Polynomial

class flopt.polynomial.Monomial(terms={}, coeff=1)[source]

Parameters:

terms (dict(Variable=exponentiation)) – this monomial is represented as coeff * prod( var_i ^ {exp_i} for var_i, exp_i in terms.items() ), where exp_i is positive integer.
coeff (int or float) – coefficient of monomial

Notes

If terms is empty dictionary, then this monomial is constant whose value is self.coeff

clone()[source]

Return type:: Monomial

diff(x)[source]

Parameters:: x (VarElement family) –
Returns:: the monomial differentiated by x
Return type:: Monomial

isConstant()[source]

Returns:: return True if it is constant else False
Return type:: bool

isLinear()[source]

Returns:: Return True if it is linear else False
Return type:: bool

isQuadratic()[source]

Returns:: Return True if it is quadratic else False
Return type:: bool

maxDegree()[source]

Returns:: maximum degree of variables
Return type:: int

simplify()[source]

Simplify this monomial

Return type:: Monomial

toExpression()[source]

Return type:: Expression

toPolynomial()[source]

Return type:: Polynomial

class flopt.polynomial.Polynomial(terms={}, constant=0)[source]

Parameters:

terms (dict(Monomial=coeff)) – sum( coeff_i * mono_i for mono_i, coeff_i in terms.items() ) + constant
constant (int of float) – constant of polynomial

coeff(*args)[source]

Returns:: coefficient of monomial
Return type:: int or float

Examples

from flopt import Variable
x = Variable('x')
y = Variable('y')
e = x ** 2 + 3 * y ** 3
e.polynomial
>>> x^2+3*y^3+0

get coefficient of x^2 term

e.polynomial.coeff(x, x)
>>> 1

get coefficient of x term, it is 0

e.polynomial.coeff(x)
>>> 0

get coefficient of y^3 term, it is 0

e.polynomial.coeff(y**3)
>>> 3

constant()[source]

Return type:: int or float