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Research draft

mathematical operation

vr.tr.mathematical-operation · XCT.QLT

Let an agent handle mathematical operations by arity, domain, properties and notation, and apply them correctly.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent handle mathematical operations by arity, domain, properties and notation, and apply them correctly.

A function or rule that takes one or more inputs (operands) and produces an output, such as addition, multiplication, negation, composition, clamping or cancelling; operations may be unary, binary or n-ary.

What it is for: Building calculations, algebraic structures and algorithms.

It can be identify the operation and its arity; check properties such as associativity; apply order of operations; implement operations in code.

Distinguishing features

Maps inputs to output

Has arity and domain

Properties define structures

Precedence rules in notation

What it looks like

Symbols such as +, x, -, composition and function notation.

How it is recognised

Unary, binary or n-ary

Notation and precedence

Operations in computing such as clamping

Related models

is a kind of - category

function

includes - example

addition

defines - structure

algebraic structure

is implemented in - computing

algorithm

In practice

Families and kinds

arithmetic operations

unary operations such as negation

binary operations

set and logical operations

function composition

Standards and regulation

ISO 80000-2 notation

IEEE 754 floating-point operations

Failure modes and hazards

Precedence errors

Operations undefined on some inputs

Floating-point surprises

Also called

cancelling outcross-cancelingtransclusionself-mappingclampingunary functionstring operationgraph operationMicro-operationpolygonalizationdirect sum of modulesarithmetic operationwavelet extractionweighted sumdirect sumternary operationhyperoperationinternal operationEuclidean space transformationknot operationpolytope operationmorphological operationset operationpushforwardLeft Factorialclassical operationsemidirect productcircular shiftleft factoringclosure of a relationoperation on data structurealgebraic operationnullary operationrelational algebra operationblowing downextension and contraction of idealsfunction applicationvector multiplicationiterated binary operationjoin and meet

+33

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Operation Which operation.

Arity and domain.

Arity

Number of inputs.

Arity

Arity.

  1. How many operands does it take? definition
  2. On which set is it defined? definition

Notation

Symbols.

Notation

Notation.

  1. How is it written? definition
  2. What precedence does it have? definition
Properties Laws.

Properties enable reasoning.

Laws

Associativity and more.

Laws

Algebraic laws.

  1. Is it associative, commutative or distributive? boundary
  2. Does it have an identity or inverse? boundary

Closure

Staying in the set.

Closure

Closure.

  1. Is the set closed under the operation? boundary
  2. Where is it undefined? boundary
Computing Implementation.

Code implements operations.

Implementation

Code.

Implementation

Implementation.

  1. How is the operation implemented in code? action
  2. Are edge cases handled? boundary

Precision

Floating point.

Precision

Precision.

  1. Could rounding change the result? boundary
  2. Is exact arithmetic needed? action
Learning Teaching.

Order of operations confuses.

Order

Precedence.

Order

Order of operations.

  1. What result does the order of operations give here? measurement
  2. Would brackets make it clearer? action

Examples

Illustrations.

Examples

Examples.

  1. Which examples illustrate the operation? action
  2. What misconceptions are common? boundary

What the second pass must settle

  • Should operation classes be separate entries?
  • How should notation conventions be recorded?
  • How should computing operations be linked?
Draft as JSON