def __init__(self, monomial1=None, monomial2=None):
"""Initialize the binomial with 2 monomials.
The arguments can also be 2-tuples in the form:
(coefficient, degree)
"""
if not monomial1:
monomial1 = Monomial(1, 1)
if not monomial2:
monomial2 = Monomial(1, 2)
Polynomial.__init__(self, [monomial1, monomial2], from_monomials=True)
def __init__(self, monomial1=None, monomial2=None, monomial3=None):
"""Initialize the trinomial with 3 monomials.
The arguments can also be 2-tuples in the form:
(coefficient, degree)
"""
if not monomial1:
monomial1 = Monomial(1, 1)
if not monomial2:
monomial2 = Monomial(1, 2)
if not monomial3:
monomial3 = Monomial(1, 3)
args = [monomial1, monomial2, monomial3]
Polynomial.__init__(self, args, from_monomials=True)
def complex_factors(self):
"""Return (a, (x-x_0), (x-x_1)), where x_0 and x_1 are the roots."""
roots = self.complex_roots
return (Constant(self.a), Polynomial([1, -roots[0]]),
Polynomial([1, -roots[1]]))
def __init__(self, a=1, b=1, c=1):
"""Initialize the trinomial as ax^2 + bx + c."""
if a == 0:
raise ValueError("Object not a quadratic trinomial since a==0!")
Polynomial.__init__(self, a, b, c)
def __init__(self, *args, **kwargs):
"""Create a polynomial from the args, and then freeze it."""
Polynomial.__init__(self, *args, **kwargs)
self._vector = tuple(self._vector)
self._trim = self._no_op
self._freeze()
def __init__(self, a=1, b=1):
"""Initialize the binomial as ax + b."""
if a == 0:
raise ValueError("object not a linear binomial since a = 0!")
Polynomial.__init__(self, [a, b])