A guide to the PureScript numeric hierarchy
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Introduction
Logic
Monoids
Groups
Rings
Matrices
Integral domains
Fields
Complex numbers
The Euclidean Algorithm
Polynomials
Euclidean rings
Quaternions
Epilogue
Appendix
A guide to the PureScript numeric hierarchy
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A guide to the PureScript numeric hierarchy
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A guide to the PureScript numeric hierarchy
¶
Table of contents
¶
Introduction
Why?
Prerequisites
How to read this guide
License
Logic
Truth tables
Logical equivalence
Logical negation
Logical implication
Converses
Contrapositives
Sets
Quantifiers
Monoids
Uniqueness of identity elements
Some more examples
Groups
Uniqueness of inverses
Modular arithmetic
Permutations
Cancellation
Abelian groups
A final note on groups
Rings
The definition
Properties of rings
Semirings
Matrices
Vectors
Linear mappings
Representation of linear mappings as matrices
Properties of matrix operations
Integral domains
The cancellation law for integral domains
Fields
A quick diversion into set theory
Every field is an integral domain
Every finite integral domain is a field
Complex numbers
The Euclidean Algorithm
Integer division
Greatest common divisors
The Euclidean Algorithm
Polynomials
Polynomial division
Euclidean rings
Divisors, again
Generalising the Euclidean Algorithm
Summary
Quaternions
Multiplicative inverses
Dividing quaternions
Using quaternions for rotations
Further references
Epilogue
Appendix
Cheatsheet
PureScript implementations of objects discussed in this guide
Solutions to Exercises
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