Polynomials with many integral points
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These programs computes a sequence of polynomials from a
paper
of F. Rodríguez Villegas and J. F. Voloch. These are polynomials
Pd of
degree d in two variables and integer coefficients such that Pd=0
has many integral points. One defines Tk by the recurrence
Tk+1=tTk+k(x+k-1)Tk-1 and Pd by
Pd(-x,t2)=T2d(x,t).
- Enter an integer k to compute Tk
(and then double-click on it).
k=5
Result
Tk=rec(k)
Result
- Enter an integer d to compute Pd
(and then double-click on it).
d=5
Result
Pd=polz(d)
Result
- Now compute the number N of integral points on Pd=0 and
height at most
h=10
Result
N=countz(Pd,h)
Result
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