{"id":20754311,"url":"https://github.com/mrigankpawagi/numericalmethods","last_synced_at":"2025-04-28T16:28:58.599Z","repository":{"id":187431976,"uuid":"676898155","full_name":"mrigankpawagi/NumericalMethods","owner":"mrigankpawagi","description":"Numerical Methods and Functions Library","archived":false,"fork":false,"pushed_at":"2024-05-02T13:11:01.000Z","size":68,"stargazers_count":6,"open_issues_count":3,"forks_count":2,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-03-30T11:22:55.413Z","etag":null,"topics":["math-library","numerical-methods","python"],"latest_commit_sha":null,"homepage":"","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/mrigankpawagi.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null}},"created_at":"2023-08-10T09:08:18.000Z","updated_at":"2025-02-15T19:44:38.000Z","dependencies_parsed_at":"2023-08-10T11:54:31.643Z","dependency_job_id":"7c769dfe-7baf-4319-bf52-de06df47761c","html_url":"https://github.com/mrigankpawagi/NumericalMethods","commit_stats":null,"previous_names":["mrigankpawagi/numericalmethods"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mrigankpawagi%2FNumericalMethods","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mrigankpawagi%2FNumericalMethods/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mrigankpawagi%2FNumericalMethods/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mrigankpawagi%2FNumericalMethods/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/mrigankpawagi","download_url":"https://codeload.github.com/mrigankpawagi/NumericalMethods/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":251345284,"owners_count":21574684,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["math-library","numerical-methods","python"],"created_at":"2024-11-17T09:17:04.879Z","updated_at":"2025-04-28T16:28:58.577Z","avatar_url":"https://github.com/mrigankpawagi.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Numerical Methods and Functions Library\n\n**Created during UMC 202 at the Indian Institute of Science, Bengaluru**\n\n\u003cdetails\u003e\n  \u003csummary\u003e\u003cb\u003eFunctions\u003c/b\u003e\u003c/summary\u003e\n\n- Support for polynomials\n- Support for function arithmetic, composition and other methods\n- Support for derivatives and differentiation\n    - Forward difference\n    - Backward difference\n    - Central difference\n    - n-th order derivative\n- Allows probing algorithms\n- Support for integration\n    - Rectangular\n    - Midpoint\n    - Trapezoidal \n    - Simpson's\n    - Gaussian Quadrature (n = 1, 2)\n- Support for multivariable functions\n- Support for vectors and vector-valued functions\n- Support for matrices (vector of vectors)\n\n**Other Utilities**\n- Plotting (requires `matplotlib`)\n\u003c/details\u003e\n\n\u003cdetails\u003e\n  \u003csummary\u003e\u003cb\u003eMethods\u003c/b\u003e\u003c/summary\u003e\n\n- Root finding\n    - Bisection\n    - Newton-Raphson and Modified Newton\n    - Fixed-point iteration\n    - Secant\n    - Regula-Falsi\n- Interpolating Polynomial\n    - Lagrange\n    - Newton's divided difference\n    - Forward difference\n    - Backward difference\n- Solving initial value problems on one-dimensional first order linear ODEs (and systems of such ODEs)\n    - Euler's method\n    - Taylor's method (for n = 1, 2)\n    - Runga Kutta (for n = 1, 2, 3, 4)\n    - Trapezoidal\n    - Adam-Bashforth (for n = 2, 3, 4)\n    - Adam-Moulton (for n = 2, 3, 4)\n    - Predictor-Corrector (with initial approximation from Runga-Kutta order-4, predictor as Adam-Bashforth order-4 and corrector as Adam-Moulton order-3)\n- Solving boundary value problems on one-dimensional second order linear ODEs\n    - Shooting method\n    - Finite difference method\n- Solving initial value problems on one-dimensional second order ODEs\n    - All methods from solving first order linear ODEs\n- Solving boundary value problems on one-dimensional second order ODEs\n    - Shooting method\n        - Newton method\n- Solving systems of linear equations\n    - Gaussian elimination with backward substitution\n    - Gauss-Jacobi method\n    - Gauss-Seidel method\n\u003c/details\u003e\n\n## Usage\n\nThe file `function.py` contains all the important classes and methods, and is the main file to be imported. The file `util.py` has a few helper methods required by the main file. Some practice problem sets have been included in the `examples` directory to demonstrate the usage of the library.\n\n\u003e [!NOTE]  \n\u003e Documentation below was generated automatically using [pdoc](https://pdoc3.github.io/).\n\n# Module `function` \n\n\n\n\n\n\n\n\n## Classes\n\n\n\n### Class `BivariateFunction` \n\n\n\n\n\u003e     class BivariateFunction(\n\u003e         function\n\u003e     )\n\n\n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.MultiVariableFunction](#function.MultiVariableFunction)\n\n\n\n\n\n\n\n### Class `Cos` \n\n\n\n\n\u003e     class Cos(\n\u003e         f: function.Function\n\u003e     )\n\n\n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.Function](#function.Function)\n\n\n\n\n\n\n\n### Class `Exponent` \n\n\n\n\n\u003e     class Exponent(\n\u003e         f: function.Function,\n\u003e         base: float = 2.718281828459045\n\u003e     )\n\n\n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.Function](#function.Function)\n\n\n\n\n\n\n\n### Class `FirstOrderLinearODE` \n\n\n\n\n\u003e     class FirstOrderLinearODE(\n\u003e         f: function.BivariateFunction,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         y0: float\n\u003e     )\n\n\ny'(x) = f(x, y(x))\nThese are initial value problems.\n\nf is a function of x and y(x)\n\n\n\n#### Ancestors (in MRO)\n\n* [function.LinearODE](#function.LinearODE)\n* [function.OrdinaryDifferentialEquation](#function.OrdinaryDifferentialEquation)\n\n\n\n\n\n\n\n#### Methods\n\n\n\n##### Method `solve` \n\n\n\n\n\u003e     def solve(\n\u003e         self,\n\u003e         h: float = 0.1,\n\u003e         method: Literal['euler', 'runge-kutta', 'taylor', 'trapezoidal', 'adam-bashforth', 'adam-moulton', 'predictor-corrector'] = 'euler',\n\u003e         n: int = 1,\n\u003e         step: int = 2,\n\u003e         points: list[float] = []\n\u003e     )\n\n\n\n\n\n##### Method `solve_adam_bashforth` \n\n\n\n\n\u003e     def solve_adam_bashforth(\n\u003e         self,\n\u003e         h: float,\n\u003e         step: int,\n\u003e         points: list[float]\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n##### Method `solve_adam_moulton` \n\n\n\n\n\u003e     def solve_adam_moulton(\n\u003e         self,\n\u003e         h: float,\n\u003e         step: int,\n\u003e         points: list[float]\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n##### Method `solve_predictor_corrector` \n\n\n\n\n\u003e     def solve_predictor_corrector(\n\u003e         self,\n\u003e         h: float\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n##### Method `solve_runge_kutta` \n\n\n\n\n\u003e     def solve_runge_kutta(\n\u003e         self,\n\u003e         h: float,\n\u003e         n: int\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n##### Method `solve_taylor` \n\n\n\n\n\u003e     def solve_taylor(\n\u003e         self,\n\u003e         h: float,\n\u003e         n: int\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n##### Method `solve_trapezoidal` \n\n\n\n\n\u003e     def solve_trapezoidal(\n\u003e         self,\n\u003e         h: float\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n### Class `Function` \n\n\n\n\n\u003e     class Function(\n\u003e         function\n\u003e     )\n\n\n\n\n\n\n\n#### Descendants\n\n* [function.Cos](#function.Cos)\n* [function.Exponent](#function.Exponent)\n* [function.Log](#function.Log)\n* [function.Polynomial](#function.Polynomial)\n* [function.Sin](#function.Sin)\n* [function.Tan](#function.Tan)\n\n\n\n\n\n\n#### Methods\n\n\n\n##### Method `bisection` \n\n\n\n\n\u003e     def bisection(\n\u003e         self,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         TOLERANCE=1e-10,\n\u003e         N=100,\n\u003e         early_stop: int = None\n\u003e     )\n\n\n\n\n\n##### Method `differentiate` \n\n\n\n\n\u003e     def differentiate(\n\u003e         self,\n\u003e         func=None,\n\u003e         h=1e-05,\n\u003e         method: Literal['forward', 'backward', 'central'] = 'forward'\n\u003e     )\n\n\nSets or returns the derivative of the function.\nIf func is None, returns the derivative.\nIf func is a Function, sets the derivative to func.\nIf func is a lambda, sets the derivative to a Function with the lambda.\n\n\n##### Method `differentiate_central` \n\n\n\n\n\u003e     def differentiate_central(\n\u003e         self,\n\u003e         h\n\u003e     )\n\n\n\n\n\n##### Method `differentiate_forward` \n\n\n\n\n\u003e     def differentiate_forward(\n\u003e         self,\n\u003e         h\n\u003e     )\n\n\n\n\n\n##### Method `fixed_point` \n\n\n\n\n\u003e     def fixed_point(\n\u003e         self,\n\u003e         p0: float,\n\u003e         TOLERANCE=1e-10,\n\u003e         N=100\n\u003e     )\n\n\n\n\n\n##### Method `integral` \n\n\n\n\n\u003e     def integral(\n\u003e         self,\n\u003e         func=None,\n\u003e         h=1e-05\n\u003e     )\n\n\nSets or returns the integral of the function.\nIf func is None, returns the integral.\nIf func is a Function, sets the integral to func.\nIf func is a lambda, sets the integral to a Function with the lambda.\n\n\n##### Method `integrate` \n\n\n\n\n\u003e     def integrate(\n\u003e         self,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         method: Literal['rectangular', 'midpoint', 'trapezoidal', 'simpson', 'gauss'] = None,\n\u003e         n: int = None\n\u003e     )\n\n\nDefinite integral of the function from a to b.\n\n\n##### Method `integrate_gauss` \n\n\n\n\n\u003e     def integrate_gauss(\n\u003e         self,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         n: int = None\n\u003e     )\n\n\n\n\n\n##### Method `integrate_midpoint` \n\n\n\n\n\u003e     def integrate_midpoint(\n\u003e         self,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         n: int = None\n\u003e     )\n\n\n\n\n\n##### Method `integrate_rectangular` \n\n\n\n\n\u003e     def integrate_rectangular(\n\u003e         self,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         n: int = None\n\u003e     )\n\n\n\n\n\n##### Method `integrate_simpson` \n\n\n\n\n\u003e     def integrate_simpson(\n\u003e         self,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         n: int = None\n\u003e     )\n\n\n\n\n\n##### Method `integrate_trapezoidal` \n\n\n\n\n\u003e     def integrate_trapezoidal(\n\u003e         self,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         n: int = None\n\u003e     )\n\n\n\n\n\n##### Method `modified_newton` \n\n\n\n\n\u003e     def modified_newton(\n\u003e         self,\n\u003e         p0: float,\n\u003e         TOLERANCE=1e-10,\n\u003e         N=100,\n\u003e         early_stop: int = None\n\u003e     )\n\n\n\n\n\n##### Method `multi_differentiate` \n\n\n\n\n\u003e     def multi_differentiate(\n\u003e         self,\n\u003e         n: int,\n\u003e         h=1e-05,\n\u003e         method: Literal['forward', 'backward', 'central'] = 'forward'\n\u003e     )\n\n\nReturns the nth derivative of the function.\n\n\n##### Method `newton` \n\n\n\n\n\u003e     def newton(\n\u003e         self,\n\u003e         p0: float,\n\u003e         TOLERANCE=1e-10,\n\u003e         N=100,\n\u003e         early_stop: int = None\n\u003e     )\n\n\n\n\n\n##### Method `plot` \n\n\n\n\n\u003e     def plot(\n\u003e         self,\n\u003e         min: float,\n\u003e         max: float,\n\u003e         N=1000,\n\u003e         file: str = '',\n\u003e         clear: bool = False\n\u003e     )\n\n\n\n\n\n##### Method `regula_falsi` \n\n\n\n\n\u003e     def regula_falsi(\n\u003e         self,\n\u003e         p0: float,\n\u003e         p1: float,\n\u003e         TOLERANCE=1e-10,\n\u003e         N=100,\n\u003e         early_stop: int = None\n\u003e     )\n\n\n\n\n\n##### Method `root` \n\n\n\n\n\u003e     def root(\n\u003e         self,\n\u003e         method: Literal['bisection', 'newton', 'secant', 'regula_falsi', 'modified_newton'],\n\u003e         a: float = None,\n\u003e         b: float = None,\n\u003e         p0: float = None,\n\u003e         p1: float = None,\n\u003e         TOLERANCE=1e-10,\n\u003e         N=100,\n\u003e         return_iterations=False,\n\u003e         early_stop: int = None\n\u003e     )\n\n\n\n\n\n##### Method `secant` \n\n\n\n\n\u003e     def secant(\n\u003e         self,\n\u003e         p0: float,\n\u003e         p1: float,\n\u003e         TOLERANCE=1e-10,\n\u003e         N=100,\n\u003e         early_stop: int = None\n\u003e     )\n\n\n\n\n\n### Class `LinearODE` \n\n\n\n\n\u003e     class LinearODE\n\n\n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.OrdinaryDifferentialEquation](#function.OrdinaryDifferentialEquation)\n\n\n\n#### Descendants\n\n* [function.FirstOrderLinearODE](#function.FirstOrderLinearODE)\n* [function.SecondOrderLinearODE_BVP](#function.SecondOrderLinearODE_BVP)\n\n\n\n\n\n\n### Class `LinearSystem` \n\n\n\n\n\u003e     class LinearSystem(\n\u003e         A: function.Matrix,\n\u003e         b: function.Vector\n\u003e     )\n\n\nA system of linear equations.\n\n\n\n\n\n\n\n\n#### Methods\n\n\n\n##### Method `solve` \n\n\n\n\n\u003e     def solve(\n\u003e         self,\n\u003e         method: Literal['gauss_elimination', 'gauss_jacobi', 'gauss_seidel'] = 'gauss_elimination',\n\u003e         TOL: float = 1e-05,\n\u003e         initial_approximation: function.Vector = None,\n\u003e         MAX_ITERATIONS: int = 100\n\u003e     )\n\n\n\n\n\n##### Method `solve_gauss_elimination` \n\n\n\n\n\u003e     def solve_gauss_elimination(\n\u003e         self\n\u003e     ) ‑\u003e function.Vector\n\n\n\n\n\n##### Method `solve_gauss_jacobi` \n\n\n\n\n\u003e     def solve_gauss_jacobi(\n\u003e         self,\n\u003e         TOL: float,\n\u003e         initial_approximation: function.Vector,\n\u003e         MAX_ITERATIONS\n\u003e     ) ‑\u003e function.Vector\n\n\n\n\n\n##### Method `solve_gauss_seidel` \n\n\n\n\n\u003e     def solve_gauss_seidel(\n\u003e         self,\n\u003e         TOL: float,\n\u003e         initial_approximation: function.Vector,\n\u003e         MAX_ITERATIONS\n\u003e     ) ‑\u003e function.Vector\n\n\n\n\n\n### Class `Log` \n\n\n\n\n\u003e     class Log(\n\u003e         f: function.Function,\n\u003e         base: float = 2.718281828459045\n\u003e     )\n\n\n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.Function](#function.Function)\n\n\n\n\n\n\n\n### Class `Matrix` \n\n\n\n\n\u003e     class Matrix(\n\u003e         *rows: list[function.Vector]\n\u003e     )\n\n\n\n\n\n\n\n\n\n\n\n### Class `MultiVariableFunction` \n\n\n\n\n\u003e     class MultiVariableFunction(\n\u003e         function\n\u003e     )\n\n\n\n\n\n\n\n#### Descendants\n\n* [function.BivariateFunction](#function.BivariateFunction)\n\n\n\n\n\n\n### Class `OrdinaryDifferentialEquation` \n\n\n\n\n\u003e     class OrdinaryDifferentialEquation\n\n\n\n\n\n\n\n#### Descendants\n\n* [function.LinearODE](#function.LinearODE)\n* [function.SecondOrderODE_BVP](#function.SecondOrderODE_BVP)\n* [function.SecondOrderODE_IVP](#function.SecondOrderODE_IVP)\n\n\n\n\n\n\n### Class `Polynomial` \n\n\n\n\n\u003e     class Polynomial(\n\u003e         *coefficients\n\u003e     )\n\n\ncoefficients are in the form a_0, a_1, ... a_n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.Function](#function.Function)\n\n\n\n\n\n\n#### Static methods\n\n\n\n##### `Method interpolate` \n\n\n\n\n\u003e     def interpolate(\n\u003e         data: tuple,\n\u003e         method: Literal['lagrange', 'newton'] = 'newton',\n\u003e         f: function.Function = None,\n\u003e         form: Literal['standard', 'backward_diff', 'forward_diff'] = 'standard'\n\u003e     )\n\n\ndata is a list of (x, y) tuples.\nalternative: f is a Function that returns the y values and data is a list of x values.\n\n\n##### `Method interpolate_lagrange` \n\n\n\n\n\u003e     def interpolate_lagrange(\n\u003e         data: tuple\n\u003e     )\n\n\ndata is a tuple of (x, y) tuples\n\n\n##### `Method interpolate_newton` \n\n\n\n\n\u003e     def interpolate_newton(\n\u003e         data: tuple\n\u003e     )\n\n\ndata is a tuple of (x, y) tuples\n\n\n##### `Method interpolate_newton_backward_diff` \n\n\n\n\n\u003e     def interpolate_newton_backward_diff(\n\u003e         data: tuple\n\u003e     )\n\n\ndata is a tuple of (x, y) tuples\n\n\n##### `Method interpolate_newton_forward_diff` \n\n\n\n\n\u003e     def interpolate_newton_forward_diff(\n\u003e         data: tuple\n\u003e     )\n\n\ndata is a tuple of (x, y) tuples\n\n\n\n### Class `SecondOrderLinearODE_BVP` \n\n\n\n\n\u003e     class SecondOrderLinearODE_BVP(\n\u003e         p: function.Function,\n\u003e         q: function.Function,\n\u003e         r: function.Function,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         y0: float,\n\u003e         y1: float\n\u003e     )\n\n\ny''(x) = p(x)y'(x) + q(x)y(x) + r(x)\nThese are boundary value problems.\n\n\n\n#### Ancestors (in MRO)\n\n* [function.LinearODE](#function.LinearODE)\n* [function.OrdinaryDifferentialEquation](#function.OrdinaryDifferentialEquation)\n\n\n\n\n\n\n\n#### Methods\n\n\n\n##### Method `solve` \n\n\n\n\n\u003e     def solve(\n\u003e         self,\n\u003e         h: float = 0.1,\n\u003e         method: Literal['shooting', 'finite_difference'] = 'shooting'\n\u003e     )\n\n\n\n\n\n##### Method `solve_finite_difference` \n\n\n\n\n\u003e     def solve_finite_difference(\n\u003e         self,\n\u003e         h: float\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n##### Method `solve_shooting` \n\n\n\n\n\u003e     def solve_shooting(\n\u003e         self,\n\u003e         h: float\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n### Class `SecondOrderODE_BVP` \n\n\n\n\n\u003e     class SecondOrderODE_BVP(\n\u003e         f: function.MultiVariableFunction,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         y0: float,\n\u003e         y1: float\n\u003e     )\n\n\ny''(x) = f(x, y(x), y'(x))\nThese are boundary value problems.\n\nf is a function of x, y(x), and y'(x)\n\n\n\n#### Ancestors (in MRO)\n\n* [function.OrdinaryDifferentialEquation](#function.OrdinaryDifferentialEquation)\n\n\n\n\n\n\n\n#### Methods\n\n\n\n##### Method `solve` \n\n\n\n\n\u003e     def solve(\n\u003e         self,\n\u003e         h: float = 0.1,\n\u003e         method: Literal['shooting_newton'] = 'shooting_newton',\n\u003e         M: int = 100,\n\u003e         TOL: float = 1e-05,\n\u003e         initial_approximation=None\n\u003e     )\n\n\n\n\n\n##### Method `solve_shooting_newton` \n\n\n\n\n\u003e     def solve_shooting_newton(\n\u003e         self,\n\u003e         h: float,\n\u003e         M,\n\u003e         TOL,\n\u003e         initial_approximation\n\u003e     ) ‑\u003e function.Polynomial\n\n\n\n\n\n### Class `SecondOrderODE_IVP` \n\n\n\n\n\u003e     class SecondOrderODE_IVP(\n\u003e         f: function.MultiVariableFunction,\n\u003e         a: float,\n\u003e         b: float,\n\u003e         y0: float,\n\u003e         y1: float\n\u003e     )\n\n\ny''(x) = f(x, y(x), y'(x))\nThese are initial value problems.\n\nf is a function of x, y(x), and y'(x)\n\n\n\n#### Ancestors (in MRO)\n\n* [function.OrdinaryDifferentialEquation](#function.OrdinaryDifferentialEquation)\n\n\n\n\n\n\n\n#### Methods\n\n\n\n##### Method `solve` \n\n\n\n\n\u003e     def solve(\n\u003e         self,\n\u003e         h: float = 0.1,\n\u003e         method: Literal['euler', 'runge-kutta', 'taylor', 'trapezoidal', 'adam-bashforth', 'adam-moulton', 'predictor-corrector'] = 'euler',\n\u003e         n: int = 1,\n\u003e         step: int = 2,\n\u003e         points: list[float] = []\n\u003e     )\n\n\n\n\n\n### Class `Sin` \n\n\n\n\n\u003e     class Sin(\n\u003e         f: function.Function\n\u003e     )\n\n\n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.Function](#function.Function)\n\n\n\n\n\n\n\n### Class `Tan` \n\n\n\n\n\u003e     class Tan(\n\u003e         f: function.Function\n\u003e     )\n\n\n\n\n\n\n#### Ancestors (in MRO)\n\n* [function.Function](#function.Function)\n\n\n\n\n\n\n\n### Class `Vector` \n\n\n\n\n\u003e     class Vector(\n\u003e         *components\n\u003e     )\n\n\n\n\n\n\n\n\n\n\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmrigankpawagi%2Fnumericalmethods","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmrigankpawagi%2Fnumericalmethods","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmrigankpawagi%2Fnumericalmethods/lists"}