equations library
This package is used to solve numerical analysis problems, such as:
- finding roots of polynomial equations;
- finding roots of nonlinear equations;
- solving linear systems of equations;
- evaluating definite integrals;
- manipulating and decomposing matrices;
- interpolate data points using interpolation algorithms.
Additionally, the package also has utilities to work with complex numbers, real/complex matrices, fractions, and expression parsing.
Classes
- AdaptiveQuadrature
- The "Adaptive quadrature" is a technique for approximating the value of a definite integral.
- Algebraic
- Abstract class representing an algebraic equation, also know as polynomial equation, which has a single variable with a maximum degree.
- AlgebraicDivision
-
This utility class holds the quotient and the remainder of a division
between two polynomials. When you use
operator/on two Algebraic objects, this class is returned. For example: - Bisection
- Implements the 'bisection' method to find the roots of a given equation.
- Brent
- Implements Brent's method to find the roots of a given equation.
- CholeskySolver
- Implementation of the "Cholesky decomposition" algorithm for solving a system of linear equations. It only works with square, Hermitian, positive-definite matrices.
- 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 + biwhereais the real part andbiis the imaginary (or complex) part. - ComplexMatrix
-
A simple Dart implementation of an
m x nmatrix whose data type is Complex. - Constant
-
Concrete implementation of Algebraic that represents a constant value
a. It can be either real or complex. - Cubic
-
Concrete implementation of Algebraic that represents a third degree
polynomial equation in the form
ax^3 + bx^2 + cx + d = 0. - DurandKerner
- The Durand–Kerner method, also known as Weierstrass method, is a root finding algorithm for solving polynomial equations. With this class, you can find all roots of a polynomial of any degree.
- ExpressionParser
-
Parses mathematical expressions with real numbers and the
xvariable (if any). The only allowed variable name isx: 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
- Implementation of the "Gaussian elimination" algorithm, also known as "row reduction", for solving a system of linear equations. This method only works with square matrices.
- GaussSeidelSolver
- Solves a system of linear equations using the Gauss-Seidel iterative method. The given input matrix, representing the system of linear equations, must be square.
- 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 algorithms implemented by this package are:
- InterpolationNode
-
A point in the cartesian coordinate system used by Interpolation types to
represent interpolation nodes. This class simply represents the
xandycoordinates 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 currently are
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. The given input matrix, representing the system of linear equations, must be square.
-
Matrix<
T> -
A simple Dart implementation of a matrix whose size is
m x n. Thanks to its generic nature, you can decide to work with int, double, Complex or any other kind of numerical type. This library implements: - MidpointRule
- The "midpoint rule" is a technique for approximating the value of a definite integral.
- 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 <= denominatoris true. - Newton
- Implements Newton's method to find the roots of a given equation.
- NewtonInterpolation
- Newton interpolation is an interpolation polynomial for a given set of data points. It can be expressed using forward or backward 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 is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the data set.
- PolynomialLongDivision
- The "Polynomial long division" algorithm divides a polynomial by another polynomial of the same or lower degree.
- 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 simple Dart implementation of an
m x nmatrix whose data type is double. - RegulaFalsi
- Implements the regula falsi method (also known as "false position method") to find the roots of a given equation.
- Riddler
- Implements the Riddler's method to find the roots of a given equation.
- Secant
- Implements the secant method to find the roots of a given equation.
- SimpsonRule
- The "Simpson rule" is a technique for approximating the value of a definite integral.
- SORSolver
- Solves a system of linear equations using the SOR iterative method. The given input matrix, representing the system of linear equations, must be square.
- 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 Seffensen's method to find the roots of a given equation.
- SylvesterMatrix
- A Sylvester matrix is used to compute the discriminant of a polynomial starting from its coefficients.
- 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 technique for approximating the value of a definite integral.
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.
Exceptions / Errors
- AlgebraicException
- Exception object thrown by Algebraic.
- ComplexException
- Exception object thrown by Complex.
- EquationException
- Base class for exception objects in this 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.