Q1: {3*x+6*y-5*z, 3*x^2+4*x*y+6*y^2+7*x*z+8*y*z+9*z^2, 81*x^3 + 9*x^2*y +
18*x*y^2-81*y^3 + 3*x^2*z + x*y*z +6*y^2*z + 4*x*z^2 +7*y*z^2 +9*z^3}


Q3:  t^{143}x_0^3 + x_0^2x_1 + t^{64}x_0^2x_2 + t^{122}x_0^2x_3 +
  x_0x_1^2 + t^{2}x_0x_1x_2 + x_0x_1x_3 + t^{15}x_0x_2 +
  t^{55}x_0x_2x_3 + t^{107}x_0x_3^2 + t^{36}x_1^3 + t^{23}x_1^2x_2 +
  t^{39}x_1^2x_3 + t^{16}x_1x_2^2 + t^{14}x_1x_2x_3 + t^{48}x_1x_3^2 +
  t^{12}x_2^3 + t^{12}x_2^2x_3 + t^{49}x_2x_3^2 + t^{95}x_3^3

Q5: {3*x_1+2*x_2-5*x_3+4*x_4, x_1+x_2-x_3+17*x_4,5*x_1+10*x_2+15*x_3-x_4 }




Q6: 
R=QQ[t,x,y];
I=ideal(t^101*x^2+37*x*y+43*x+t^137*y^2+71*y+t^56,
t^29*x^2+37*t^340*x*y+43*t^340*x+t^725*y^2+17*t^340*y+t^31,
t^2*x+t^140*y+3)


Q7: {3*x+2*y+1,5*x+7*y+2, x+4*y+12,8*x-y+4}