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D.4.12.4 henselGlobal
Procedure from library integralbasis.lib (see integralbasis_lib).
- Usage:
- henselGlobal(f,g,h,order); h is polynomial in x and y.
f and g are polynomials in y such that f(y)*g(y) = h(0,y) and <f, g> = 1.
- Return:
- polynomials f1 and g1 such that
1) h = f1*g1 up to the required order in x.
2) f1(0,y) = f, g1(0,y) = g
Example:
| | LIB "integralbasis.lib";
ring R = 0, (x,y), dp;
// Polynomial of degree 6 in y with an ordinary multiple point
// at the origin of order k.
poly h = (y2 + 3xy + x3 + x4)*(y3 + 2x + 1);
poly f = y2;
poly g = y3 + 1;
henselGlobal(f, g, h, 3);
==> [1]:
==> x3+3xy+y2
==> [2]:
==> y3+2x+1
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