#!/usr/bin/ruby
# Testing the implementation of the Euler and Bernoulli polynomials.
3.times {
    var n = 100.irand(2)
    var x = 100.irand(2)
    assert_eq(sum(0..n, {|k| binomial(n, k) * euler_number(k) / 2**k * (x - 1/2)**(n-k) }), euler(n, x), "error for euler(#{n}, #{x})")
    assert_eq(sum(0..n, {|k| binomial(n, k) * (-1)**(n-k) * bernoulli(n-k) * x**k }), bernoulli(n, x), "error for bernoulli(#{n}, #{x})")
    assert_eq(2**n * (2**(n+1) / (n+1)) * (bernoulli(n+1, 3/4) - bernoulli(n+1, 1/4)), euler_number(n), "error for euler_number(#{n})")
    assert_eq((bernoulli(x+1, n+1) - bernoulli(x+1)) / (x+1), faulhaber_sum(n,x), "error for faulhaber_sum(#{n}, #{x})")
    assert_eq(euler(n, x) + (1/2 * sum(^n, {|k| binomial(n, k) * euler(k, x) })), x**n, "error for euler -> #{x}^#{n}")
    assert_eq(sum(0..n, {|k| binomial(n+1, k) * bernoulli(k, x) }) / (n+1), x**n, "error for bernoulli -> #{x}^#{n}")
    assert_eq(euler(n, x), 2**(n+1) / (n+1) * (bernoulli(n+1, (x+1)/2) - bernoulli(n+1, x/2)), "euler-bernoulli relation with (#{n}, #{x})")
    assert_eq(euler(n), 2**n * euler(n, 1/2), "euler number from euler polyonimial with (#{n}, #{x})")
}
assert_eq(0..10 -> map {|n| euler_number(n) }, [1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521])
assert_eq(1..10 -> map {|n| 2*n*euler_polynomial(2*n - 1, 0) }, [-1, 1, -3, 17, -155, 2073, -38227, 929569, -28820619, 1109652905])
say "** Test passed!"