/* =========================================

   Filename:  integer.c
   Filedate:  January 17, 2006

   This program treats integers as eqivalence classes
   of natural numbers. 

   =========================================  */

#include<stdio.h>
#include<stdlib.h>


struct myinteger {

  long a;
  long b;

};

int is_equal(struct myinteger x, struct myinteger y);
int is_less(struct myinteger x, struct myinteger y);
int is_less_equal(struct myinteger x, struct myinteger y);
struct myinteger sum_up(struct myinteger x, struct myinteger y);
struct myinteger multiply(struct myinteger x, struct myinteger y);
void printbig(struct myinteger x);

int is_equal(struct myinteger x, struct myinteger y) {
  if (x.a + y.b == x.b +y.a) {
    return(1);
  }
  else {
    return(0);
  }
}

int is_less(struct myinteger x, struct myinteger y) {
  if (x.a + y.b < x.b + y.a) {
    return(1);
  }
  else {
    return(0);
  }
}

int is_less_equal(struct myinteger x, struct myinteger y) {
  if (x.a + y.b <= x.b + y.a) {
    return(1);
  }
  else {
    return(0);
  }
}

struct myinteger sum_up(struct myinteger x, struct myinteger y) {
  struct myinteger z;
  z.a = x.a + y.a;
  z.b = x.b + y.b;
  return(z);
}

struct myinteger multiply(struct myinteger x, struct myinteger y) {
  struct myinteger z;
  z.a = x.a * y.a + x.b*y.b;
  z.b = x.a * y.b + x.b*y.a;
  return(z);
}

void printbig(struct myinteger x) {
  printf("<(%ld, %ld)>", x.a, x.b);
}

/*  =====   Main  ======  */ 

int main() {

  long i,j;

  struct myinteger integer_1;
  struct myinteger integer_2;
  struct myinteger integer_3;
  struct myinteger integer_4;
  struct myinteger integer_5;

  printf("Give a value a for the assets of your first integer.\n");
  scanf("%ld", &integer_1.a);
  printf("Give a value b for the liabilities of your first integer.\n");
  scanf("%ld", &integer_1.b);
  printf("Give a value a for the assets of your second integer.\n");
  scanf("%ld", &integer_2.a);
  printf("Give a value b for the liabilities of your second integer.\n");
  scanf("%ld", &integer_2.b);

  if (is_equal (integer_1,integer_2)) {
    printf("The first integer is equal to the second.\n\n");
  }
  else {
    printf("The first integer is NOT equal to the second.\n\n");
  }
  if (is_less(integer_1,integer_2)) {
    printf("The first integer is less than the second.\n\n");
  }
  else {
    printf("The first integer is NOT less than the second.\n\n");
  }
  if (is_less_equal (integer_1,integer_2)) {
    printf("The first integer is less equal the second.\n\n");
  }
  else {
    printf("The first integer is NOT less equal the second.\n\n");
  }
  
  integer_3 = sum_up(integer_1, integer_2);
  printf("The sum of your integers is ");
  printbig(integer_3);
  printf("\n\n");
  integer_4 = multiply(integer_1, integer_2);
  printf("The product of your integers is ");
  printbig(integer_4);
  printf("\n\n");

  i = integer_1.a-integer_1.b;
  j = integer_2.a-integer_2.b;

  printf("As a check, the first integer you input\n");
  printf("can be written more compactly as %ld\n", i);
  printf("Also, the second integer you input\n");
  printf("can be written as %ld\n", j);
  printf("\n");
  printf("So the sum is %ld\n", i+j);
  printf("\n");
  printf("And the product is %ld\n", i*j);
  printf("\n");
  i = integer_3.a;
  j = integer_3.b;
  printf("Note that %ld minus %ld is %ld\n\n", i, j, i-j);
  i = integer_4.a;
  j = integer_4.b;
  printf("Also, note that %ld minus %ld is %ld\n\n", i, j, i-j);

  return(0);
}