Omnimaga
General Discussion => Other Discussions => Math and Science => Topic started by: Munchor on January 24, 2011, 09:42:18 am
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Hello everybody,
I know the basics of factorials:
5! = 5*4*3*2*1 = 120
However, I do not know about negative numbers and how to use them in calculus and what they are useful for.
I know floats won't work ;D
Can someone tell me some more about them?
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Negative factorials do not work, apparently. But also keep in mind that 0!=1
*As a side note, I am working on making a way to find things like 3.1! :D That will take a few years of playing with numbers, though.
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Xeda, I'm not sure the factorial operation is defined for decimals. Isn't it just the product of all positive integers less than or equal to a number N?
Even if you do extend the definition to decimals, as I did in below screenshot, it still gives you odd results.
(http://img.removedfromgame.com/imgs/Example.gif)
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Ah, but I came up with a way to find the sum of, say, X^2 from 3.1 to 4.6.
(2X^3+3X^2+X)/6
Just plug in 4.6 and 3.1
I've been working with Pascals Triangle and I have methods of defining nCr in terms of sums as opposed to factorials. It is going to be a VERY complicated process, but I am working on a method to find, say 3.1 C 4.2
Believe me, it is a really messed up, convoluted process that doesn't use 3.1*2.1*1.1. Many mathematicians have done similar things and they started with an easy, finite equation and resulted in an infinite equation when they applied decimals.
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Might I interest you in the Gamma function?
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You may...
Also note that I do a lot of things just for fun and so that I can figure it out... I've also done work that leads to the Zeta functions.
So about this Gamma function...
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The gamma function gives out the same answers as the Factorial function, but works for all Real and Complex numbers :)
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ooooh! That sounds very nice! When I get back from my classes I'll have to check out Wolfram... For now, I have to go :'(
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Just know that Omnicalc has a build in Gamma function :D
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Oh yeah, I'd forgotten about the Gamma function :P
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Hmm, Omnicalc has proven quite useful for that kind of thing. I always seem to think of it as a sprite program and whatnot, but then again, I started using it before I appreciated all the math functions.
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A small caveat to the gamma function: it still does not take negative integers.
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Ah, so there is still something for me to figure out :D
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The wikiedpia article on factorials (http://en.wikipedia.org/wiki/Factorial#Non-extendability_to_negative_integers) maybe be an enjoyable read if you're in to this sort of stuff. The link I posted is specifically talking about some negative stuff.
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Maybe I should have rephrased a bit differently: The gamma function for positive integers follows the following property: gamma(x)=(x-1)!. Hence gamma(1)=0!=1, for instance.
However, what is gamma(0)? It would equal to (-1)!. But using the factorial recurrence formula would give us 0(-1)!=0!=1. In other words, (-1)! = 1/0. This is bad; hence, (-1)! is not defined, and so is gamma(0).
Most other numbers still have a gamma function attached to it, for example gamma(-1/2), gamma(3+4i), and gamma(1337.42i), but zero and negative numbers when plugged into gamma generate an undefined result, because their respective factorials are undefined as well.
EDIT: Aw darn, sniped
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Maybe I should have rephrased a bit differently: The gamma function for positive integers follows the following property: gamma(x)=(x-1)!. Hence gamma(1)=0!=1, for instance.
However, what is gamma(0)? It would equal to (-1)!. But using the factorial recurrence formula would give us 0(-1)!=0!=1. In other words, (-1)! = 1/0. This is bad; hence, (-1)! is not defined, and so is gamma(0).
Most other numbers still have a gamma function attached to it, for example gamma(-1/2), gamma(3+4i), and gamma(1337.42i), but zero and negative numbers when plugged into gamma generate an undefined result, because their respective factorials are undefined as well.
EDIT: Aw darn, sniped
We prefer to say you got ninja'd, but yes. yes you did. ;-)
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Still, it's an interesting concept I hadn't thought about!
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def getFactorial(x):
if x == 0:
return 1
else:
soma = 1
for i in range(x,0,-1):
soma=soma*i
return soma
I just made a Python function that gets the factorial of a n number.
A simpler way of doing this is:
import math
print math.factorial(x)
But mine is much cooler.
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Ah, but does it work like the gamma function?
(3.1)! is not the same as 3.1*2.1*1.1
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two ways in java, out of boredom:
public int factorial(int x){
if(x == 0)
return 1;
return x * factorial(x - 1);
}
public int factorial(int x){
int sum = x == 0 ? 1 : x;
for(int i = x; --i > 0;)
sum *= i;
return sum;
}
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Yet another cool way to compute factorials, this way is for factorials of very very large numbers without multi-precision containers.
No multiplication required ^-^
double sum=0;
for (int i=1; i<Max; i++) {
sum += log(i);
}
int exponent = floor(sum);
double coeff = Pow(10,sum-exponent);
print("Answer is: ",coeff,"x10^",exponent);
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Cool, is there a TI-BASIC representation of that?! That looks really cool!
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Yeah, I actually use it in my program "MISCPRGM (http://www.ticalc.org/archives/files/fileinfo/408/40870.html)" if you want to see it. It can do up to 999! I think as long as you have enough memory.
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COOL! Awesome! Wow! (and a half)
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def getFactorial(x):
if x == 0:
return 1
else:
soma = 1
for i in range(x,0,-1):
soma=soma*i
return soma
I just made a Python function that gets the factorial of a n number.
A simpler way of doing this is:
import math
print math.factorial(x)
But mine is much cooler.
I note some variables names in maybe portuguese... Depending on the project I also code with names and comments in portuguese. ^^ Although I try to not mix 2 languages.
Yet another cool way to compute factorials, this way is for factorials of very very large numbers without multi-precision containers.
No multiplication required ^-^
double sum=0;
for (int i=1; i<Max; i++) {
sum += log(i);
}
int exponent = floor(sum);
double coeff = Pow(10,sum-exponent);
print("Answer is: ",coeff,"x10^",exponent);
Nice code, for some time I didn't see a trick like that. Where/How did you learn it?
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def getFactorial(x):
if x == 0:
return 1
else:
sum = 1
for i in range(x,0,-1):
sum =sum *i
return sum English Version
def calcularFactorial(x):
if x == 0:
return 1
else:
soma = 1
for i in range(x,0,-1):
soma = soma *i
return soma Portuguese Version
/OFFTOPIC: Galandros, do you know portuguese? Where are you from?
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Oh, you didn't need to correct the variables names. It was just an future advice. Sometimes I also end mixing different conventions.
I speak Portuguese. See your personal messages. ;)
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Oh, you didn't need to correct the variables names. It was just an future advice. Sometimes I also end mixing different conventions.
I speak Portuguese. See your personal messages. ;)
I don't usually mix, it's all in english, this challenges, however, were made for a portuguese website.