/* Magma Lecture 2 */

/* This is how you make a comment.  It is good to annotate your code with comments for those who have to read it. */





/* Let's begin by looking at some basic control structures. */

for i in [1..10] do
	i;
	end for;

/* We all know this will count to 10, right? */
/* So how would we do this using repeat or while? */

i := 0;
while i le 9 do
	i := i + 1;
	i;
	end while;

i := 0;
repeat
	i := i + 1;
	i;
	until i eq 10;

/* Note here a subtle difference.  After using the above while / repeat codes, i still exists. */
/* This is not so after the for loop.  For makes its own iterator i, which is deleted after the loop finishes.*/




/* More simple programs: */


c := 0;
for i in [1..10] do
	c := c + 1;
	end for;
c;


/* &&&&&&&&&&&&& */


c := 0;
ss := 100;
for i in [1..ss] do
	if i mod 2 eq 0 then
		c := c + 1;
		end if;
	end for;
c/ss;


/* &&&&&&&&&&&&& */


i := 0;
repeat
	i := i + 1;
	until i gt 10;
i;


/* &&&&&&&&&&&&& */


repeat
	i := Random(0,100);
	until i mod 20 eq 0;
i;




/* The program we wrote together in class */

for j in [1..100] do
	G := SymmetricGroup(j);
	c := 0;
	n := 100;
	ss := 100000;
	for i in [1..ss] do
		m := Random(G);
		if Order(m) mod 2 eq 0 then
			c := c + 1;
			end if;
		end for;
	RealField(5)!c/ss;
end for;

/* Results: as n->infinity, the fraction of elements of even order in Sn goes to 1. */






/* Writing output to a file. */

SetOutputFile("C:/Users/anotherghost/Documents/out.txt" : Overwrite := true);

for i in [1..10] do
	i;
	end for;

UnsetOutputFile();