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Factoring of addition?

  1. Mar 25, 2004 #1
    "Factoring" of addition?

    Is there a name for "factoring" addition? For example....let's say I'm working in a basis of all integers greater than 3. I can make 7 from 3+4; 8 from 4+4 or 3+5; 9 from 3+3+3 or 4+5 or 6+3.......

    Is there a name for this? And if so...are there computer programs that will generate these sets for me?
     
  2. jcsd
  3. Mar 26, 2004 #2

    matt grime

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    Science Advisor
    Homework Helper

    Look up partition functions.
     
  4. Apr 9, 2004 #3

    pig

    User Avatar

    try this

    Code (Text):

    #include <stdio.h>

    #define LOWEST 3

    int n, c[1024];
    FILE *out;

    void add (int pos, int a, int sum) {
        int i;
        c[pos]=a;
        if (sum>n) return;
        if (sum==n) {
            for (i=0;i<=pos;i++) fprintf(out, "%d ", c[i]);
            fprintf(out, "\n");
            return;
        }
        for (i=a;i>=LOWEST;i--) add(pos+1, i, sum+i);
    }

    int main () {
        int i;
        printf("n: ");
        scanf("%d", &n);
        out=fopen("results.txt", "wt");
        for (i=n-LOWEST;i>=LOWEST;i--) add(0, i, i);
        fclose(out);
        return 0;
    }
     
    this is very slow, i'll try to think of a way to make it faster.

    if source code is not allowed in the math forum, i am sorry, delete the post.
     
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