*1) * k/(4*3) + k/(2*1) * k/(4*3) * k/(6*5)

It looks like you are using this approach. I think you'll need to remember the current approximation ( y ), the last term ( ?? ), and the value -(x^2). Each time through the loop, you need to update the last term using k and d.

Is this the level of suggestions you wanted?

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Re: Taylor Series[HELP]

Postby Mekire » Fri May 24, 2013 5:04 am

My first recommendation would be to use a for loop instead of a while loop. Something like:
Code: Select all
for i in xrange(2,prec*2+1,2):
Also if all you care about is the expansion then use the math module for the factorials. If you want to manually calculate your factorials then that should be written in a separate function.

Basically this can be one lined if you are stubborn enough (gets a bit ugly though).

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