[edit] Numbers

[edit] Complex numbers

[edit] Argument

Principial value of argument of complex number in turns carg produces results in the range (-pi, pi] . It can be mapped to [0, 2*pi) by adding 2*pi to the negative values

carg_t(z):=
 block(
 [t],
 t:carg(z)/(2*%pi),  /* now in turns */
 if t<0 then t:t+1, /* map from (-1/2,1/2] to [0, 1) */
 return(t)
)$

[edit] Square root

Square root of complex number : $c s q r t (x + y * i) = s q r t ((r + x) / 2) + i * y / s q r t (2 * (r + x))$

gives principal value of square root : -Pi <arg<Pi

csqrt(z):=
 block(
  [t,w,re,im],
  t:abs(z)+realpart(z),
  if t>0 
   then (re:sqrt(t/2), im:imagpart(z)/sqrt(2*t))
   else  (im:abs(z), re:0),
  w:re+im*%i,
  return(w)
)$

[edit] Algorithms

[edit] Stack ( LIFO)

Stack implementation using list:

/* create stack */
stack:[1];
/* push on stack */
stack:endcons(2,stack);
stack:endcons(3,stack);
block
(
  loop,
  stack:delete(last(stack),stack), /* pop from stack */
  disp(stack), /* display */
  if is(not emptyp(stack)) then go(loop)
);
stack;