Cubic class

Concrete implementation of Algebraic that represents a third degree polynomial equation in the form ax^3 + bx^2 + cx + d = 0.

This equation has exactly 3 solutions:

The above cases depend on the value of the discriminant.

Inheritance

Constructors

Cubic.new({Complex a = const Complex.fromReal(1), Complex b = const Complex.zero(), Complex c = const Complex.zero(), Complex d = const Complex.zero()}): These are examples of cubic equations, where the coefficient with the highest degree goes first:
Cubic.realEquation({double a = 1, double b = 0, double c = 0, double d = 0}): The only coefficient of the polynomial is represented by a double (real) number a.

a → Complex: The first coefficient of the equation in the form f(x) = ax^3 + bx^2 + cx + d = 0
no setter
b → Complex: The second coefficient of the equation in the form f(x) = ax^3 + bx^2 + cx + d = 0
no setter
c → Complex: The third coefficient of the equation in the form f(x) = ax^3 + bx^2 + cx + d = 0
no setter
coefficients → UnmodifiableListView<Complex>: An unmodifiable list with the coefficients of the polynomial.
finalinherited
d → Complex: The fourth coefficient of the equation in the form f(x) = ax^3 + bx^2 + cx + d = 0
no setter
degree → int: The degree of the polynomial.
no setteroverride
hashCode → int: The hash code for this object.
no setterinherited
isRealEquation → bool: Determines whether the polynomial is real or not.
no setterinherited
isValid → bool: A polynomial equation is valid if the coefficient associated to the variable of highest degree is different from zero. In other words, the polynomial is valid if a is different from zero.
no setterinherited
runtimeType → Type: A representation of the runtime type of the object.
no setterinherited

coefficient(int degree) → Complex?: Returns the coefficient of the polynomial whose degree is degree. For example:
inherited
copyWith({Complex? a, Complex? b, Complex? c, Complex? d}) → Cubic: Creates a deep copy of this object with the given fields replaced with the new values.
derivative() → Algebraic: The derivative of the polynomial.
override
discriminant() → Complex: The discriminant of the algebraic equation if it exists.
override
evaluateIntegralOn(double lower, double upper) → Complex: Integrates the polynomial between lower and upper and computes the result.
inherited
evaluateOn(Complex x) → Complex: Evaluates the polynomial on the given complex number x.
inherited
noSuchMethod(Invocation invocation) → dynamic: Invoked when a nonexistent method or property is accessed.
inherited
realEvaluateOn(double x) → Complex: Evaluates the polynomial on the given real number x.
inherited
solutions() → List<Complex>: Calculates the roots (the solutions) of the equation.
override
toString() → String: A string representation of this object.
inherited
toStringWithFractions() → String: Returns a string representation of the polynomial where the coefficients are converted into their fractional representation.
inherited

operator *(Algebraic other) → Algebraic: The product of two polynomials is performed by multiplying the corresponding coefficients of the polynomials. The degrees of the two polynomials don't need to be the same so you can multiply a Constant with a DurandKerner for example.
inherited
operator +(Algebraic other) → Algebraic: The addition of two polynomials is performed by adding the corresponding coefficients. The degrees of the two polynomials don't need to be the same so you can sum a Cubic with a Linear for example.
inherited
operator -(Algebraic other) → Algebraic: The difference of two polynomials is performed by subtracting the corresponding coefficients. The degrees of the two polynomials don't need to be the same so you can subtract a Quadratic and a Quartic for example.
inherited
operator /(Algebraic other) → AlgebraicDivision: This operator divides a polynomial by another polynomial of the same or lower degree.
inherited
operator ==(Object other) → bool: The equality operator.
inherited
operator [](int index) → Complex: Returns the coefficient of the polynomial at the given index position. For example:
inherited
operator unary-() → Algebraic: The 'negation' operator changes the sign of every coefficient of the polynomial. For example:
inherited