/* ============================================================== */
/* file: ezgcd.dem   */

nolabels:true$
time:all$
/* this is the run for case 1 of ez gcd paper. */

 d:rat(u+y+1,y)$
 f:(-2+d)*(u+y+2)$
 g:d*(u^2-3*u*y^2-1)^2$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 d:rat(a+u+y+1,y)$
 f:(-2+d)*(a+u+y+2)$
 g:d*(u^2-3*u*y^2-1)^2$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 d:rat(b+a+u+y+1,y)$
 f:(-2+d)*(b+a+u+y+2)$
 g:d*(u^2-3*u*y^2-1)^2$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 d:rat(c+b+a+u+y+1,y)$
 f:(-2+d)*(c+b+a+u+y+2)$
 g:d*(u^2-3*u*y^2-1)^2$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);





/* this is the run for case 2. table 1 of ez gcd paper */

 n:2$
 d:z^n+y^n+1$
 f:rat(d*(z^n+y^n-2))$
 g:rat(d*(z^n+y^n+2))$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 n:3$
 d:z^n+x^n+y^n+1$
 f:rat(d*(z^n+x^n+y^n-2))$
 g:rat((z^n+x^n-y^n+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 n:4$
 d:a^n+z^n+x^n+y^n+1$
 f:rat(d*(a^n+z^n+x^n+y^n-2))$
 g:rat((a^n+z^n+x^n-y^n+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 n:5$
 d:b^n+a^n+z^n+x^n+y^n+1$
 f:rat(d*(b^n+a^n+z^n+x^n+y^n-2))$
 g:rat((b^n+a^n+z^n+x^n-y^n+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);

 n:6$
 d:c^n+b^n+a^n+z^n+x^n+y^n+1$
 f:rat(d*(c^n+b^n+a^n+z^n+x^n+y^n-2))$
 g:rat((c^n+b^n+a^n+z^n+x^n-y^n+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);

 n:7$
 d:p^n+c^n+b^n+a^n+z^n+x^n+y^n+1$
 f:rat(d*(p^n+c^n+b^n+a^n+z^n+x^n+y^n-2))$
 g:rat((p^n+c^n+b^n+a^n+z^n+x^n-y^n+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);





/* this is the run for case 2, table 2 of ezgcd paper */

 n:2$
 d:z^n+y^n+1$
 f:rat(d*(z^n+y^n-2))$
 g:rat(d*(z^(n-1)+y^(n-1)+2))$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 n:3$
 d:z^n+x^n+y^n+1$
 f:rat(d*(z^n+x^n+y^n-2))$
 g:rat((z^(n-1)+x^(n-1)-y^(n-1)+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 n:4$
 d:a^n+z^n+x^n+y^n+1$
 f:rat(d*(a^n+z^n+x^n+y^n-2))$
 g:rat((a^(n-1)+z^(n-1)+x^(n-1)-y^(n-1)+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 n:5$
 d:b^n+a^n+z^n+x^n+y^n+1$
 f:rat(d*(b^n+a^n+z^n+x^n+y^n-2))$
 g:rat((b^(n-1)+a^(n-1)+z^(n-1)+x^(n-1)-y^(n-1)+2)*d)$
ezgcdswitch:true$
 gcdswitch:false$
 
gcd(f,g);
 n:6$
 d:c^n+b^n+a^n+z^n+x^n+y^n+1$
 f:rat(d*(c^n+b^n+a^n+z^n+x^n+y^n-2))$
 g:rat((c^(n-1)+b^(n-1)+a^(n-1)+z^(n-1)+x^(n-1)-y^(n-1)+2)*d)$
 gcd(f,g);

 n:7$
 d:p^n+c^n+b^n+a^n+z^n+x^n+y^n+1$
 f:rat(d*(p^n+c^n+b^n+a^n+z^n+x^n+y^n-2))$
 g:rat((p^(n-1)+c^(n-1)+b^(n-1)+a^(n-1)+z^(n-1)+x^(n-1)-y^(n-1)
+2)*d)$
 gcd(f,g);

/* i let the rest of file */



/* this is the run for case 3 of the ez gcd paper */

 d:rat(x^2*y^2+1)$
 f:d*(x*y+2)^2$
 g:(x^2-y^2-1)*d$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 d:rat(a^2+x^2*y^2+1)$
 f:d*(x*y+a+2)^2$
 g:(a^2+x^2-y^2-1)*d$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 d:rat(b^2+a^2+x^2*y^2+1)$
 f:d*(x*y+a+b+2)^2$
 g:(b^2+a^2+x^2-y^2-1)*d$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);

 d:rat(c^2+b^2+a^2+x^2*y^2+1)$
 f:d*(x*y+a+b+c+2)^2$
 g:(c^2+b^2+a^2+x^2-y^2-1)*d$
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);





/* this is the run for case 4 of the ez gcd paper */

 kill(all)$
 m:1$
 n:2$
 a:z-x*y+1$
 b:z+3*x-y$
 f:rat(a^m*b^n)$
 g:rat(a^n*b^m)$
 
ezgcdswitch:true$
 gcdswitch:false$
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$

 kill(all)$
 m:1$
 n:3$
 a:z-x*y+1$
 b:z+3*x-y$
 f:rat(a^m*b^n)$
 g:rat(a^n*b^m)$
 
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$

 kill(all)$
 m:1$
 n:4$
 a:z-x*y+1$
 b:z+3*x-y$
 f:rat(a^m*b^n)$
 g:rat(a^n*b^m)$
 
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$

 kill(all)$
 m:2$
 n:4$
 a:z-x*y+1$
 b:z+3*x-y$
 f:rat(a^m*b^n)$
 g:rat(a^n*b^m)$
 
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$



/* this is the run for case 5 of the ez gcd paper */
 kill(all)$
 d:rat((z+1)*(y+1)-3)$
 f:d*(z-2)*(y-2)$
 g:d*(z+2)*(y+2)$
 
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$
 kill(all)$
 d:rat((z+1)*(y+1)*(x+1)-3)$
 f:d*(z-2)*(y-2)*(x-2)$
 g:d*(z+2)*(y+2)*(x+2)$
 
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$
 kill(all)$
 d:rat((z+1)*(y+1)*(x+1)*(a+1)-3)$
 f:d*(z-2)*(y-2)*(x-2)*(a-2)$
 g:d*(z+2)*(y+2)*(x+2)*(a+2)$
 
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$
 kill(all)$
 d:rat((z+1)*(y+1)*(x+1)*(a+1)*(b+1)-3)$
 f:d*(z-2)*(y-2)*(x-2)*(a-2)*(b-2)$
 g:d*(z+2)*(y+2)*(x+2)*(a+2)*(b+2)$
 
 gcd(f,g);
ezgcdswitch:false$
 
 gcd(f,g);
 gcdswitch:true$
 
 gcd(f,g);
ezgcdswitch:true$
 gcdswitch:false$
