19 lines
648 B
Python
19 lines
648 B
Python
|
def naive_hensel(fct, F, start = 1, prec=10):
|
||
|
|
'''given field F and polynomial fct over F((t)), find root of this polynomial in F((t)), using Hensel method with first value equal to start.'''
|
||
|
|
Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
|
||
|
|
RtQ = FractionField(Rt)
|
||
|
|
RptW.<W> = PolynomialRing(RtQ)
|
||
|
|
RptWQ = FractionField(RptW)
|
||
|
|
fct = RptWQ(fct)
|
||
|
|
fct = RptW(numerator(fct))
|
||
|
|
#return(fct)
|
||
|
|
#while fct not in RptW:
|
||
|
|
# print(fct)
|
||
|
|
# fct *= W
|
||
|
|
alpha = (fct.derivative())(W = start)
|
||
|
|
w0 = Rt(start)
|
||
|
|
i = 1
|
||
|
|
while(i < prec):
|
||
|
|
w0 = w0 - fct(W = w0)/alpha + O(t^(prec))
|
||
|
|
i += 1
|
||
|
|
return w0
|