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Categories for the working programmers
Monads
Monad categories and algebras defined by actual group theoretic examples of Action groups and η, μ Natural Transformations naturally defined and finally programmed.
Transformations η , μ
Simplex Category Δ
Δ is a category defined with finite ordered integers set as objects and non-decreasing maps as morphisms.
ΔSys: String and Term Rewriting for Simplex Category
Hamiltonian, Lagrangian things
Collections of scripts, custom programming containers elucidating the algebra and the physics of myriad of solved dynamical system.
𝓗synth
Programming container called 𝓗synth allows the programmers to design and solve sophisticated Lagrangian and Hamiltonian dynamical systems.
𝓗synth: An Introduction
Graph Lagrangian for CO2 and Benzene to compute vibrational spectra
Legendre things
Dara's Research
Dara O Shayda's cutting edge R&D software and writings, majority are actual live computational notebooks readily accessibly by all!
Vector Algebra
Elementary Vector Algebra and programming
What is Vector Algebra?
What is a Vector?
Any set of objects with addition, subtraction and multiplication is an algebra. Any such object requiring a fixed number of symbols to describe itself is called a vector. These are informal definitions. A collection of such vectors with operations such as + or...
What is Algebra?
What: Concept of AlgebraWhy: What is an algebra why you need algebraTime To Complete: 1 hour Nature of Algebra Algebra is a set of finitely many symbols with functions and operators acting on these symbols in such a fashion that all these functions and oper...
Symbolic Computing
What: Concept of Symbolic ComputingWhy: Computing with symbols and non-numeralsTime To Complete: 1 hour Why? As discussed in previous class notes, the nature of algebra is conducive to expand our abilities to understand and compute geometries. Symbolic Comp...
Vector Arithmetic
+ and - operators
What: Addition and Subtraction of VectorsWhy: Detailed computationsTime To Complete: 2 hour + //+ addition ; v1 = {a,2,c}+{1,b,3}; show v1; save as addition; Output: v1 = {1 + a, 2 + b, 3 + c} '//' : Comment Operator instructing the Grammarian ...