In formal methods of computer science, a paramorphism (from Greek παρά, meaning "close together") is an extension of the concept of catamorphism first introduced by Lambert Meertens to deal with a form which “eats its argument and keeps it too”, as exemplified by the factorial function. Its categorical dual is the apomorphism. It is a more convenient version of catamorphism in that it gives the combining step function immediate access not only to the result value recursively computed from each recursive subobject, but the original subobject itself as well. Example Haskell implementation, for lists: cata :: (a -> b -> b) -> b -> [a] -> bpara :: (a -> ([a], b) -> b) -> b -> [a] -> bana :: (b -> (a, b)) -> b -> [a]apo :: (b -> (a, Either [a] b)) -> b -> [a]cata f b (a:as) = f a (cata f b as)cata _ b [] = bpara f b (a:as) = f a (as, para f b as)para _ b [] = bana u b = case u b of (a, b') -> a : ana u b'apo u b = case u b of (a, Right b') -> a : apo u b' (a, Left as) -> a : as (Wikipedia).
Introduction to Parametric Equations
This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
From playlist Parametric Equations
Learn how to eliminate the parameter given sine and cosine of t
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
Calculus 2: Parametric Equations (1 of 20) What is a Parametric Equation?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a parametric equation. A parametric equation is an equation that expresses each variable of an equation in terms of another variable. Next video in the series can be seen at: https://
From playlist CALCULUS 2 CH 17 PARAMETRIC EQUATIONS
Eliminating the parameter for parametric trigonometric
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
Parametric equations on one Cartesian path (1 of 2: Introduction)
More resources available at www.misterwootube.com
From playlist Mathematical Exploration
Introduction to Homotopy Theory: Part 6- Projective and Injective Morphisms
Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtube Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track L
From playlist Introduction to Homotopy Theory
Learn how to eliminate the parameter with trig functions
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
Learn how to eliminate the parameter with trig
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
How to eliminate the parameter to identify the linear equation
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
Eliminating the parameter for parametric equations quadratic
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations
Sylvie Paycha: A Galois group on meromorphic germs and locality evaluators
Talk by Sylvie Paycha in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on February 9, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Live CEOing Ep 387: Calculus & Algebra Features Design Review for Wolfram Language
In this episode of Live CEOing, Stephen Wolfram reviews the design of calculus and algebra features and functionality for the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch
From playlist Behind the Scenes in Real-Life Software Design
Learn to eliminate the parameter
Learn how to eliminate the parameter in a parametric equation. A parametric equation is a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as parameters. Eliminating the parameter allows us to write parametric equation in r
From playlist Parametric Equations