| dbo:abstract
|
- En arithmétique modulaire, une racine k-ième de l'unité modulo n, pour des entiers k, n ≥ 2, est une racine de l'unité dans l'anneau ℤ/nℤ, c'est-à-dire une solution de l'équation . Si k est l'ordre de modulo n, alors est appelé racine k-ième primitive de l'unité modulo n. Les racines primitives modulo n sont les racines -ièmes primitives de l'unité modulo n, où est l'indicatrice d'Euler. (fr)
- In mathematics, namely ring theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n, that is, a solution x to the equation (or congruence) . If k is the smallest such exponent for x, then x is called a primitive kth root of unity modulo n. See modular arithmetic for notation and terminology. Software to compute modular roots is available in the python library sympy.ntheory.residue_ntheory using the function nthroot_mod. See https://docs.sympy.org/latest/modules/ntheory.html. Do not confuse this with a primitive root modulo n, which is a generator of the group of units of the ring of integers modulo n. The primitive roots modulo n are the primitive -roots of unity modulo n, where is Euler's totient function. This topic deals with roots of unity modulo n where n is at times not a prime number. Finite field § Roots of unity addresses the special case where n is prime and Root of unity covers (non-modular) roots of unity in the field of complex numbers. (en)
|
| dbo:wikiPageExternalLink
| |
| dbo:wikiPageID
| |
| dbo:wikiPageLength
|
- 11055 (xsd:nonNegativeInteger)
|
| dbo:wikiPageRevisionID
| |
| dbo:wikiPageWikiLink
| |
| dbp:wikiPageUsesTemplate
| |
| dcterms:subject
| |
| rdfs:comment
|
- En arithmétique modulaire, une racine k-ième de l'unité modulo n, pour des entiers k, n ≥ 2, est une racine de l'unité dans l'anneau ℤ/nℤ, c'est-à-dire une solution de l'équation . Si k est l'ordre de modulo n, alors est appelé racine k-ième primitive de l'unité modulo n. Les racines primitives modulo n sont les racines -ièmes primitives de l'unité modulo n, où est l'indicatrice d'Euler. (fr)
- In mathematics, namely ring theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n, that is, a solution x to the equation (or congruence) . If k is the smallest such exponent for x, then x is called a primitive kth root of unity modulo n. See modular arithmetic for notation and terminology. Software to compute modular roots is available in the python library sympy.ntheory.residue_ntheory using the function nthroot_mod. See https://docs.sympy.org/latest/modules/ntheory.html. (en)
|
| rdfs:label
|
- Racine de l'unité modulo n (fr)
- Root of unity modulo n (en)
|
| owl:sameAs
| |
| prov:wasDerivedFrom
| |
| foaf:isPrimaryTopicOf
| |
| is dbo:wikiPageWikiLink
of | |
| is foaf:primaryTopic
of | |
