#
# PYTHON • MyCompiler
# https://[Log in to view URL]
# Teoria das Partições
# Estudo Fórmula Pentagonal de Euler
#
# 2026 Abril Dom, 26
# by
# j
# 

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm

def euler(m):
    p = []
    p.append(1)
    p.append(1)
    for n in range(0,m+1):
        flag = True
        k = 1
        sum = 0
        while (flag):
            j = 0
            while ( (j <= 1) and flag):
                exp = (-1)**j
                kk = exp*k
                Gk = int(kk*(3*kk - 1) / 2)
                if ( (n - Gk) >= 0 ):
                    sum += ( (-1)**(kk-1) )*p[n-Gk]
                    j += 1
                else:
                    flag = False
            k += 1
        if (n>=2):
            p.append(int(sum))
    return p[m]

def prod(x):
    max = 700
    p = 1
    for m in range(1,max+1):
        p = p*(1/(1-x**m))
    return p

def sum(x):
    max = 100
    s = 0
    for n in range(0,max+1):
        s += euler(n)*x**n
    return s

def list():
    x = []
    y = []
    z = []
    delta = 0.01
    xstart = 0.1
    xend = 0.7
    xk = xstart
    while (xk < xend):
        yk = prod(xk)
        zk = sum(xk)
        x.append(xk)
        y.append(yk)
        z.append(zk)
        xk = xk + delta
        
    plt.plot(x, y, marker='o', linestyle='-', color='b', label='prod(x)')
    plt.plot(x, z, marker='o', linestyle='-', color='r', label='sum(x)')
    
    plt.title("Pentagonal Euler")
    plt.xlabel("x")
    plt.ylabel("prod(x),sum(x)")
    plt.legend()
    plt.grid(True)
    plt.show()
    
list()