? print("this is how to print")
this is how to print
? print("reading from a file")
reading from a file
? \rData/Aks/aks.gp
? aks(n,ver,r,s)=s=1;if(n==1,s=0;if(ver,print(n" is a unit")),if(n==2||n==3,if(ver,print(n" is prime")),if(n%2==0||n%3==0,s=0;if(ver,print(n" is composite")),if(ispower(n),s=0;if(ver,print(n" is a perfect power")),r=5;while(r<n,if(gcd(n,r)!=1,s=0;if(ver,print(n" is composite"));break);if(r>0.062*log(n)^2&&aks(r,0)&&aks((r-1)/2,0)&&n^2%r!=1,break);r++);if(s==1&&r<sqrt(n),if(ver,print("entered loop with r="r));for(a=1,floor(0.043*log(n)^2+10),if(Mod(Mod(1,n)*(x-a),Mod(1,n)*(x^r-1))^n!=Mod(Mod(1,n)*x,Mod(1,n)*(x^r-1))^n-Mod(Mod(a,n),Mod(1,n)*(x^r-1)),s=0;if(ver,print(n" is composite and "a" is a witness"));break)));if(s==1,if(ver,print(n" is prime")))))));s
? aks(12345,1)
12345 is composite
%1 = 0
? 2+3
%2 = 5
? a=[1,2,4]
%3 = [1, 2, 4]
? a[2]
%4 = 2
? a[3]
%5 = 4
? a[2]+a[3]
%6 = 6
? b=a=a
%7 = [1, 2, 4]
? b=a+a
%8 = [2, 4, 8]
? b
%9 = [2, 4, 8]
? b[1]
%10 = 2
? bezout(5,13)
%11 = [-5, 2, 1]
? ?bezout
bezout(x,y): gives a 3-dimensional row vector [u,v,d] such that d=gcd(x,y) 
and u*x+v*y=d.

? a=Mod(2,19)
%12 = Mod(2, 19)
? a^100
%13 = Mod(17, 19)
? a+1/a
%14 = Mod(12, 19)
? 1/a
%15 = Mod(10, 19)
? isprime(73732737)
%16 = 0
? factor(73732737)
%17 = 
[3 1]

[13 1]

[107 1]

[17669 1]

? for(n=1,10,print(n))
1
2
3
4
5
6
7
8
9
10
? for(n=1,10,s=n^2;print(s" is the square of "n))
1 is the square of 1
4 is the square of 2
9 is the square of 3
16 is the square of 4
25 is the square of 5
36 is the square of 6
49 is the square of 7
64 is the square of 8
81 is the square of 9
100 is the square of 10
? for(n=1,40,if(issquare(n,r),print(r" is the square root of "n)))
  ***   expected character: '&' instead of: for(n=1,40,if(issquare(n,
  ***   r),print(r" is the s
        ^--------------------
? for(n=1,40,if(issquare(n,&r),print(r" is the square root of "n)))
1 is the square root of 1
2 is the square root of 4
3 is the square root of 9
4 is the square root of 16
5 is the square root of 25
6 is the square root of 36
? for(n=1,20,if(issquare(n,&r),print(r" is the square root of "n),print(n" is not a perfect square)))

  ***   expected character: '"' instead of: ... not a perfect square)))
                                                                       ^
? for(n=1,20,if(issquare(n,&r),print(r" is the square root of "n),print(n" is not a perfect square))))

  ***   expected character: '"' instead of: ...not a perfect square))))
                                                                       ^
? for(n=1,20,if(issquare(n,&r),print(r" is the square root of "n),print(n" is not a perfect square"))))
  ***   Warning: unused characters: ).
1 is the square root of 1
2 is not a perfect square
3 is not a perfect square
2 is the square root of 4
5 is not a perfect square
6 is not a perfect square
7 is not a perfect square
8 is not a perfect square
3 is the square root of 9
10 is not a perfect square
11 is not a perfect square
12 is not a perfect square
13 is not a perfect square
14 is not a perfect square
15 is not a perfect square
4 is the square root of 16
17 is not a perfect square
18 is not a perfect square
19 is not a perfect square
20 is not a perfect square
? i=0;while(i<10,print(i);i++)
0
1
2
3
4
5
6
7
8
9
? \q
Goodbye!