Idele

An idèle: a unit of the adèle ring — a real together with principal everywhere except at a listed finite set of primes, where distinguished units override it.

Idele(r, s, units)real , principal value at every prime not named in `units`

Idele(q)the principal idèle of a non-zero rational : at every place

Domain: Adèles and idèles

Details

• `Multiply` on idèles multiplies real parts, principal values and any shared or distinguished unit parts; an idèle is invertible whenever and .
• `units` is a list of AdicNumeral values at distinct primes, each overriding the principal value there.
• Adele`(idele)` forgets the idèle structure and keeps only its value as an adèle.

Examples

See also: Adele, ProfiniteNumber