equations library

Classes

AdaptiveQuadrature: The "Adaptive quadrature" is a technique for approximating the value of a definite integral that automatically adjusts the step size based on the local behavior of the function being integrated.
Algebraic: An abstract class that represents an algebraic equation, also known as a polynomial equation, which has a single variable and a maximum degree.
AlgebraicInequalityAllRealNumbers: A solution of an Algebraic inequality that includes all real numbers.
AlgebraicInequalityGreaterThan: A solution of an Algebraic inequality that is greater than value.
AlgebraicInequalityInterval: A solution of an Algebraic inequality that is an interval between start and end values.
AlgebraicInequalitySmallerThan: A solution of an Algebraic inequality that is smaller than value.
AlgebraicInequalitySolution: A solution of an Algebraic inequality.
Bisection: Implements the bisection method to find a root of a given equation.
Brent: Implements Brent's method to find the roots of a given equation.
CholeskySolver: Solves a system of linear equations using the Cholesky decomposition method.
Chords: Implements the 'chords' method to find the roots of a given equation.
Complex: A Dart representation of a complex number in the form a + bi where a is the real part and bi is the imaginary (or complex) part.
ComplexMatrix: A simple Dart implementation of an m x n matrix whose data type is Complex.
Constant: Concrete implementation of Algebraic that represents a constant value a. It can be either a real or complex number, such as:
Cubic: Concrete implementation of Algebraic that represents a third degree polynomial equation in the form ax^3 + bx^2 + cx + d = 0.
ExpressionParser: Parses mathematical expressions with real numbers and the x variable (if any). The only allowed variable name is x: any other type of value isn't recognized. Some expressions examples are:
Fraction: Dart representation of a fraction having both numerator and denominator as integers. If the denominator is zero, a FractionException object is thrown.
GaussianElimination: Solves a system of linear equations using the Gaussian elimination algorithm, also known as row reduction.
GaussSeidelSolver: Solves a system of linear equations using the Gauss-Seidel iterative method.
GenericAlgebraic: Concrete implementation of Algebraic that approximates all roots of a polynomial of any degree.
Interpolation: An abstract class that represents an interpolation strategy, used to find new data points based on a given discrete set of data points (called nodes). The available interpolation algorithms are:
InterpolationNode: A point in the cartesian coordinate system used by Interpolation types to represent interpolation nodes. This class simply represents the x and y coordinates of a point on a cartesian plane.
IntervalsIntegration: This class is extended by classes whose algorithms divide the integration bounds into smaller intervals to compute the result. There are currently three subclasses of IntervalsIntegration:
JacobiSolver: Solves a system of linear equations using the Jacobi iterative method. The given input matrix, representing the system of linear equations, must be square.
Linear: Concrete implementation of Algebraic that represents a first degree polynomial equation in the form ax + b = 0.
LinearInterpolation: Linear interpolation is a curve fitting method that uses linear polynomials to construct new data points within the range of a discrete set of known data points.
LUSolver: Solves a system of linear equations using the LU decomposition method.
Matrix<T>: A matrix with rowCount rows and columnCount columns. This abstract type allows the implementation of different types of matrices, each with their own specific methods and types. This library implements:
MidpointRule: The midpoint rule is a numerical integration technique for approximating definite integrals using Riemann sums. Given a definite integral in the form ∫[a,b] f(x) dx, the midpoint rule approximates it as:
MixedFraction: Dart representation of a 'mixed fraction', which is made up by the whole part and a proper fraction. A proper fraction is a fraction in which the relation numerator <= denominator is true.
Newton: Implements Newton's method (also known as the Newton-Raphson method) to find the roots of a given equation.
NewtonInterpolation: Newton interpolation (also known as Newton's divided difference interpolation) is a polynomial interpolation method that constructs an interpolation polynomial for a given set of data points using divided differences.
NonLinear: An abstract class that represents a nonlinear equation, which can be solved with a particular root-finding algorithm. No complex numbers are allowed.
NumericalIntegration: When it comes to analysis, the term numerical integration indicates a group of algorithms for calculating the numerical value of a definite integral on an interval.
PolarComplex: A wrapper class, returned by a Complex object, that represents a complex number in polar coordinates.
PolynomialInterpolation: Polynomial interpolation using Lagrange's interpolation formula to find the unique polynomial of degree n-1 that passes through n given data points.
PolynomialLongDivision: Implements the polynomial long division algorithm, which divides one polynomial by another polynomial.
Quadratic: Concrete implementation of Algebraic that represents a second degree polynomial equation in the form ax^2 + bx + c = 0.
Quartic: Concrete implementation of Algebraic that represents a fourth degree polynomial equation in the form ax^4 + bx^3 + cx^2 + dx + e = 0.
Rational: Dart representation of a rational number.
RealMatrix: A Dart implementation of an MxM matrix whose data type is double.
RegulaFalsi: Implements the regula falsi method (also known as the "false position method") to find the roots of a given equation.
Riddler: Implements Riddler's method (also known as the Ridders' method) to find the roots of a given equation.
Secant: Implements the secant method to find the roots of a given equation. It is similar to Newton's method but does not require the computation of derivatives.
SimpsonRule: Simpson's Rule is a numerical integration technique that approximates the value of a definite integral using quadratic polynomials. Given a definite integral in the form ∫[a,b] f(x) dx, Simpson's rule approximates it as:
SORSolver: Solves a system of linear equations using the Successive Over-Relaxation (SOR) iterative method.
SplineInterpolation: Performs spline interpolation given a set of control points. The algorithm can compute a "monotone cubic spline" or a "linear spline" based on the properties of the control points.
Steffensen: Implements Steffensen's method to find the roots of a given equation.
SylvesterMatrix: The Sylvester matrix is used to compute the discriminant of a polynomial of any degree.
SystemSolver: An abstract class that represents a system of equations, which can be solved using various algorithms that manipulate the data of a matrix and a vector.
TrapezoidalRule: The trapezoidal rule is a numerical integration technique for approximating definite integrals using linear interpolation. Given a definite integral in the form ∫[a,b] f(x) dx, the trapezoidal rule approximates it as:

Enums

AlgebraicInequalityType: The kind of Algebraic inequality to solve.

Extensions

ExpressionParserX on String: Extension method for ExpressionParser on String types.
FractionNum on num: Extension method that adds Fraction functionalities to num.
FractionString on String: Extension method that adds Fraction functionalities to String.
MixedFractionNum on num: Extension method that adds MixedFraction functionalities to num.
MixedFractionString on String: Extension method that adds MixedFraction functionalities to String.

Typedefs

AlgebraicDivision = ({Algebraic quotient, Algebraic remainder}): A record type that holds the quotient and the remainder of a division between two polynomials. When you use operator/ on two Algebraic objects, this type is returned. The quotient represents the result of the division, while the remainder represents what's left after the division.

Exceptions / Errors

AlgebraicException: Exception object thrown by Algebraic.
ComplexException: Exception object thrown by Complex.
EquationException: Base class for exception objects in the equations package.
ExpressionParserException: Exception object thrown by ExpressionParser.
FractionException: Exception object thrown by a Fraction object.
InterpolationException: Exception object thrown by Interpolation.
MatrixException: Exception object thrown by Matrix.
MixedFractionException: Exception object thrown by a MixedFraction object.
NonlinearException: Exception object thrown by NonLinear.
PolynomialLongDivisionException: Exception object thrown by PolynomialLongDivision.
SystemSolverException: Exception object thrown by SystemSolver.

equations library

Classes

Enums

Extensions

Typedefs

Exceptions / Errors

equations package

equations library