discrete-mathematics

I am looking for a method to compute a derivative using a discrete and fast method. Since now I do not know the type of equation I have, I am looking for discrete methods analog to the ones that we can find for the integral such as, the Euler method. Andrea Ambu I think you are looking for the derivative calculated in a point. If this is the case, here there is a simple way to do that. You need to know the derivative in a point, say a . It is given by the limit of the difference quotient for h->0: You actually need to implement the limit function. So you: Define an epsilon, set it more small

I'm trying to write a piece of code that can automatically factor an expression. For example, if I have two lists [1,2,3,4] and [2,3,5], the code should be able to find the common elements in the two lists, [2,3], and combine the rest of the elements together in a new list, being [1,4,5]. From this post: How to find list intersection? I see that the common elements can be found by set([1,2,3,4]&set([2,3,5]). Is there an easy way to retrieve non-common elements from each list, in my example being [1,4] and [5]? I can go ahead and do a for loop: lists = [[1,2,3,4],[2,3,5]] conCommon = [] common

I use the following function to calculate log base 2 for integers: public static int log2(int n){ if(n <= 0) throw new IllegalArgumentException(); return 31 - Integer.numberOfLeadingZeros(n); } Does it have optimal performance? Does someone know ready J2SE API function for that purpose? UPD1 Surprisingly for me, float point arithmetics appears to be faster than integer arithmetics. UPD2 Due to comments I will conduct more detailed investigation. UPD3 My integer arithmetic function is 10 times faster than Math.log(n)/Math.log(2). If you are thinking about using floating-point to help with

I saw this algorithm that will take numbers or words and find all possible combinations And I'm using it, but it does NOT return all "real" combinations. PHP: <?php require_once 'Math/Combinatorics.php'; $words = array('cat', 'dog', 'fish'); $combinatorics = new Math_Combinatorics; foreach($combinatorics->permutations($words, 2) as $p) { echo join(' ', $p), "\n"; } ?> And it returns: cat dog dog cat cat fish fish cat dog fish fish dog But these are not all real combinations, all real combinations includes these too: cat cat dog dog fish fish And that is what I need, the method to get all real