 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
param(Hne);
==> // ** Warning: result is exact up to order 20 in x and 104 in y !
==> _[1]=x14
==> _[2]=3x98x109
// 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);
==> y = 3*x^7+z(1)*x^7
==> x = z(1)*z(2)
==> z(1) = z(2)^3*z(3)
==> z(2) = z(3)*z(4)
==> z(3) = z(4)^2 + ..... (terms of degree >=9)
