LIB "ringgb.lib";
ring RG = (integer, 65536, 1, 65536), (x,y,z), dp;
// Polynomial 1:
poly p1 = 3795162112*x^3+587202566*x^2*y+2936012853*x*y*z+2281701376*x+548767119*y^3+16777216*y^2+268435456*y*z          +1107296256*y+4244635648*z^3+4244635648*z^2+16777216*z;
// Polynomial 2:
poly p2 = 1647678464*x^3+587202566*x^2*y+2936012853*x*y*z+134217728*x+548767119*y^3+16777216*y^2+268435456*y*z          +1107296256*y+2097152000*z^3+2097152000*z^2+16777216*z;
// Polynomial3:
poly p3 = 1647678464*x^3+587202566*x^2*y+2936012853*x*y*z+134217728*x+548767119*y^3+16777216*y^2+268435456*y*z          +1107296256*y+2097152000*z^3+2097152000*z^2+16777216*z;
zeroReduce(p1-p2);
zeroReduce(p1-p3);
zeroReduce(p2-p3);

//ring r = (integer, 65536), (x,y,z), dp;
ring R = (integer, 2, 16), (x,y,z), dp;
// Polynomial 1:
poly p1 = 16384*x^4+y^4+57344*z^4+64767*x*y^3+16127*y^2*z^2+8965*x^3*z+19275*x^2*y*z+51903*x*y*z+32768*x^2*y +40960*z^2+32768*x*y^2+49152*x^2+4869*y;
// Polynomial 2:
poly p2 = 8965*x^3*z+19275*x^2*y*z+31999*x*y^3+51903*x*y*z+32768*x*y+y^4+32768*y^3+16127*y^2*z^2+32768*y^2    +4869*y+57344*z^4+40960*z^2;
// Polynomial 3:
poly p3 = 8965*x^3*z+19275*x^2*y*z+31999*x*y^3+51903*x*y*z+32768*x*y+y^4+16127*y^2*z^2+4869*y+16384*z^3+16384*z;
zeroReduce(p1-p2);
zeroReduce(p1-p3);
zeroReduce(p2-p3);


ring s = (integer, 65536), (v,w,x,y,z), dp;
//ring S = (integer, 2, 16), (v,w,x,y,z), dp;
// Polynomial 1:
poly p1 = 25000*v^2*y+37322*v^2+22142*v*w*z+50356*w^3+58627*w^2+17797*w+17797*x^3+62500*x^2*z+41667*x         +22142*y^3+23870*y^2+59464*y+41667*z+58627;
// Polynomial 2:
poly p2 = 25000*v^2*y+4554*v^2+22142*v*w*z+32768*v+17588*w^3+25859*w^2+17797*w+17797*x^3+29732*x^2*z+32768*x^2         +32768*x*z+8899*x+22142*y^3+23870*y^2+59464*y+41667*z+58627;
// Polynomial 3:
poly p3 = 25000*v^2*y+4554*v^2+22142*v*w*z+32768*v+17588*w^3+25859*w^2+17797*w+17797*x^3+29732*x^2*z+32768*x*z         +41667*x+22142*y^3+23870*y^2+59464*y+41667*z+58627;
zeroReduce(p1-p2);
zeroReduce(p1-p3);
zeroReduce(p2-p3);

//ring t = (integer, 65536), c, dp;
ring T = (integer, 2, 16), c, dp;
// Polynomial 1:
poly p1 = 156*c^6+62724*c^5+17968*c^4+18661*c^3+43593*c^2+40224*c+13281;
// Polynomial 2:
poly p2 = 156*c^6+5380*c^5+1584*c^4+43237*c^3+27209*c^2+40224*c+13281;
// Polynomial 3:
poly p3 = 156*c^6+5380*c^5+1584*c^4+10469*c^3+27209*c^2+7456*c+13281;
zeroReduce(p1-p2);
zeroReduce(p1-p3);
zeroReduce(p2-p3);

ring u = (integer, 65536), (x,y), dp;
//ring U = (integer, 2, 16), (x,y), dp;
// Polynomial 1:
poly p1 = 4166*x^4+16666*x^3*y+25000*x^2*y^2+15536*x^2+16666*x*y^4+31072*x*y+4166*y^4+15536*y^2+34464;
// Polynomial 2:
poly p2 = 4166*x^4+16666*x^3*y+8616*x^2*y^2+16384*x^2*y+15536*x^2+282*x*y^4+47456*x*y+53318*y^4+31920*y^2+34464;
// Polynomial 3:
poly p3 = 4166*x^4+16666*x^3*y+8616*x^2*y^2+16384*x^2*y+15536*x^2+282*x*y^4+47456*x*y+4166*y^4+15536*y^2+34464;
zeroReduce(p1-p2);
zeroReduce(p1-p3);
zeroReduce(p2-p3);

// Polynomial 1:
poly f = 1024*x^8*y^2+11264*x^8*y+28672*x^8+45056*x^7*y^2+36864*x^7*y+16384*x^7+40960*x^6*y^2+57344*x^6*y+32768*x^6+30720*x^5*y^2+10240*x^5*y+8192*x^5+35840*x^4*y^2+1024*x^4*y+20480*x^4+30720*x^3*y^2+10240*x^3*y+8192*x^3+4096*x^2*y^2+45056*x^2*y+49152*x^2+40960*x*y^2+57344*x*y+32768*x;
zeroReduce(f);


//LIB "ringgb.lib";
//ring u = (integer, 65536), (x,y), dp;
//poly f = 1024*x^8*y^2+11264*x^8*y+28672*x^8+45056*x^7*y^2+36864*x^7*y+16384*x^7+40960*x^6*y^2+57344*x^6*y+32768*x^6+30720*x^5*y^2+10240*x^5*y+8192*x^5+35840*x^4*y^2+1024*x^4*y+20480*x^4+30720*x^3*y^2+10240*x^3*y+8192*x^3+4096*x^2*y^2+45056*x^2*y+49152*x^2+40960*x*y^2+57344*x*y+32768*x;
//testZero(f);
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