On this page you'll find 10+ example sentences with Factorization. Discover the meaning, synonyms such as factoring or resolution and how to use the word correctly in a sentence.
Factorization meaning
- The process of creating a list of factors.
- An expression listing items that, when multiplied together, will produce a desired quantity.
- A list of factors.
Synonyms of Factorization
Using Factorization
- The main meaning on this page is: The process of creating a list of factors. | An expression listing items that, when multiplied together, will produce a desired quantity. | A list of factors.
- Useful related words include: factorisation, factoring, resolution, resolving.
- In the example corpus, factorization often appears in combinations such as: unique factorization, integer factorization, factorization of.
Context around Factorization
- Average sentence length in these examples: 19.1 words
- Position in the sentence: 10 start, 6 middle, 4 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Factorization
- In this selection, "factorization" usually appears near the start of the sentence. The average example has 19.1 words, and this corpus slice is mostly made up of statements.
- Around the word, unique, integer, prime, domain, problem and records stand out and add context to how "factorization" is used.
- Recognizable usage signals include a factorization system for and a unique factorization domain is. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "factorization" sits close to words such as aarhus, abdu and abetted, which helps place it inside the broader word index.
Example types with factorization
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
An integer factorization algorithm can decide primality. (7 words)
Both integer factorization and discrete log are in BQP. (9 words)
A unique factorization domain is not necessarily a noetherian ring. (10 words)
In 1979, Michael O. Rabin published a related cryptosystem that is probably secure as long as the factorization of the public key remains difficult – it remains an assumption that RSA also enjoys this security. (34 words)
When the coefficients belong to integers, rational numbers or a finite field, there are algorithms to test irreducibility and to compute the factorization into irreducible polynomials (see Factorization of polynomials ). (30 words)
Euclid's lemma and unique factorization Bézout's identity is essential to many applications of Euclid's algorithm, such as demonstrating the unique factorization of numbers into prime factors. (29 words)
Example sentences (20)
Euclid's lemma and unique factorization Bézout's identity is essential to many applications of Euclid's algorithm, such as demonstrating the unique factorization of numbers into prime factors.
For instance the statement "an integer's prime factorization is unique up to ordering", means that the prime factorization is unique if we disregard the order of the factors.
Like all recent factorization records, this factorization was completed with a highly optimized implementation of the general number field sieve run on hundreds of machines.
When the coefficients belong to integers, rational numbers or a finite field, there are algorithms to test irreducibility and to compute the factorization into irreducible polynomials (see Factorization of polynomials ).
The researchers employed innovative techniques to optimize the mapping of the factorization problem onto the quantum annealer.
A factorization system for a category also gives rise to a notion of embedding.
An integer factorization algorithm can decide primality.
Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true.
A unique factorization domain is not necessarily a noetherian ring.
Both integer factorization and discrete log are in BQP.
Elliptic curves over finite fields are notably applied in cryptography and for the factorization of large integers.
Euclid's lemma suffices to prove that every number has a unique factorization into prime numbers.
Factorization may or may not have a polynomial-time algorithm.
Given a general algorithm for integer factorization, any integer can be factored down to its constituent prime factors simply by repeated application of this algorithm.
Given the factorization in terms of these matrices, one can now write down immediately an equation : with κ to be determined.
However, it was also discovered that unique factorization does not always hold.
In 1979, Michael O. Rabin published a related cryptosystem that is probably secure as long as the factorization of the public key remains difficult – it remains an assumption that RSA also enjoys this security.
In a unique factorization domain (or more generally, a GCD domain ), an irreducible element is a prime element.
It is not known exactly which complexity classes contain the decision version of the integer factorization problem.
Its factorization, by a state-of-the-art distributed implementation, took around fifteen hundred CPU years (two years of real time, on many hundreds of computers).
Common combinations with factorization
These word pairs occur most frequently in English texts:
- unique factorization 9×
- integer factorization 9×
- factorization of 8×
- the factorization 6×
- prime factorization 5×
- factorization is 4×
- factorization domain 4×
- factorization into 3×
- factorization for 3×
- factorization records 2×