multiplication
Let an agent explain multiplication and its properties across number systems, describe generalisations such as scalar, matrix and Hadamard products, relay algorithms and teaching approaches, and help compute or check products.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define What multiplication is.
Definition
Definition and properties.
Definition
Definition.
- What is multiplication, and what properties does it have across number systems? definition
- Is the question about number multiplication or a generalisation? boundary
Generalisations
Generalisations.
Generalisations
Generalisations.
- How do scalar, matrix, Hadamard and abstract multiplications differ? definition
- Which entry fits the specific generalisation? action
Compute Computation.
Algorithms
Algorithms.
Algorithms
Algorithms.
- How are products computed by hand and by algorithms such as long multiplication and Karatsuba? action
- What is the result for the values in question? measurement
Computers
Computer arithmetic.
Computers
Computers.
- How do computers multiply integers and floating-point numbers, and where do errors arise? provenance
- Which entry fits computer arithmetic? action
Theory Algebraic structure.
Structure
Rings and groups.
Structure
Structure.
- How is multiplication axiomatised in rings, fields and groups? provenance
- Which references are standard? provenance
Matrices
Matrix multiplication.
Matrices
Matrices.
- Why is matrix multiplication non-commutative, and how does it represent composition? provenance
- Which entry fits linear algebra? action
Context History and teaching.
History
History.
History
History.
- How did multiplication methods develop, from Egyptian doubling to modern algorithms? provenance
- Which entry fits the history of arithmetic? action
Teach
Teaching.
Teach
Teaching.
- How is multiplication taught, and which misconceptions arise? provenance
- Which sources are cited? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- scalar multiplication, matrix multiplication, doubling, Hadamard product
What it is Filled
A binary arithmetic operation that combines two numbers to give their product, defined for natural numbers as repeated addition and extended to integers, rationals, reals and complex numbers, and generalised to scalar multiplication of vectors, matrix multiplication, the element-wise Hadamard product and multiplication in rings and groups; multiplication is commutative and associative for numbers, distributes over addition, and is a foundation of arithmetic and algebra.
Why it exists Filled
Let an agent explain multiplication and its properties across number systems, describe generalisations such as scalar, matrix and Hadamard products, relay algorithms and teaching approaches, and help compute or check products.
Distinguishing features Filled
- Commutative and associative for numbers
- Distributive over addition
- Identity one and inverses for nonzero numbers
- Non-commutative generalisations
What robots and AI may and may not do Filled
Must not
- Present a result computed with rounding or overflow as exact.
- Confuse matrix and element-wise multiplication in calculations.
- Give multiplication results for money or doses without showing the inputs.
Only with a human decision
- Relying on a computed product for doses, money or engineering loads.
May
- Compute products and explain multiplication from arithmetic to matrices.
- Check results and state the number system or algebra used.
Moral aspects Filled
- Calculation errors in doses or money cause real harm.
- Maths education shapes opportunity; teaching must be patient with learners.
Who is affected
- Learners
- Users of calculations
- Patients and clients
Owners Filled
Steward
Nobody owns an operation; it is held in common.
Links to other meta-models Filled
parent
- Q164307 - registry parent class
related
- binary operation - in registry terms
- division - for nonzero divisors
- matrix multiplication - in linear algebra
- addition - the distributive law
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.multiplication
- Wikidata: Q40276 (https://www.wikidata.org/wiki/Q40276)
- symbols: times sign, middle dot, asterisk notation
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Binary operation giving a product
- Numbers, vectors, matrices and abstract structures
- Addition combines by summing; exponentiation is repeated multiplication
- Not a visible object; expressions with times signs, dots or juxtaposition.
Capabilities and actions required Filled
- explain the operation and properties
- describe generalisations
- relay algorithms and teaching
- compute or check products
Hazards and failure modes required Filled
- Assuming commutativity in matrix multiplication
- Overflow in computer arithmetic
- Confusing element-wise and matrix products
Standards and interfaces required Filled
- ISO 80000-2 notation for multiplication
- Curriculum standards for arithmetic
Context of use required Filled
- Combining quantities by scaling.
- multiplication of natural numbers, integers, rationals, reals and complex numbers
- scalar multiplication of vectors
- matrix multiplication
- Hadamard element-wise product
- multiplication in rings, fields and groups
- doubling as a special case
Sources Filled
- Wikidata item Q40276: multiplication - identity and sense of the item
- Wikipedia: Multiplication - general description of the item
Open questions
- Should matrix multiplication be a separate primary entry?
- How should notation standards be linked?
- The registry entry has merged aliases naming generalisations; should they be split off?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q40276/spec.json