polynomial multiplication

use poly ADT:

#include <stdio.h>
#include <stdlib.h>
#define MAX_DEGREE  9999

struct polynomial
{
    int coeff_array[MAX_DEGREE];
    int maxpower;
};
typedef struct polynomial *ptr_to_poly;
typedef ptr_to_poly poly;


void zero_polynomial(poly p)
{
    int i;
    for(i=MAX_DEGREE;i>=0;i--)
    {
        p->coeff_array[i]=0;
    }

    p->maxpower=0;
}

poly add_polynomial(const poly p1,const poly p2)
{
    poly sum=malloc(sizeof(struct polynomial));
    zero_polynomial(sum);
    if(p1->maxpower>p2->maxpower)
    {
        sum->maxpower=p1->maxpower;
    }
    else
    {
        sum->maxpower=p2->maxpower;
    }

    int i;
    for(i=sum->maxpower;i>=0;i--)
    {
        sum->coeff_array[i]=p1->coeff_array[i]+p2->coeff_array[i];
    }
    return sum;
}

poly multiply(const poly p1,const poly p2)
{
    poly res=malloc(sizeof(struct polynomial));
    zero_polynomial(res);
    res->maxpower=p1->maxpower+p2->maxpower;

    int i,j;
    for(i=0;i<=p1->maxpower;i++)
    {
        for(j=0;j<=p2->maxpower;j++)
        {
            res->coeff_array[i+j]+=p1->coeff_array[i]*p2->coeff_array[j];
        }
    }
    return res;
}

void print_poly(poly p)
{
    int i;
    printf("%d*X(%d)",p->coeff_array[p->maxpower],p->maxpower);
    for(i=p->maxpower-1;i>=0;i--)
    {
        if(p->coeff_array[i]!=0)
        {
            printf("+%d*X(%d)",p->coeff_array[i],i);
        }
    }
    printf("\n");
}

int main()
{
    poly p1=malloc(sizeof(struct polynomial));
    poly p2=malloc(sizeof(struct polynomial));
    zero_polynomial(p1);
    zero_polynomial(p2);
    p1->maxpower=9;
    p1->coeff_array[9]=9;
    p1->coeff_array[8]=8;

    p2->maxpower=9;
    p2->coeff_array[9]=9;
    p2->coeff_array[8]=8;
    print_poly(p1);
    print_poly(p2);
    poly p3=add_polynomial(p1,p2);
    print_poly(p3);
    poly p4=multiply(p1,p2);
    print_poly(p4);
    return 0;
}