Vectors

The following block creates a new vector storing the "roots of unity" without the imaginary component.

vector(float) roots;
integer i := 0;
float pi := 3.1415926, e := 2.7182818, sum1 := 0;
resize(roots, 8);  // new size is 8, with each element set to null
while (i < 8) {
  roots[i] := e ^ ((pi * i) / 4);
  i++;
}

It creates an empty vector, resizes it with resize, and assigns values to elements in the vector. The first element of the vector has index 0, the second index 1, and so forth. You can also add new elements to the end of a vector with the push_back operator, for example, push_back(roots, e^pi).

Here's a way to calculate the sum of the values of the roots vector:

i := 0;
while (i < size(roots)) {
  sum1 := sum1 + roots[i];
  i++;
}

The size operation returns the size of the vector. You can also loop through the elements of a vector using a for loop:

for (root in roots) {
  sum1 := sum1 + root;
}

The variable root is a new variable whose scope is restricted to the loop body. The first time through the loop, it is roots[0], the second time roots[1], and so forth. The loop stops when roots[n] is null or there are no more elements in roots.

Two other operations on vectors are useful. You can create a new vector with the new operation:

roots := new vector(float);

The old vector is automatically thrown away.