int main( int argc, char *argv[] )
{
char err[2048]; /* command input and error string buffers */
MKernelVector kv; /* Maple kernel handle */
MCallBackVectorDesc cb = { textCallBack,
0, /* errorCallBack not used */
0, /* statusCallBack not used */
0, /* readLineCallBack not used */
0, /* redirectCallBack not used */
0, /* streamCallBack not used */
0, /* queryInterrupt not used */
0 /* callBackCallBack not used */
};
ALGEB r, l; /* Maple data-structures */
/* initialize Maple */
if( (kv=StartMaple(argc,argv,&cb,NULL,NULL,err)) == NULL ) {
printf("Fatal error, %s\n",err);
return( 1 );
}
/* example 1: find out where maple is installed */
r = MapleKernelOptions(kv,"mapledir",NULL);
if( IsMapleString(kv,r) )
printf("Maple directory = \"%s\"\n\n",MapleToString(kv,r));
/* example 2: compute an integral */
/* output goes through the textCallBack */
printf("Evaluate an integral: \n\t");
r = EvalMapleStatement(kv,"int(1/(x^4+1),x);");
/* example 3: assign x a value and reevaluate the integral */
MapleAssign(kv,
ToMapleName(kv,"x",TRUE),
ToMapleInteger(kv,0));
r = MapleEval(kv,r);
MapleALGEB_Printf(kv,"\nEvaluated at x=0, the integral is: %a\n",r);
/* example 4: create a list with 3 elements */
l = MapleListAlloc(kv,3);
MapleListAssign(kv,l,1,r);
MapleListAssign(kv,l,2,ToMapleBoolean(kv,1));
MapleListAssign(kv,l,3,ToMapleFloat(kv,3.14));
MapleALGEB_Printf(kv,"\nHere's the list: %a\n",l);
return( 0 );
}
int
aks (mpz_t n)
{
mpz_t r;
mpz_t a;
mpz_t max_a;
mpz_t gcd_rslt;
mpz_t totient_r;
mpf_t ftotient_r;
mpf_t sqrt_rslt;
mpf_t sqrt_rslt2;
mpf_t temp;
mpf_t temp2;
sli_t logn;
/* For the sake of maple kernel */
int argc = 0;
char **argv;
char err[2048];
mpz_init (r);
mpz_init (a);
mpz_init (max_a);
mpz_init (gcd_rslt);
mpz_init (totient_r);
mpf_init (ftotient_r);
mpf_init (sqrt_rslt);
mpf_init (sqrt_rslt2);
mpf_init (temp);
mpf_init (temp2);
/* 1. If (n = a^k for a in N and b > 1) output COMPOSITE */
if (mpz_perfect_power_p (n) != 0)
{
printf ("Step 1 detected composite\n");
return FALSE;
}
/* 2. Find the smallest r such that or(n) > 4(log n)^2 */
find_smallest_r (r, n);
gmp_printf ("good r seems to be %Zd\n", r);
/* 3. If 1 < gcd(a, n) < n for some a <= r, output COMPOSITE */
/* for (a = 1; a <= r; a++) {
* gcd_rslt = gcd(a, n);
* if (gcd_rslt > 1 && gcd_rslt < n) {
* return FALSE;
* }
* }
*/
for (mpz_set_ui (a, 1);
mpz_cmp (a, r) < 0 || mpz_cmp (a, r) == 0; mpz_add_ui (a, a, 1))
{
mpz_gcd (gcd_rslt, a, n);
if (mpz_cmp_ui (gcd_rslt, 1) > 0 && mpz_cmp (gcd_rslt, n) < 0)
{
printf ("Step 3 detected composite\n");
return FALSE;
}
}
/* 4. If n <= r, output PRIME */
if (mpz_cmp (n, r) < 0 || mpz_cmp (n, r) == 0)
{
printf ("Step 4 detected prime\n");
return TRUE;
}
/* 5. For a = 1 to floor(2*sqrt(totient(r))*(log n)
* if ( (X+a)^n != X^n + a (mod X^r-1, n) ), output COMPOSITE
*
* Choices of implementation to evaluate the polynomial equality:
* (1) Implement powermodreduce on polynomial ourselves (tough manly way)
* (2) Use MAPLE (not so manly, but less painful)
*/
/* Compute totient(r), since r is prime, this is simply r-1 */
mpz_sub_ui (totient_r, r, 1);
/* Compute log n (ceilinged) */
mpz_logbase2cl (&logn, n);
/* Compute sqrt(totient(r)) */
mpf_set_z (ftotient_r, totient_r);
mpf_sqrt (sqrt_rslt, ftotient_r);
/* Compute 2*sqrt(totient(r)) */
mpf_mul_ui (sqrt_rslt2, sqrt_rslt, 2);
/* Compute 2*sqrt(totient(r))*(log n) */
mpf_set (temp, sqrt_rslt2);
mpf_set_si (temp2, logn);
mpf_mul (temp, temp, temp2);
/* Finally, compute max_a, after lots of singing and dancing */
mpf_floor (temp, temp);
mpz_set_f (max_a, temp);
gmp_printf ("max_a = %Zd\n", max_a);
/* Now evaluate the polynomial equality with the help of maple kernel */
/* Set up maple kernel incantations */
MKernelVector kv;
MCallBackVectorDesc cb = { textCallBack,
0, /* errorCallBack not used */
0, /* statusCallBack not used */
0, /* readLineCallBack not used */
0, /* redirectCallBack not used */
0, /* streamCallBack not used */
0, /* queryInterrupt not used */
0 /* callBackCallBack not used */
};
/* Initialize Maple */
if ((kv = StartMaple (argc, argv, &cb, NULL, NULL, err)) == NULL)
{
printf ("Could not start Maple, %s\n", err);
exit (666);
}
/* Here comes the complexity and bottleneck */
/* for (a = 1; a <= max_a; a++) {
* if (!poly_eq_holds(kv, a, n, r)) {
* return FALSE;
* }
* }
*/
/* Make max_a only up to 5 */
mpz_set_ui (max_a, 5);
for (mpz_set_ui (a, 1);
mpz_cmp (a, max_a) < 0 || mpz_cmp (a, max_a) == 0;
mpz_add_ui (a, a, 1))
{
if (!poly_eq_holds (kv, a, n, r))
{
printf ("Step 5 detected composite\n");
return FALSE;
}
}
/* 6. Output PRIME */
printf ("Step 6 detected prime\n");
return TRUE;
}
