fix #5 loop optimization

fixed arguments modifying bug
added samples and samplebooks w/tests

docs/samples/combinatorics.lyng.md

@@ -0,0 +1,44 @@
+# Sample combinatorics calculations
+
+The trivial to start with, the factorialorial calculation:
+
+    fun factorial(n) {
+        if( n < 1 )
+            1
+        else {
+            var result = 1
+            var cnt = 2
+            while( cnt <= n ) result = result * cnt++
+        }
+    }
+
+Let's test it:
+    
+    assert(factorial(2) == 2)
+    assert(factorial(3) == 6)
+    assert(factorial(4) == 24)
+    assert(factorial(5) == 120)
+
+Now let's calculate _combination_, or the polynomial coefficient $C^n_k$. It is trivial also, the formulae is:
+
+$$C^n_k = \frac {n!} {k! (n-k)!} $$
+
+We can simplify it a little, as $ n ≥ k $, we can remove $k!$ from the fraction:
+
+$$C^n_k = \frac {(k+1)(k+1)...n} { (n-k)!} $$
+
+Now the code is much more effective:
+
+    fun C(n,k) {
+        var result = k+1
+        var ck = result + 1
+        while( ck <= n ) result *= ck++
+        result / factorial(n-k)
+    }
+
+    println(C(10,3))
+    assert( C(10, 3) == 120 )
+
+to be continued...
+
+