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die Multiplikation wird als Faltung definiert:
(a0,a1,a2,…)⋅(b0,b1,b2,…)(a0​,a1​,a2​,…)⋅(b0​,b1​,b2​,…):=(a0⋅b0,a0⋅b1+a1⋅b0,…,cn,…):=(a0​⋅b0​,a0​⋅b1​+a1​⋅b0​,…,cn​,…).
wobei für die n-te Komponente gilt: cn:=∑k=0nak⋅bn−kcn​:=k=0∑n​ak​⋅bn−k​

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#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <iostream>

using namespace std;


#define num(t) (int)(sizeof(t)/sizeof(t[0]))

double a[] = {1,0,2,0,0};
double b[] = {-1,3,-4,0,0};

int n = num(a);
int m = num(b);

double c[5];


int main()
{
    printf("sizes: a:%d b:%d\n", n,m);
    memset(c, 0, sizeof(c));
    cout << "a: ";
    for (auto x : a) {
        cout << " " << x ;
    }
    cout << endl;
    cout << "b: ";
    for (auto x : b) {
        cout << " " << x;
    }
    cout << endl;


    for(int n=0; n<=5; n++) {
        for(int k=0; k<=n; k++) {
            c[n] = c[n] + a[k]*b[n-k];
        }
    }

    cout << "c=a*b: ";
    for (auto x : c) {
        cout << " " << x;
    }
    cout << endl;


    return 0;
}

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sizes: a:5 b:5
a:  1 0 2 0 0
b:  -1 3 -4 0 0
c=a*b:  -1 3 -6 6 -8