def __init__(self, coefficients, modulo):
""" input: coefficients are in the form a_0, a_1 ...a_n
"""
self.coefficients = coefficients
while self.coefficients[-1] == 0 and len(self.coefficients) > 1:
self.coefficients.pop()
if type(self.coefficients[0]) == int:
self.coefficients = [Bn.from_num(i) for i in coefficients]
self.degree = len(self.coefficients)
self.modulo = modulo
if modulo and type(coefficients[0]) != Bn:
self.coefficients = [Bn.from_num(x) for x in self.coefficients]
def from_roots_opt(roots, modulo):
"""
Calculate polynomial from roots, optimally
Example:
>>> a = Polynomial.from_roots_opt([Bn.from_num(1), Bn.from_num(1)], Bn.from_num(7))
>>> a.eval(1)
0
>>> a = Polynomial.from_roots_opt([1, 2, 3, 3, 4, 5], Bn.from_num(7))
>>> a.coefficients
[3, 3, 4, 3, 4, 3, 1]
>>> a.eval(3)
0
>>> a.eval(5)
0
>>> a.eval(6)
3
>>> order = Bn.from_decimal("52137169930799554717614356857506293818498877974737694294258188871929297414763123103907744062376810056827189091305705434921846346757741920691072816664704800302679217118985586829201265273391676324053123901757229727135241424267879269925766038354395247471758947327023181961662857375240340094119735806654078071568415490759313899749642836086369437285822445537863499850137938649445050574793896418443324129366783154447555359885480360150449533448644540185781810834062108093885074870413486811350157518533438291933078172819638193255100503198570696887787567964374981238663391668092217407521167528524716096503249760795640678745829")
>>> roots = [Bn.from_decimal('24328626682289136570751536147321521934883276496444403637200791710959330225351187858816284221467749949170967552592192324486105274675745073644298833869379510880054061897691638487850358168087009962101666739301242027780261176000688299869458451077243785452946211728488732020837306283402441986288004713904032620106051702880664181957060410226643578290964003019109479261826859822942513350862756778747973875209750342357933539552875979843312957639435564366361012366291495216191958522420513908595748516389774971404368853339932587005401457667821996489027145786706555858193202229433265835452932244580820310037045608574782179678733') for _ in range(4)]
>>> big_poly = Polynomial.from_roots_opt(roots, order)
>>> big_poly.eval(roots[0])
0
>>> Polynomial.from_roots_opt([1, 2, 3, 3, 4, 5], Bn.from_num(1000)).coefficients
[360, 58, 949, 520, 130, 982, 1]
"""
if type(modulo) == int:
modulo = Bn.from_num(modulo)
if type(roots[0]) == int:
roots = [Bn.from_num(a) for a in roots]
degree_poly = len(roots)
polynomial = [0] * degree_poly
polynomial[0] = 1
for i in range(degree_poly):
new_poly = []
new_poly.append((-polynomial[0] * roots[i]).mod(modulo))
for j in range(1, i + 1):
new_poly.append(
(-polynomial[j] * roots[i] + polynomial[j - 1]).mod(modulo)
)
new_poly.append(1)
polynomial = new_poly
return Polynomial(polynomial, modulo)
def zip_longest(iter1, iter2, fillchar=Bn.from_num(0)):
for i in range(max(len(iter1), len(iter2))):
if i >= len(iter1):
yield (fillchar, iter2[i])
elif i >= len(iter2):
yield (iter1[i], fillchar)
else:
yield (iter1[i], iter2[i])
i += 1
def eval(self, point):
"""
Evaluation of a polynomial
Example:
>>> a = Polynomial([1, 2], 7)
>>> a.eval(2)
5
>>> a.eval(3)
0
"""
if type(point) == int:
point = Bn.from_num(point)
result = Bn.from_num(0)
for index, coefficient in enumerate(self.coefficients):
result = result.mod_add(
coefficient * point.mod_pow(index, self.modulo), self.modulo
)
return result
def __mul__(self, other):
"""
Multiply poly
Example:
>>> a = Polynomial([1, 2], 13)
>>> b = Polynomial([3, 3], 13)
>>> c = a * b
>>> c.coefficients
[3, 9, 6]
>>> cc = a * Polynomial([1, 0], 13)
>>> cc.coefficients
[1, 2]
>>> d = a * 3
>>> d.coefficients
[3, 6]
>>> e = a.to_big_number(Bn.from_num(5))
>>> f = e * 12
>>> f.coefficients
[2, 4]
"""
if type(other) == Polynomial:
if self.modulo != other.modulo:
raise TypeError("Expecting the same modulo out of both polynomials")
if isinstance(other, Polynomial):
self_coefficients = self.coefficients
other_coefficients = other.coefficients
res = [Bn.from_num(0)] * (
len(self_coefficients) + len(other_coefficients) - 1
)
for self_index, self_coefficient in enumerate(self_coefficients):
for other_index, other_coefficient in enumerate(other_coefficients):
if self.modulo:
res[self_index + other_index] = res[
self_index + other_index
].mod_add(self_coefficient * other_coefficient, self.modulo)
else:
res[self_index + other_index] += (
self_coefficient * other_coefficient
)
else:
if self.modulo:
res = [co.mod_mul(other, self.modulo) for co in self.coefficients]
else:
res = [co * other for co in self.coefficients]
return self.__class__(res, modulo=self.modulo)
def to_big_number(self, modulo):
return Polynomial([Bn.from_num(x) for x in self.coefficients], modulo=modulo)
