About
Calculator
Ordering
FAQ
Download
Download Magma
Databases
User Contributions
Documentation
Handbook
Overview
Release Notes
Discovering Maths with Magma
First Steps in Magma (pdf)
Solving Problems with Magma (pdf)
Acknowledgements
Citations
Conferences
Links
Contact
CAG
Login
Magma
Computer • algebra
Documentation
Up
Contents
Index
Search
Expand all
Collapse all
Introduction
Creation Functions
Creation of Cyclotomic Fields
CyclotomicField(m) : RngIntElt -> FldCyc
CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
MinimalField(a) : FldRatElt -> FldRat
MinimalField(S) : [ FldCycElt ] -> FldCyc
Example
FldCyc_creation (H38E1)
Creation of Elements
RootOfUnity(n) : RngIntElt -> FldCycElt
RootOfUnity(n, K) : RngIntElt, FldCyc -> FldCycElt
Minimise(~a) : FldCycElt ->
Minimise(~s) : [ FldCycElt ] ->
Minimise(a) : FldCycElt -> RngElt
Minimise(s) : { FldCycElt } -> { RngElt }
Structure Operations
Invariants
Conductor(K) : FldCyc -> RngIntElt, [RngIntElt]
CyclotomicOrder(K) : FldCyc -> RngIntElt
CyclotomicAutomorphismGroup(K) : FldCyc -> GrpAb, Map
CyclotomicRelativeField(k, K) : FldCyc, FldCyc -> FldNum
Element Operations
Predicates on Elements
IsReal(a) : FldCycElt -> BoolElt
Conjugates
ComplexConjugate(a) : FldCycElt -> FldCycElt
Conjugate(a, n) : FldCycElt, RngIntElt -> FldCycElt
Conjugate(a, r) : FldCycElt, FldCycElt -> FldCycElt
Example
FldCyc_GaussianPeriods (H38E2)
Up
Contents
Index
Search
V2.28, 28 February 2025