| LIB "hnoether.lib";
ring exring = 7,(x,y),ds;
list hne=develop(4x98+2x49y7+x11y14+2y14);
print(hne[1]);
→ 0,0, 0,0,0,0,3,x,
→ 0,x, 0,0,0,0,0,0,
→ 0,0, 0,x,0,0,0,0,
→ 0,x, 0,0,0,0,0,0,
→ 0,-1,0,0,0,0,0,0
// therefore the HNE is:
// z(-1)= 3*z(0)^7 + z(0)^7*z(1),
// z(0) = z(1)*z(2), (there is 1 zero in the 2nd row before x)
// z(1) = z(2)^3*z(3), (there are 3 zeroes in the 3rd row)
// z(2) = z(3)*z(4),
// z(3) = -z(4)^2 + 0*z(4)^3 +...+ 0*z(4)^8 + ?*z(4)^9 + ...
// (the missing x in the last line indicates that it is not complete.)
hne[2];
→ 7,1,3,1,-1
parametrisation(hne);
→ [1]:
→ _[1]=-x14
→ _[2]=-3x98-x109
// parametrization: x(t)= -t^14+O(t^21), y(t)= -3t^98+O(t^105)
// (the term -t^109 in y may have a wrong coefficient)
displayHNE(hne);
→ HNE[1]=-y+3*z(0)^7+z(0)^7*z(1)
→ HNE[2]=-x+z(1)*z(2)
→ HNE[3]=z(2)^3*z(3)
→ HNE[4]=z(3)*z(4)
→ HNE[5]=-z(4)^2
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