KANT

\ KASH (KANT Shell) program: Class number computation
\ Computes the class group of a quadratic number field Q(sqrt(d))

\ Create the polynomial ring over the integers
_<x> := PolynomialRing(Integers());

\ Define the minimal polynomial for Q(sqrt(-23))
f := x^2 + 23;

\ Create the number field
K := NumberField(f);

\ Compute its ring of integers (maximal order)
OK := MaximalOrder(K);

\ Compute the class group
CG := ClassGroup(OK);

\ Print results
Print("Number field: Q(sqrt(-23))\n");
Print("Discriminant: ", Discriminant(OK), "\n");
Print("Class group: ", CG, "\n");
Print("Class number: ", #CG, "\n");