Complexity

Markiyan Hirnyk — Mon, 16 Jan 2012 14:10:02 Z

The output of the showstat(isprime) command

isprime := proc(n)
local btor, nr, p, r;
   1   if not type(n,'integer') then
   2     if type(n,('complex')('numeric')) then
   3       error "argument must be an integer"
         else
   4       return 'isprime(n)'
         end if
       end if;
   5   if n < 2 then
   6     return false
       elif member(n,special_primes) then
   7     return true
       elif igcd(2305567963945518424753102147331756070,n) <> 1 then
   8     return false
       elif n < 10201 then
   9     return true
       elif igcd(8496969489233418110532339909187349965926062586648932736611545426342203893270769390909069477309509137509786917118668028861499333825097682386722983737962963066757674131126736578936440788157186969893730633113066478620448624949257324022627395437363639038752608166758661255956834630697220447512298848222228550062683786342519960225996301315945644470064720696621750477244528915927867113,n) <> 1 then
10     return false
       elif n < 1018081 then
11     return true
       else
12     r := gmp_isprime(n);
13     if not r or n 14       return r
         end if;
15     nr := igcd(408410100000,n-1);
16     nr := igcd(nr^5,n-1);
17     r := iquo(n-1,nr);
18     btor := modp(('power')(2,r),n);
19     if cyclotest(n,btor,2,r) = false or irem(nr,3) = 0 and cyclotest(n,btor,3,r) = false or irem(nr,5) = 0 and cyclotest(n,btor,5,r) = false or irem(nr,7) = 0 and cyclotest(n,btor,7,r) = false then
20       return false
         end if;
21     if isqrt(n)^2 = n then
22       return false
         end if;
23     for p from 3 while numtheory:-jacobi(p^2-4,n) <> -1 do
24       NULL
         end do;
25     return evalb(TraceModQF(p,n+1,n) = [2, p])
       end if
end proc
gives to understand the complexity of this.

PS. Look at ?CodeGeneration[C] to understand the capabilities of this package.

Alternative: call Maple via OpenMaple from you C program

Thomas Richard — Mon, 16 Jan 2012 18:36:15 Z

As the error message indicates, the isprime function is not available in C. And code generation does not cover Maple's internal procedures. You might consider the OpenMaple API instead. However, this requires Maple to be installed on the target computer.

MaplePrimes - answers and comments on Question, How can I use the isprime function in C?

Complexity

Alternative: call Maple via OpenMaple from you C program