Abstract class representing an algebraic equation, also know as polynomial equation, which has a single variable with a maximum degree.
The coefficients of the algebraic equations can be real numbers or complex numbers. These are examples of an algebraic equations of third degree:
- x3 + 5x + 2 = 0
- 2x3 + (6+i)x + 8i = 0
This class stores the coefficients list starting from the one with the highest degree.
Constructors
-
Algebraic(List<
Complex> coefficients) - Creates a new algebraic equation by taking the coefficients of the polynomial starting from the one with the highest degree.
-
Algebraic.from(List<
Complex> coefficients) -
Creates an Algebraic subtype according with the length of the
coefficients
list. In particular:factory -
Algebraic.fromReal(List<
double> coefficients) -
Creates an Algebraic subtype according with the length of the
coefficients
list. In particular:factory -
Algebraic.realEquation(List<
double> coefficients) - Creates a new algebraic equation by taking the coefficients of the polynomial starting from the one with the highest degree.
Properties
-
coefficients
→ List<
Complex> -
The list with the polynomial coefficients.
final
- degree → num
-
The degree of the polynomial.
no setter
- hashCode → int
-
The hash code for this object.
no setteroverride
- isRealEquation → bool
-
Determines whether the polynomial is real or not.
no setter
- runtimeType → Type
-
A representation of the runtime type of the object.
no setterinherited
Methods
-
coefficient(
int degree) → Complex? -
Returns the coefficient of the polynomial whose degree is
degree
. For example: -
derivative(
) → Algebraic - The derivative of the polynomial.
-
discriminant(
) → Complex - The polynomial discriminant, if it exists.
-
evaluateIntegralOn(
double lower, double upper) → Complex -
Evaluates the integral of the the polynomial between
lower
andupper
. -
evaluateOn(
Complex x) → Complex -
Evaluates the polynomial on the given
x
value. -
noSuchMethod(
Invocation invocation) → dynamic -
Invoked when a nonexistent method or property is accessed.
inherited
-
realEvaluateOn(
double x) → Complex -
Evaluates the polynomial on the given decimal
x
value. -
solutions(
) → List< Complex> - Finds the roots (the solutions) of the associated P(x) = 0 equation.
-
toString(
) → String -
A string representation of this object.
override
-
toStringWithFractions(
) → String - Returns a string representation of the polynomial where the coefficients are converted into their fractional representation.
Operators
-
operator *(
Algebraic other) → Algebraic - The product of two polynomials is performed by multiplying the corresponding coefficients of the polynomials.
-
operator +(
Algebraic other) → Algebraic - The sum of two polynomials is performed by adding the corresponding coefficients.
-
operator -(
Algebraic other) → Algebraic - The difference of two polynomials is performed by subtracting the corresponding coefficients.
-
operator /(
Algebraic other) → AlgebraicDivision - This operator divides a polynomial by another polynomial of the same or lower degree.
-
operator ==(
Object other) → bool -
The equality operator.
override
-
operator [](
int index) → Complex -
Returns the coefficient of the polynomial at the given
index
position. For example: -
operator unary-(
) → Algebraic - The 'negation' operator changes the sign of every coefficient of the polynomial. For example: