def test_mul_1(self):
one = Polynomial([2, 4, 7, 3])
two = Polynomial([5, 2, 4, 2])
r = one * two
self.assertEqual(list(r.coefficients), [10, 24, 51, 49, 42, 26, 6])
def test_add_1(self):
one = Polynomial([2, 4, 7, 3])
two = Polynomial([5, 2, 4, 2])
r = one + two
self.assertEqual(list(r.coefficients), [7, 6, 11, 5])
def test_scale_1(self):
one = Polynomial([2, 4, 7, 3])
scalar = 12
r = one.scale(12)
self.assertEqual(list(r.coefficients), [24, 48, 84, 36])
def test_add(self):
one = Polynomial(map(GF2int, [8, 3, 5, 1]))
two = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
r = one + two
self.assertEqual(list(r.coefficients), [5, 3, 9, 2, 3, 9])
def test_scale(self):
one = Polynomial(map(GF2int, [2, 14, 7, 3]))
scalar = 12
r = one.scale(12)
self.assertEqual(list(r.coefficients), [24, 72, 36, 20])
def test_scale(self):
one = Polynomial(map(GF2int, [2,14,7,3]))
scalar = 12
r = one.scale(12)
self.assertEqual(list(r.coefficients), [24, 72, 36, 20])
def test_add_3(self):
one = Polynomial([7, 3, 5, 2])
two = Polynomial([6, 8, 5, 2, 4, 2])
r = one + two
self.assertEqual(list(r.coefficients), [6, 8, 12, 5, 9, 4])
def test_scale_1(self):
one = Polynomial([2,4,7,3])
scalar = 12
r = one.scale(12)
self.assertEqual(list(r.coefficients), [24, 48, 84, 36])
def test_getcoeff(self):
p = Polynomial([9, 3, 3, 2, 2, 3, 1, -2, -4])
self.assertEqual(p.get_coefficient(0), -4)
self.assertEqual(p.get_coefficient(2), 1)
self.assertEqual(p.get_coefficient(8), 9)
self.assertEqual(
p.get_coefficient(9), 0
) # try to get a higher coefficient than the length of the polynomial, it should return 0 (non significant high coefficients are removed)
def test_div_scalar2(self):
"""Test that dividing by a scalar is the same as multiplying by the
scalar's inverse"""
a = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
scalar = GF2int(50)
self.assertEqual(a * Polynomial(x0=scalar),
a // Polynomial(x0=scalar.inverse()))
def test_mul_at(self):
one = Polynomial(map(GF2int, [2,4,7,3]))
two = Polynomial(map(GF2int, [5,2,4,2]))
k = 3
r1 = one * two
r2 = one.mul_at(two, k)
self.assertEqual(r1.get_coefficient(k), r2)
def test_mul_at(self):
one = Polynomial(map(GF2int, [2, 4, 7, 3]))
two = Polynomial(map(GF2int, [5, 2, 4, 2]))
k = 3
r1 = one * two
r2 = one.mul_at(two, k)
self.assertEqual(r1.get_coefficient(k), r2)
def test_div(self):
one = Polynomial(map(GF2int, [8, 3, 5, 1]))
two = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
q, r = divmod(two, one)
self.assertEqual(list(q.coefficients), [101, 152, 11])
self.assertEqual(list(r.coefficients), [183, 185, 3])
# Make sure they multiply back out okay
self.assertEqual(q * one + r, two)
def test_div_2(self):
one = Polynomial([1, 0, 0, 2, 2, 0, 1, 2, 1])
two = Polynomial([1, 0, -1])
q, r = divmod(one, two)
self.assertEqual(q, one // two)
self.assertEqual(r, one % two)
self.assertEqual(list(q.coefficients), [1, 0, 1, 2, 3, 2, 4])
self.assertEqual(list(r.coefficients), [4, 5])
def test_div_1(self):
one = Polynomial([1, 4, 0, 3])
two = Polynomial([1, 0, 1])
q, r = divmod(one, two)
self.assertEqual(q, one // two)
self.assertEqual(r, one % two)
self.assertEqual(list(q.coefficients), [1, 4])
self.assertEqual(list(r.coefficients), [-1, -1])
def test_div_fast(self):
one = Polynomial(map(GF2int, [8,3,5,1]))
two = Polynomial(map(GF2int, [5,3,1,1,6,8]))
q, r = two._fastdivmod(one)
self.assertEqual(list(q.coefficients), [101, 152, 11])
self.assertEqual(list(r.coefficients), [183, 185, 3])
# Make sure they multiply back out okay
self.assertEqual(q*one + r, two)
def test_div_fast_1(self):
# no remander
one = Polynomial([1,0,0,2,2,0,1,-2,-4])
two = Polynomial([1,0,-1])
q, r = one._fastdivmod(two)
self.assertEqual(q, one._fastfloordiv(two))
self.assertEqual(r, one._fastmod(two))
self.assertEqual(list(q.coefficients), [1,0,1,2,3,2,4])
self.assertEqual(list(r.coefficients), [0])
def test_div_scalar(self):
"""Tests division by a scalar"""
numbers = map(GF2int,
[5, 20, 50, 100, 134, 158, 0, 148, 233, 254, 4, 5, 2])
scalar = GF2int(17)
poly = Polynomial(numbers)
scalarpoly = Polynomial(x0=scalar)
self.assertEqual(list((poly // scalarpoly).coefficients),
map(lambda x: x / scalar, numbers))
def test_div_4(self):
# no remander
one = Polynomial([1, 0, 0, 2, 2, 0, 1, -2, -4])
two = Polynomial([1, 0, -1])
q, r = divmod(one, two)
self.assertEqual(q, one // two)
self.assertEqual(r, one % two)
self.assertEqual(list(q.coefficients), [1, 0, 1, 2, 3, 2, 4])
self.assertEqual(list(r.coefficients), [0])
def test_div_3(self):
# 0 quotient
one = Polynomial([1, 0, -1])
two = Polynomial([1, 1, 0, 0, -1])
q, r = divmod(one, two)
self.assertEqual(q, one // two)
self.assertEqual(r, one % two)
self.assertEqual(list(q.coefficients), [0])
self.assertEqual(list(r.coefficients), [1, 0, -1])
def test_div_gffast(self):
one = Polynomial(map(GF2int, [1,3,5,1])) # must be monic! (because the function is optimized for monic divisor polynomial)
two = Polynomial(map(GF2int, [5,3,1,1,6,8]))
q, r = two._gffastdivmod(one) # optimized for monic divisor polynomial
q2, r2 = two._fastdivmod(one)
self.assertEqual(q, q2)
self.assertEqual(r, r2)
self.assertEqual(list(q.coefficients), [5, 12, 4])
self.assertEqual(list(r.coefficients), [52, 30, 12])
# Make sure they multiply back out okay
self.assertEqual(q*one + r, two)
def test_div_gffast(self):
one = Polynomial(
map(GF2int, [1, 3, 5, 1])
) # must be monic! (because the function is optimized for monic divisor polynomial)
two = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
q, r = two._gffastdivmod(one) # optimized for monic divisor polynomial
q2, r2 = two._fastdivmod(one)
self.assertEqual(q, q2)
self.assertEqual(r, r2)
self.assertEqual(list(q.coefficients), [5, 12, 4])
self.assertEqual(list(r.coefficients), [52, 30, 12])
# Make sure they multiply back out okay
self.assertEqual(q * one + r, two)
def test_div_fast_1(self):
# no remander
one = Polynomial([1, 0, 0, 2, 2, 0, 1, -2, -4])
two = Polynomial([1, 0, -1])
q, r = one._fastdivmod(two)
self.assertEqual(q, one._fastfloordiv(two))
self.assertEqual(r, one._fastmod(two))
self.assertEqual(list(q.coefficients), [1, 0, 1, 2, 3, 2, 4])
self.assertEqual(list(r.coefficients), [0])
def test_evaluate(self):
a = Polynomial([5,3,1,1,6,8])
e = a.evaluate(3)
self.assertEqual(e, 1520)
def test_derive(self):
a = Polynomial([5, 3, 1, 1, 6, 8])
r = a.derive()
self.assertEqual(list(r), [25, 12, 3, 2, 6])
def test_evaluate_array(self):
a = Polynomial([5, 3, 1, 1, 6, 8])
arr, sum = a.evaluate_array(3)
self.assertEqual(sum, 1520)
self.assertEqual(list(arr), [1215, 243, 27, 9, 18, 8])
def test_evaluate(self):
a = Polynomial([5, 3, 1, 1, 6, 8])
e = a.evaluate(3)
self.assertEqual(e, 1520)
def test_mul(self):
one = Polynomial(map(GF2int, [8, 3, 5, 1]))
two = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
r = one * two
self.assertEqual(list(r.coefficients),
[40, 23, 28, 1, 53, 78, 7, 46, 8])
def test_derive(self):
a = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
r = a.derive()
self.assertEqual(list(r), [17, 12, 3, 2, 6])
def test_derive(self):
a = Polynomial([5,3,1,1,6,8])
r = a.derive()
self.assertEqual(list(r), [25, 12, 3, 2, 6])
def test_evaluate(self):
a = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
e = a.evaluate(3)
self.assertEqual(e, 196)
def test_evaluate_array(self):
a = Polynomial(map(GF2int, [5, 3, 1, 1, 6, 8]))
arr, sum = a.evaluate_array(3)
self.assertEqual(sum, 196)
self.assertEqual(list(arr), [255, 51, 15, 5, 10, 8])
def test_getcoeff(self):
p = Polynomial([9,3,3,2,2,3,1,-2,-4])
self.assertEqual(p.get_coefficient(0), -4)
self.assertEqual(p.get_coefficient(2), 1)
self.assertEqual(p.get_coefficient(8), 9)
self.assertEqual(p.get_coefficient(9), 0) # try to get a higher coefficient than the length of the polynomial, it should return 0 (non significant high coefficients are removed)
def test_derive(self):
a = Polynomial(map(GF2int, [5,3,1,1,6,8]))
r = a.derive()
self.assertEqual(list(r), [17, 12, 3, 2, 6])
def test_evaluate_array(self):
a = Polynomial([5,3,1,1,6,8])
arr, sum = a.evaluate_array(3)
self.assertEqual(sum, 1520)
self.assertEqual(list(arr), [1215, 243, 27, 9, 18, 8])
def test_evaluate(self):
a = Polynomial(map(GF2int, [5,3,1,1,6,8]))
e = a.evaluate(3)
self.assertEqual(e, 196)
def test_evaluate_array(self):
a = Polynomial(map(GF2int, [5,3,1,1,6,8]))
arr, sum = a.evaluate_array(3)
self.assertEqual(sum, 196)
self.assertEqual(list(arr), [255, 51, 15, 5, 10, 8])