bash-2.05a$ gp
Reading GPRC: /home/his/.gprc ...Done.

                  GP/PARI CALCULATOR Version 2.1.4 (released)
                       i386 running netbsd 32-bit version
               (readline v4.2a enabled, extended help available)

                       Copyright (C) 2002 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and 
comes WITHOUT ANY WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?12 for how to get moral (and possibly technical) support.

   realprecision = 28 significant digits
   seriesprecision = 16 significant terms
   format = g0.28

parisize = 50000000, primelimit = 500000
gp> read("syzygy.gp")
time = 38 ms.
gp> U(x,y)
time = 4 ms.
%1 = a0*x^4 + 4*a1*y*x^3 + 6*a2*y^2*x^2 + 4*a3*y^3*x + a4*y^4
gp> g(x,y)
time = 20 ms.
%2 = (-a2*a0 + a1^2)*x^4 + (-2*a3*a0 + 2*a2*a1)*y*x^3 + (-a4*a0 + (-2*a3*a1 + 3*a2^2))*y^2*x^2 + (-2*a1*a4 + 2*a2*a3)*y^3*x + (-a2*a4 + a3^2)*y^4
gp> h(x,y)
time = 32 ms.
%3 = (-a3*a0^2 + 3*a2*a1*a0 - 2*a1^3)*x^6 + (-a4*a0^2 + (-2*a3*a1 + 9*a2^2)*a0 - 6*a2*a1^2)*y*x^5 + ((-5*a1*a4 + 15*a2*a3)*a0 - 10*a3*a1^2)*y^2*x^4 + (10*a3^2*a0 - 10*a1^2*a4)*y^3*x^3 + (5*a3*a4*a0 + (-15*a2*a1*a4 + 10*a3^2*a1))*y^4*x^2 + (a4^2*a0 + ((2*a3*a1 - 9*a2^2)*a4 + 6*a2*a3^2))*y^5*x + (a1*a4^2 - 3*a2*a3*a4 + 2*a3^3)*y^6
gp> ii
time = 0 ms.
%4 = a4*a0 + (-4*a3*a1 + 3*a2^2)
gp> jj
time = 0 ms.
%5 = (a2*a4 - a3^2)*a0 + (-a1^2*a4 + (2*a2*a3*a1 - a2^3))
gp> h(x,y)^2-(4*g(x,y)^3-ii*g(x,y)*z^4*y^4-jj*z^6*y^6)
time = 38 ms.
%6 = (a3^2*a0^4 + (-6*a2*a3*a1 + 4*a2^3)*a0^3 + (4*a3*a1^3 - 3*a2^2*a1^2)*a0^2)*x^12 + (2*a3*a4*a0^4 + (-6*a2*a1*a4 + (4*a3^2*a1 + 6*a2^2*a3))*a0^3 + (4*a1^3*a4 + (-48*a2*a3*a1^2 + 30*a2^3*a1))*a0^2 + (32*a3*a1^4 - 24*a2^2*a1^3)*a0)*y*x^11 + (a4^2*a0^4 + ((14*a3*a1 - 6*a2^2)*a4 + 18*a2*a3^2)*a0^3 + (-42*a2*a1^2*a4 + (-24*a3^2*a1^2 - 18*a2^2*a3*a1 + 45*a2^4))*a0^2 + (32*a1^4*a4 + (-48*a2*a3*a1^3 + 12*a2^3*a1^2))*a0 + (64*a3*a1^5 - 48*a2^2*a1^4))*y^2*x^10 + ((10*a1*a4^2 + 18*a2*a3*a4 + 12*a3^3)*a0^3 + ((12*a3*a1^2 - 114*a2^2*a1)*a4 + 102*a2^3*a3)*a0^2 + (-96*a3^2*a1^3 - 168*a2^2*a3*a1^2 + 144*a2^4*a1)*a0 + (64*a1^5*a4 + (192*a2*a3*a1^4 - 176*a2^3*a1^3)))*y^3*x^9 + ((12*a2*a4^2 + 18*a3^2*a4)*a0^3 + (33*a1^2*a4^2 + (-42*a2*a3*a1 - 60*a2^3)*a4 + (36*a3^3*a1 + 153*a2^2*a3^2))*a0^2 + ((-24*a3*a1^3 - 270*a2^2*a1^2)*a4 + (-384*a2*a3^2*a1^2 + 240*a2^3*a3*a1 + 108*a2^5))*a0 + (288*a2*a1^4*a4 + (144*a2^2*a3*a1^3 - 252*a2^4*a1^2)))*y^4*x^8 + (12*a3*a4^2*a0^3 + (60*a2*a1*a4^2 + (48*a3^2*a1 - 36*a2^2*a3)*a4 + 144*a2*a3^3)*a0^2 + (48*a1^3*a4^2 + (-480*a2*a3*a1^2 - 372*a2^3*a1)*a4 + (-96*a3^3*a1^2 + 72*a2^2*a3^2*a1 + 360*a2^4*a3))*a0 + ((96*a3*a1^4 + 504*a2^2*a1^3)*a4 + (-192*a2*a3^2*a1^3 + 48*a2^3*a3*a1^2 - 216*a2^5*a1)))*y^5*x^7 + (2*a4^3*a0^3 + ((60*a3*a1 + 24*a2^2)*a4^2 + 72*a2*a3^2*a4 + 48*a3^4)*a0^2 + (72*a2*a1^2*a4^2 + (-144*a3^2*a1^2 - 876*a2^2*a3*a1 - 126*a2^4)*a4 + (144*a2*a3^3*a1 + 516*a2^3*a3^2))*a0 + (48*a1^4*a4^2 + (144*a2*a3*a1^3 + 516*a2^3*a1^2)*a4 + (-128*a3^3*a1^3 - 192*a2^2*a3^2*a1^2 - 72*a2^4*a3*a1 - 108*a2^6)))*y^6*x^6 + ((12*a1*a4^3 + 60*a2*a3*a4^2 + 48*a3^3*a4)*a0^2 + ((48*a3*a1^2 - 36*a2^2*a1)*a4^2 + (-480*a2*a3^2*a1 - 372*a2^3*a3)*a4 + (96*a3^4*a1 + 504*a2^2*a3^3))*a0 + (144*a2*a1^3*a4^2 + (-96*a3^2*a1^3 + 72*a2^2*a3*a1^2 + 360*a2^4*a1)*a4 + (-192*a2*a3^3*a1^2 + 48*a2^3*a3^2*a1 - 216*a2^5*a3)))*y^7*x^5 + (((12*a2*a4^3 + 33*a3^2*a4^2)*a0^2 + (18*a1^2*a4^3 + (-42*a2*a3*a1 - 60*a2^3)*a4^2 + (-24*a3^3*a1 - 270*a2^2*a3^2)*a4 + 288*a2*a3^4)*a0 + ((36*a3*a1^3 + 153*a2^2*a1^2)*a4^2 + (-384*a2*a3^2*a1^2 + 240*a2^3*a3*a1 + 108*a2^5)*a4 + (144*a2^2*a3^3*a1 - 252*a2^4*a3^2)))*y^8 + (-z^4*a2*a4*a0^2 + (z^4*a1^2*a4 + (4*z^4*a2*a3*a1 - 3*z^4*a2^3))*a0 + (-4*z^4*a3*a1^3 + 3*z^4*a2^2*a1^2))*y^4)*x^4 + ((10*a3*a4^3*a0^2 + (18*a2*a1*a4^3 + (12*a3^2*a1 - 114*a2^2*a3)*a4^2 + 64*a3^5)*a0 + (12*a1^3*a4^3 + 102*a2^3*a1*a4^2 + (-96*a3^3*a1^2 - 168*a2^2*a3^2*a1 + 144*a2^4*a3)*a4 + (192*a2*a3^4*a1 - 176*a2^3*a3^3)))*y^9 + (-2*z^4*a3*a4*a0^2 + (2*z^4*a2*a1*a4 + (8*z^4*a3^2*a1 - 6*z^4*a2^2*a3))*a0 + (-8*z^4*a2*a3*a1^2 + 6*z^4*a2^3*a1))*y^5)*x^3 + ((a4^4*a0^2 + ((14*a3*a1 - 6*a2^2)*a4^3 - 42*a2*a3^2*a4^2 + 32*a3^4*a4)*a0 + (18*a2*a1^2*a4^3 + (-24*a3^2*a1^2 - 18*a2^2*a3*a1 + 45*a2^4)*a4^2 + (-48*a2*a3^3*a1 + 12*a2^3*a3^2)*a4 + (64*a3^5*a1 - 48*a2^2*a3^4)))*y^10 + (-z^4*a4^2*a0^2 + 2*z^4*a3*a1*a4*a0 + (8*z^4*a3^2*a1^2 - 18*z^4*a2^2*a3*a1 + 9*z^4*a2^4))*y^6)*x^2 + (((2*a1*a4^4 - 6*a2*a3*a4^3 + 4*a3^3*a4^2)*a0 + ((4*a3*a1^2 + 6*a2^2*a1)*a4^3 + (-48*a2*a3^2*a1 + 30*a2^3*a3)*a4^2 + (32*a3^4*a1 - 24*a2^2*a3^3)*a4))*y^11 + ((-2*z^4*a1*a4^2 + 2*z^4*a2*a3*a4)*a0 + ((8*z^4*a3*a1^2 - 6*z^4*a2^2*a1)*a4 + (-8*z^4*a2*a3^2*a1 + 6*z^4*a2^3*a3)))*y^7)*x + ((a1^2*a4^4 + (-6*a2*a3*a1 + 4*a2^3)*a4^3 + (4*a3^3*a1 - 3*a2^2*a3^2)*a4^2)*y^12 + ((-z^4*a2*a4^2 + z^4*a3^2*a4)*a0 + ((4*z^4*a2*a3*a1 - 3*z^4*a2^3)*a4 + (-4*z^4*a3^3*a1 + 3*z^4*a2^2*a3^2)))*y^8 + ((z^6*a2*a4 - z^6*a3^2)*a0 + (-z^6*a1^2*a4 + (2*z^6*a2*a3*a1 - z^6*a2^3)))*y^6)
gp> h(x,y)^2-(4*g(x,y)^3-ii*g(x,y)*U(x,y)^2-jj*U(x,y)^3)
time = 18 ms.
%7 = 0
gp> a0=-216;a1=252/4;a2=-315/6;a3=-1476/4;a4=-762;
time = 0 ms.
gp> g(x,y)
time = 3 ms.
%9 = -7371*x^4 - 166023*y*x^3 - 439317/4*y^2*x^2 + 134757*y^3*x + 96156*y^4
gp> h(x,y)
time = 5 ms.
%10 = 18859230*x^6 + 21401253*y*x^5 - 99967770*y^2*x^4 - 263863980*y^3*x^3 - 255695535*y^4*x^2 - 227958057/2*y^5*x - 19620711*y^6
gp> ii
time = 0 ms.
%11 = a4*a0 + (-4*a3*a1 + 3*a2^2)
gp> ii= a4*a0 + (-4*a3*a1 + 3*a2^2)
time = 0 ms.
%12 = 1063395/4
gp> jj
time = 0 ms.
%13 = (a2*a4 - a3^2)*a0 + (-a1^2*a4 + (2*a2*a3*a1 - a2^3))
gp> jj = (a2*a4 - a3^2)*a0 + (-a1^2*a4 + (2*a2*a3*a1 - a2^3))
time = 0 ms.
%14 = 211037697/8
gp> U(x,y)
time = 1 ms.
%15 = -216*x^4 + 252*y*x^3 - 315*y^2*x^2 - 1476*y^3*x - 762*y^4
gp> quit
Good bye!
bash-2.05a$