#!/usr/bin/python

from math import sqrt

""" Produce the n:th s-gonal number """
def p(s,n):
	p = ((s-2)*n**2-(s-4)*n)/2
	return p

""" Return n for the s-gonal number p """
def r(s,p):
	n = (((s-4.0)/(s-2.0))/2)\
	+sqrt((((s-4.0)/(s-2.0))/2)**2\
	+(2.0/(s-2.0))*p)
	return n

""" Check whether p is a s-gonal number """
def is_sgonal(s,p):
	n = int(((s-4.0)/(2.0*s-4.0))\
	+sqrt(((s-4.0)**2/(2*s-4.0)**2)\
	+((2.0*p)/(s-2.0))))
	q = ((s-2.0)*n**2-(s-4)*n)/2
	return p == q