;;;; modular-arithmatic-tables.lisp
;;;;
;;;; Copyright (c) 2016 Samuel W. Flint <swflint@flintfam.org>

(defpackage #:mod-arithmatic
  (:use #:cl)
  (:export :print-tables-z_n
           :make-z_n-tables))


(in-package #:mod-arithmatic)

;;; "mod-arithmatic" goes here.

(defun euclid-gcd (a b)
  (check-type a integer)
  (check-type b integer)
  (cond
    ((zerop b)
     a)
    ((= a b)
     a)
    ((< a b)
     (euclid-gcd b a))
    (t
     (euclid-gcd b (mod a b)))))

(defun z_n-divisors (n)
  (remove-if (lambda (x)
               (not (= 1 (euclid-gcd x n))))
             (loop for i from 1 to (1- n) collect i)))

(defun z_n-addition-table (n)
  (loop for i from 0 to (1- n)
     collect (loop for j from 0 to (1- n)
                collect (mod (+ i j) n))))

(defun z_n-multiplication-table (n)
  (loop for i from 0 to (1- n)
     collect (loop for j from 0 to (1- n)
                collect (mod (* i j) n))))

(defun print-z_n-addition-table (n stream)
  (format stream "~{~{~4d~}~&~}" (z_n-addition-table n)))

(defun print-z_n-multiplication-table (n stream)
  (format stream "~{~{~4d~}~&~}" (z_n-multiplication-table n)))

(defun print-tables-z_n (n stream)
  (check-type n integer)
  (format stream "Addition Table (Z_~d):~%" n)
  (print-z_n-addition-table n stream)
  (format stream "~&~%Multiplication Table (Z_~d):~%" n)
  (print-z_n-multiplication-table n stream)
  (format stream "~&~%Divisors in Z_~d:~&" n)
  (format stream "~{~a~^, ~}" (z_n-divisors n)))

(defun make-z_n-tables (n filename)
  (with-open-file (output filename
                          :direction :output
                          :if-exists :overwrite
                          :if-does-not-exist :create)
    (print-tables-z_n n output)))

;;; End mod-arithmatic