Hi Johannes, On 14 Aug., 15:09, Johannes <dajo.m...@web.de> wrote: > I have to deal with unit roots for some calculations.
I suppose you mean primitive roots of unity in CC? > And for simplicity > I want to give the n-th unit root a name (lets say xi) instead of > dealing with numeric values. > Up to know I solved this by definig xi to be the solution of > $x^n -1 == 0$ for a given $n$ but how can I name a solution of this > equation? Perhaps you want in fact compute in a cyclotomic field: sage: K.<xi> = CyclotomicField(8) sage: xi^8 == 1 True sage: xi^4 == 1 False Hence, xi is a primitive 8-th root of unity. K has a default embedding into CC, but K is not identified with a subring of CC, and also xi is not identified with its numerical evaluation: sage: CC(xi) 0.707106781186548 + 0.707106781186547*I sage: CC.is_subring(K) False sage: xi xi Also, you can easily obtain a list of all possible embeddings of K into CC: sage: K.embeddings(CC) [ Ring morphism: From: Cyclotomic Field of order 8 and degree 4 To: Complex Field with 53 bits of precision Defn: xi |--> -0.707106781186548 - 0.707106781186548*I, Ring morphism: From: Cyclotomic Field of order 8 and degree 4 To: Complex Field with 53 bits of precision Defn: xi |--> -0.707106781186548 + 0.707106781186548*I, Ring morphism: From: Cyclotomic Field of order 8 and degree 4 To: Complex Field with 53 bits of precision Defn: xi |--> 0.707106781186548 - 0.707106781186548*I, Ring morphism: From: Cyclotomic Field of order 8 and degree 4 To: Complex Field with 53 bits of precision Defn: xi |--> 0.707106781186548 + 0.707106781186548*I ] Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
