From 1c44a8d52fa77ed6cc195f410a56c1c15c893d07 Mon Sep 17 00:00:00 2001
From: Martin Wagner <martin.wagner.dev@gmail.com>
Date: Mon, 31 Mar 2025 10:48:29 +0200
Subject: [PATCH 1/4] Improve `generic_cyclotomic_ring` constructor

---
 src/Exports.jl            |  2 +
 src/GenericCyclotomics.jl | 92 ++++++++++++++++++++++++++++++++++++---
 2 files changed, 89 insertions(+), 5 deletions(-)

diff --git a/src/Exports.jl b/src/Exports.jl
index a686c4d..25fa5a1 100644
--- a/src/Exports.jl
+++ b/src/Exports.jl
@@ -20,8 +20,10 @@ export number_of_conjugacy_classes
 export number_of_parameters
 export omega
 export order
+export param
 export parameter
 export parameters
+export params
 export parent
 export scalar_product
 export set_congruence
diff --git a/src/GenericCyclotomics.jl b/src/GenericCyclotomics.jl
index 53261b2..f75ff52 100644
--- a/src/GenericCyclotomics.jl
+++ b/src/GenericCyclotomics.jl
@@ -182,10 +182,11 @@ function show(io::IO, ::MIME"text/plain", R::GenericCycloRing)
   println(io, "over ", base_ring(base_ring(R)))
   print(io, "dependent on ", join(gens(base_ring(R)), ", "))
   if R.congruence !== nothing
+    q = gen(base_ring(R), 1)^R.power
     print(
       io,
       "\nwhere ",
-      gen(base_ring(R), 1),
+      q,
       " is congruent to ",
       R.congruence[1],
       " modulo ",
@@ -489,18 +490,60 @@ end
 
 # Parent constructor
 
-# TODO Maybe don't require at least one variable?
+@doc raw"""
+    generic_cyclotomic_ring(symbol::Symbol=:E; congruence::Union{Tuple{ZZRingElem,ZZRingElem},Nothing}=nothing, variable::Symbol=:q, power::Int64=1, cached::Bool=true)
+
+Return a tuple consisting of the generic cyclotomic ring `S` with the main variable `variable`,
+a generic root generator `E` and the parameter `q` corresponding to the symbol `variable`.
+The symbol `symbol` is used as a compact placeholder for $e^{2 \pi i}$ for printing.
+In the simplification process of the elements of `S` it is assumed that `q` to the power of `power`
+always represents a whole number cungruent to `congruence[1]` modulo `congruence[2]`.
+
+Currently the optional argument `cached` is ignored.
+
+!!! warning
+    In the exponents of the generic cyclotomic numbers `q` may only occur in powers which are a multiple of `power`.
+    Otherwise the simplification will return false results.
+
+# Examples
+```jldoctest
+julia> S, E, q = generic_cyclotomic_ring()
+(Generic cyclotomic ring over Rational field, Generator of Generic cyclotomic ring over Rational field, q)
+
+julia> E(q-1)^(q-1)
+1
+
+julia> E(3)^2
+-E(3) - 1
+
+julia> S, E, q = generic_cyclotomic_ring(congruence=(ZZ(1),ZZ(3)), power=2)
+(Generic cyclotomic ring over Rational field, Generator of Generic cyclotomic ring over Rational field, q)
+
+julia> S
+Generic cyclotomic ring
+  over Rational field
+  dependent on q
+  where q^2 is congruent to 1 modulo 3
+
+julia> E(3)^(q^2-1)
+1
+
+julia> E(3)^(q^2)
+E(3)
+
+```
+"""
 function generic_cyclotomic_ring(
-  R::UPolyRing,
   symbol::Symbol=:E;
   congruence::Union{Tuple{ZZRingElem,ZZRingElem},Nothing}=nothing,
+  variable::Symbol=:q,
   power::Int64=1,
   cached::Bool=true,
 )
+  R, (q,) = universal_polynomial_ring(QQ, [variable]; cached=false)
   S = GenericCycloRing(R, symbol, congruence, power)
   E = GenericCycloRingGen(S)
-  length(gens(R)) < 1 && error("At least one free variable is needed")
-  return (S, E)
+  return (S, E, q)
 end
 
 function (E::GenericCycloRingGen)(order::RingElement)
@@ -509,6 +552,45 @@ function (E::GenericCycloRingGen)(order::RingElement)
   return S(Dict(R(1)//R(order) => R(1)))
 end
 
+# Create parameters
+
+@doc raw"""
+    param(S::GenericCycloRing, var::Symbol)
+
+Return the parameter of `S` corresponding to the symbol `var`. If there is no such paramter it creates a new one.
+
+# Examples
+```jldoctest
+julia> S, E, q = generic_cyclotomic_ring()
+(Generic cyclotomic ring over Rational field, Generator of Generic cyclotomic ring over Rational field, q)
+
+julia> param(S, :q)
+q
+
+julia> param(S, :i)
+i
+
+```
+"""
+param(S::GenericCycloRing, var::Symbol) = gen(base_ring(S), var)
+
+@doc raw"""
+    params(S::GenericCycloRing, vars::Vector{Symbol})
+
+Return the parameters of `S` corresponding to the symbols `vars`. If any of those is missing create a new one.
+
+# Examples
+```jldoctest
+julia> S, E, q = generic_cyclotomic_ring()
+(Generic cyclotomic ring over Rational field, Generator of Generic cyclotomic ring over Rational field, q)
+
+julia> params(S, [:q, :i])
+(q, i)
+
+```
+"""
+params(S::GenericCycloRing, vars::Vector{Symbol}) = gens(base_ring(S), vars)
+
 # congruence computation
 function get_substitutes!(R::GenericCycloRing)
   congruence = R.congruence

From 072bd85afa254fe1ac05a6ace5e897ddce8cacf8 Mon Sep 17 00:00:00 2001
From: Martin Wagner <martin.wagner.dev@gmail.com>
Date: Mon, 31 Mar 2025 10:56:57 +0200
Subject: [PATCH 2/4] Fix tables

---
 data/Tables/2A2/GU3.jl       | 9 ++++-----
 data/Tables/2A2/PGU3.2.jl    | 9 ++++-----
 data/Tables/2A2/PSU3.2.jl    | 9 ++++-----
 data/Tables/2A2/SU3.2.jl     | 9 ++++-----
 data/Tables/2A2/SU3.n2.jl    | 9 ++++-----
 data/Tables/2B2/2B2.jl       | 9 ++++-----
 data/Tables/2F4/2F4.1.jl     | 9 ++++-----
 data/Tables/2F4/2F4.2.jl     | 9 ++++-----
 data/Tables/2G2/2G2.jl       | 9 ++++-----
 data/Tables/3D4/3D4.0.jl     | 9 ++++-----
 data/Tables/3D4/3D4.11.jl    | 9 ++++-----
 data/Tables/3D4/3D4.13.jl    | 9 ++++-----
 data/Tables/A1/GL2.jl        | 9 ++++-----
 data/Tables/A1/GU2.jl        | 9 ++++-----
 data/Tables/A1/PGL2.1.jl     | 9 ++++-----
 data/Tables/A1/PSL2.1.jl     | 9 ++++-----
 data/Tables/A1/PSL2.3.jl     | 9 ++++-----
 data/Tables/A1/SL2.0.jl      | 9 ++++-----
 data/Tables/A1/SL2.1.jl      | 9 ++++-----
 data/Tables/A2/GL3.jl        | 9 ++++-----
 data/Tables/A2/PGL3.1.jl     | 9 ++++-----
 data/Tables/A2/PSL3.1.jl     | 9 ++++-----
 data/Tables/A2/SL3.1.jl      | 9 ++++-----
 data/Tables/A2/SL3.n1.jl     | 9 ++++-----
 data/Tables/C2/Sp4.0.jl      | 9 ++++-----
 data/Tables/C3/CSp6.1.jl     | 9 ++++-----
 data/Tables/C3/Sp6.0.jl      | 9 ++++-----
 data/Tables/F4/uniuniF4p2.jl | 5 ++---
 data/Tables/G2/G2.01.jl      | 9 ++++-----
 data/Tables/G2/G2.02.jl      | 9 ++++-----
 data/Tables/G2/G2.101.jl     | 9 ++++-----
 data/Tables/G2/G2.103.jl     | 9 ++++-----
 data/Tables/G2/G2.111.jl     | 9 ++++-----
 data/Tables/G2/G2.113.jl     | 9 ++++-----
 data/Tables/G2/G2.121.jl     | 9 ++++-----
 data/Tables/G2/G2.123.jl     | 9 ++++-----
 src/GenericCyclotomics.jl    | 2 ++
 37 files changed, 144 insertions(+), 178 deletions(-)

diff --git a/data/Tables/2A2/GU3.jl b/data/Tables/2A2/GU3.jl
index b977d17..32e7d0b 100644
--- a/data/Tables/2A2/GU3.jl
+++ b/data/Tables/2A2/GU3.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R)
-k, l, m, u, v, w, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
+k, l, m, u, v, w, _... = params(
+  S,
   [
     "k",
     "l",
diff --git a/data/Tables/2A2/PGU3.2.jl b/data/Tables/2A2/PGU3.2.jl
index 86ad73a..b9f5cca 100644
--- a/data/Tables/2A2/PGU3.2.jl
+++ b/data/Tables/2A2/PGU3.2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 3)))
-k, l, u, v, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 3)))
+R = base_ring(S)
+k, l, u, v, _... = params(
+  S,
   [
     "k",
     "l",
diff --git a/data/Tables/2A2/PSU3.2.jl b/data/Tables/2A2/PSU3.2.jl
index 55ca62d..641836d 100644
--- a/data/Tables/2A2/PSU3.2.jl
+++ b/data/Tables/2A2/PSU3.2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 3)))
-a, b, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 3)))
+R = base_ring(S)
+a, b, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/2A2/SU3.2.jl b/data/Tables/2A2/SU3.2.jl
index ff6632a..0e595e1 100644
--- a/data/Tables/2A2/SU3.2.jl
+++ b/data/Tables/2A2/SU3.2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 3)))
-a, b, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 3)))
+R = base_ring(S)
+a, b, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/2A2/SU3.n2.jl b/data/Tables/2A2/SU3.n2.jl
index 17f55cf..f35d9c8 100644
--- a/data/Tables/2A2/SU3.n2.jl
+++ b/data/Tables/2A2/SU3.n2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R)
-a, b, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
+a, b, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/2B2/2B2.jl b/data/Tables/2B2/2B2.jl
index 0e7c24e..8764937 100644
--- a/data/Tables/2B2/2B2.jl
+++ b/data/Tables/2B2/2B2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q0 = gen(R, "q0")
-S, E = generic_cyclotomic_ring(R)
-a, b, c, s, k, u, _... = gens(
-  R,
+S, E, q0 = generic_cyclotomic_ring()
+R = base_ring(S)
+a, b, c, s, k, u, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/2F4/2F4.1.jl b/data/Tables/2F4/2F4.1.jl
index e413df3..1be78de 100644
--- a/data/Tables/2F4/2F4.1.jl
+++ b/data/Tables/2F4/2F4.1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q0 = gen(R, "q0")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 3)))
-a, b, k, l, _... = gens(
-  R,
+S, E, q0 = generic_cyclotomic_ring(; congruence=ZZ.((1, 3)))
+R = base_ring(S)
+a, b, k, l, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/2F4/2F4.2.jl b/data/Tables/2F4/2F4.2.jl
index 0705a6f..fd4dcd3 100644
--- a/data/Tables/2F4/2F4.2.jl
+++ b/data/Tables/2F4/2F4.2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q0 = gen(R, "q0")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 3)))
-a, b, k, l, _... = gens(
-  R,
+S, E, q0 = generic_cyclotomic_ring(; congruence=ZZ.((-1, 3)))
+R = base_ring(S)
+a, b, k, l, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/2G2/2G2.jl b/data/Tables/2G2/2G2.jl
index 783616c..e6155bc 100644
--- a/data/Tables/2G2/2G2.jl
+++ b/data/Tables/2G2/2G2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q0 = gen(R, "q0")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 4)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q0 = generic_cyclotomic_ring(; congruence=ZZ.((-1, 4)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/3D4/3D4.0.jl b/data/Tables/3D4/3D4.0.jl
index 5b97094..932d28f 100644
--- a/data/Tables/3D4/3D4.0.jl
+++ b/data/Tables/3D4/3D4.0.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R)
-a, b, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
+a, b, k, l, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/3D4/3D4.11.jl b/data/Tables/3D4/3D4.11.jl
index 599c21a..8826581 100644
--- a/data/Tables/3D4/3D4.11.jl
+++ b/data/Tables/3D4/3D4.11.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 4)))
-a, b, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 4)))
+R = base_ring(S)
+a, b, k, l, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/3D4/3D4.13.jl b/data/Tables/3D4/3D4.13.jl
index 1efc09a..cef1be0 100644
--- a/data/Tables/3D4/3D4.13.jl
+++ b/data/Tables/3D4/3D4.13.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 4)))
-a, b, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 4)))
+R = base_ring(S)
+a, b, k, l, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/A1/GL2.jl b/data/Tables/A1/GL2.jl
index 6a52bf4..b599565 100644
--- a/data/Tables/A1/GL2.jl
+++ b/data/Tables/A1/GL2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R)
-i, j, l, k, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
+i, j, l, k, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/A1/GU2.jl b/data/Tables/A1/GU2.jl
index e71e6fa..5a069e5 100644
--- a/data/Tables/A1/GU2.jl
+++ b/data/Tables/A1/GU2.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R)
-k, l, u, v, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
+k, l, u, v, _... = params(
+  S,
   [
     "k",
     "l",
diff --git a/data/Tables/A1/PGL2.1.jl b/data/Tables/A1/PGL2.1.jl
index 7dc9a4a..75ad78f 100644
--- a/data/Tables/A1/PGL2.1.jl
+++ b/data/Tables/A1/PGL2.1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 2)))
-i, j, l, k, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 2)))
+R = base_ring(S)
+i, j, l, k, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/A1/PSL2.1.jl b/data/Tables/A1/PSL2.1.jl
index 378baac..71a7435 100644
--- a/data/Tables/A1/PSL2.1.jl
+++ b/data/Tables/A1/PSL2.1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 4)))
-i, k, _... = gens(
-  R, ["i", "k", "i1", "k1", "i2", "k2", "i3", "k3", "it1", "kt1", "it2", "kt2"]
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 4)))
+R = base_ring(S)
+i, k, _... = params(
+  S, ["i", "k", "i1", "k1", "i2", "k2", "i3", "k3", "it1", "kt1", "it2", "kt2"]
 )
 
 order = q^2 * (q^2 - 1) * (q^2 + 1) * 1//2
diff --git a/data/Tables/A1/PSL2.3.jl b/data/Tables/A1/PSL2.3.jl
index 4695ab7..0e0616f 100644
--- a/data/Tables/A1/PSL2.3.jl
+++ b/data/Tables/A1/PSL2.3.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 4)))
-i, k, _... = gens(
-  R, ["i", "k", "i1", "k1", "i2", "k2", "i3", "k3", "it1", "kt1", "it2", "kt2"]
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 4)))
+R = base_ring(S)
+i, k, _... = params(
+  S, ["i", "k", "i1", "k1", "i2", "k2", "i3", "k3", "it1", "kt1", "it2", "kt2"]
 )
 
 order = q^2 * (q^2 - 1) * (q^2 + 1) * 1//2
diff --git a/data/Tables/A1/SL2.0.jl b/data/Tables/A1/SL2.0.jl
index 6419d56..a04069c 100644
--- a/data/Tables/A1/SL2.0.jl
+++ b/data/Tables/A1/SL2.0.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((0, 2)))
-a, n, _... = gens(
-  R, ["a", "n", "a1", "n1", "a2", "n2", "a3", "n3", "at1", "nt1", "at2", "nt2"]
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((0, 2)))
+R = base_ring(S)
+a, n, _... = params(
+  S, ["a", "n", "a1", "n1", "a2", "n2", "a3", "n3", "at1", "nt1", "at2", "nt2"]
 )
 
 order = q * (q - 1) * (q + 1)
diff --git a/data/Tables/A1/SL2.1.jl b/data/Tables/A1/SL2.1.jl
index d864c0b..1a36bb5 100644
--- a/data/Tables/A1/SL2.1.jl
+++ b/data/Tables/A1/SL2.1.jl
@@ -2,12 +2,11 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q0 = gen(R, "q0")
+S, E, q0 = generic_cyclotomic_ring(; congruence=ZZ.((1, 2)), power=2)
+R = base_ring(S)
 q = q0^2
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 2)), power=2)
-i, k, _... = gens(
-  R, ["i", "k", "i1", "k1", "i2", "k2", "i3", "k3", "it1", "kt1", "it2", "kt2"]
+i, k, _... = params(
+  S, ["i", "k", "i1", "k1", "i2", "k2", "i3", "k3", "it1", "kt1", "it2", "kt2"]
 )
 
 order = q * (q - 1) * (q + 1)
diff --git a/data/Tables/A2/GL3.jl b/data/Tables/A2/GL3.jl
index 9cec068..947aed2 100644
--- a/data/Tables/A2/GL3.jl
+++ b/data/Tables/A2/GL3.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R)
-a, b, c, l, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
+a, b, c, l, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/A2/PGL3.1.jl b/data/Tables/A2/PGL3.1.jl
index b6384a8..aa32f85 100644
--- a/data/Tables/A2/PGL3.1.jl
+++ b/data/Tables/A2/PGL3.1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 3)))
-a, b, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 3)))
+R = base_ring(S)
+a, b, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/A2/PSL3.1.jl b/data/Tables/A2/PSL3.1.jl
index 271e9e0..69f6216 100644
--- a/data/Tables/A2/PSL3.1.jl
+++ b/data/Tables/A2/PSL3.1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 3)))
-a, b, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 3)))
+R = base_ring(S)
+a, b, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/A2/SL3.1.jl b/data/Tables/A2/SL3.1.jl
index 55b9aa9..e3dd06d 100644
--- a/data/Tables/A2/SL3.1.jl
+++ b/data/Tables/A2/SL3.1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 3)))
-a, b, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 3)))
+R = base_ring(S)
+a, b, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/A2/SL3.n1.jl b/data/Tables/A2/SL3.n1.jl
index 85f3eed..b4122b6 100644
--- a/data/Tables/A2/SL3.n1.jl
+++ b/data/Tables/A2/SL3.n1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E  = generic_cyclotomic_ring(R)
-a, b, m, n, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
+a, b, m, n, _... = params(
+  S,
   [
     "a",
     "b",
diff --git a/data/Tables/C2/Sp4.0.jl b/data/Tables/C2/Sp4.0.jl
index 67ff92f..188faf9 100644
--- a/data/Tables/C2/Sp4.0.jl
+++ b/data/Tables/C2/Sp4.0.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((0, 2)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((0, 2)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/C3/CSp6.1.jl b/data/Tables/C3/CSp6.1.jl
index 6633af4..6bb2237 100644
--- a/data/Tables/C3/CSp6.1.jl
+++ b/data/Tables/C3/CSp6.1.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 2)))
-i1, i2, i3, i4, k1, k2, k3, k4, i11, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 2)))
+R = base_ring(S)
+i1, i2, i3, i4, k1, k2, k3, k4, i11, _... = params(
+  S,
   [
     "i1",
     "i2",
diff --git a/data/Tables/C3/Sp6.0.jl b/data/Tables/C3/Sp6.0.jl
index 27de866..e29a344 100644
--- a/data/Tables/C3/Sp6.0.jl
+++ b/data/Tables/C3/Sp6.0.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((0, 2)))
-i1, i2, i3, k1, k2, k3, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((0, 2)))
+R = base_ring(S)
+i1, i2, i3, k1, k2, k3, _... = params(
+  S,
   [
     "i1",
     "i2",
diff --git a/data/Tables/F4/uniuniF4p2.jl b/data/Tables/F4/uniuniF4p2.jl
index e081e4b..752759a 100644
--- a/data/Tables/F4/uniuniF4p2.jl
+++ b/data/Tables/F4/uniuniF4p2.jl
@@ -2,9 +2,8 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R)
+S, E, q = generic_cyclotomic_ring()
+R = base_ring(S)
 
 order =
   q^24 * (q^4 - q^2 + 1) * (q^4 + 1) * (q^2 + q + 1)^2 * (q^2 - q + 1)^2 * (q^2 + 1)^2 *
diff --git a/data/Tables/G2/G2.01.jl b/data/Tables/G2/G2.01.jl
index 6d4230e..86cd08a 100644
--- a/data/Tables/G2/G2.01.jl
+++ b/data/Tables/G2/G2.01.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 3)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 3)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/G2/G2.02.jl b/data/Tables/G2/G2.02.jl
index 5a23abf..d0ec369 100644
--- a/data/Tables/G2/G2.02.jl
+++ b/data/Tables/G2/G2.02.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 3)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 3)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/G2/G2.101.jl b/data/Tables/G2/G2.101.jl
index 2af7a4d..0ad8718 100644
--- a/data/Tables/G2/G2.101.jl
+++ b/data/Tables/G2/G2.101.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 4)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 4)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/G2/G2.103.jl b/data/Tables/G2/G2.103.jl
index 803eca7..27f79a4 100644
--- a/data/Tables/G2/G2.103.jl
+++ b/data/Tables/G2/G2.103.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 4)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 4)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/G2/G2.111.jl b/data/Tables/G2/G2.111.jl
index 1138d8b..6fa2ca2 100644
--- a/data/Tables/G2/G2.111.jl
+++ b/data/Tables/G2/G2.111.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((1, 12)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((1, 12)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/G2/G2.113.jl b/data/Tables/G2/G2.113.jl
index 47719e8..4afd9eb 100644
--- a/data/Tables/G2/G2.113.jl
+++ b/data/Tables/G2/G2.113.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((7, 12)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((7, 12)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/G2/G2.121.jl b/data/Tables/G2/G2.121.jl
index 5fa2262..a69ee4e 100644
--- a/data/Tables/G2/G2.121.jl
+++ b/data/Tables/G2/G2.121.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-7, 12)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-7, 12)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/data/Tables/G2/G2.123.jl b/data/Tables/G2/G2.123.jl
index 964e25d..8c08993 100644
--- a/data/Tables/G2/G2.123.jl
+++ b/data/Tables/G2/G2.123.jl
@@ -2,11 +2,10 @@ using ..GenericCharacterTables
 import ..GenericCharacterTables:
   Parameters, Parameter, CharTable, GenericCyclo, GenericCycloFrac, nesum
 using ..GenericCharacterTables.Oscar
-R = universal_polynomial_ring(QQ; cached=false)
-q = gen(R, "q")
-S, E = generic_cyclotomic_ring(R; congruence=ZZ.((-1, 12)))
-i, j, k, l, _... = gens(
-  R,
+S, E, q = generic_cyclotomic_ring(; congruence=ZZ.((-1, 12)))
+R = base_ring(S)
+i, j, k, l, _... = params(
+  S,
   [
     "i",
     "j",
diff --git a/src/GenericCyclotomics.jl b/src/GenericCyclotomics.jl
index f75ff52..1328232 100644
--- a/src/GenericCyclotomics.jl
+++ b/src/GenericCyclotomics.jl
@@ -576,6 +576,7 @@ param(S::GenericCycloRing, var::Symbol) = gen(base_ring(S), var)
 
 @doc raw"""
     params(S::GenericCycloRing, vars::Vector{Symbol})
+    params(S::GenericCycloRing, vars::Vector{String})
 
 Return the parameters of `S` corresponding to the symbols `vars`. If any of those is missing create a new one.
 
@@ -590,6 +591,7 @@ julia> params(S, [:q, :i])
 ```
 """
 params(S::GenericCycloRing, vars::Vector{Symbol}) = gens(base_ring(S), vars)
+params(S::GenericCycloRing, vars::Vector{String}) = gens(base_ring(S), vars)
 
 # congruence computation
 function get_substitutes!(R::GenericCycloRing)

From a3cc5d0405b8d280013f982c3701705fd92fb70d Mon Sep 17 00:00:00 2001
From: Martin Wagner <martin.wagner.dev@gmail.com>
Date: Mon, 31 Mar 2025 11:49:38 +0200
Subject: [PATCH 3/4] Fix tests

---
 src/Congruence.jl | 11 ++++++-----
 src/SumProc.jl    | 16 ++++++----------
 src/Types.jl      | 19 ++++---------------
 test/runtests.jl  | 15 +++++----------
 4 files changed, 21 insertions(+), 40 deletions(-)

diff --git a/src/Congruence.jl b/src/Congruence.jl
index b30817a..af6210b 100644
--- a/src/Congruence.jl
+++ b/src/Congruence.jl
@@ -7,14 +7,15 @@ Return a new generic character table based on `x` where the main parameter is ad
 `congruence[2]`. So the entries of `x` can potentially be simplified further.
 """
 function set_congruence(x::CharTable, congruence::Tuple{ZZRingElem,ZZRingElem})
-  if x.ring.congruence === nothing
+  R = x.ring
+  if R.congruence === nothing
     remainder, modulus = congruence
   else
-    remainder = crt(congruence..., x.ring.congruence...)
-    modulus = lcm(congruence[2], x.ring.congruence[2])
+    remainder = crt(congruence..., R.congruence...)
+    modulus = lcm(congruence[2], R.congruence[2])
   end
-  # The coercion of `GnericCharacter` relies on `base_ring(S) == base_ring(x.ring)`
-  S, E = generic_cyclotomic_ring(base_ring(x.ring); congruence=(remainder, modulus))
+  # The coercion of `GenericCharacter` relies on `base_ring(S) == base_ring(R)`
+  S = GenericCycloRing(base_ring(R), R.symbol, (remainder, modulus), R.power)
   t = typeof(x)(
     x.order,
     deepcopy(x.classinfo),
diff --git a/src/SumProc.jl b/src/SumProc.jl
index 23e4bc4..170b05c 100644
--- a/src/SumProc.jl
+++ b/src/SumProc.jl
@@ -7,13 +7,11 @@ If `vars` is `Vector{Int64}`, then `vars[i]` represents the index of the variabl
 
 # Examples
 ```jldoctest
-julia> R = universal_polynomial_ring(QQ; cached=false);
+julia> S, E, q = generic_cyclotomic_ring();
 
-julia> q = gen(R, "q");
+julia> R = base_ring(S);
 
-julia> S, E = generic_cyclotomic_ring(R);
-
-julia> i, j, k, l = gens(R, ["i", "j", "k", "l"]);
+julia> i, j, k, l = params(S, [:i, :j, :k, :l]);
 
 julia> a = S(Dict(2//(q-1)*i*j+1//q*k^2+1//2*i*l => R(1)))
 E(2*q^2 - 2*q)^(q^2*i*l + 4*q*i*j - q*i*l + 2*q*k^2 - 2*k^2)
@@ -35,13 +33,11 @@ an exception will be thrown.
 
 # Examples
 ```jldoctest
-julia> R = universal_polynomial_ring(QQ; cached=false);
-
-julia> q = gen(R, "q");
+julia> S, E, q = generic_cyclotomic_ring();
 
-julia> S, E = generic_cyclotomic_ring(R);
+julia> R = base_ring(S);
 
-julia> i, = gens(R, ["i"]);
+julia> i = param(S, :i);
 
 julia> a = S(Dict(1//(q-1)*i => R(1)))
 E(q - 1)^i
diff --git a/src/Types.jl b/src/Types.jl
index d7ec5cb..bd39f68 100644
--- a/src/Types.jl
+++ b/src/Types.jl
@@ -11,12 +11,9 @@ The ring of generic cyclotomic numbers.
 
 # Examples
 ```jldoctest
-julia> R = universal_polynomial_ring(QQ; cached=false);
+julia> S, E, q = generic_cyclotomic_ring()
+(Generic cyclotomic ring over Rational field, Generator of Generic cyclotomic ring over Rational field, q)
 
-julia> q = gen(R, "q");
-
-julia> S, E = generic_cyclotomic_ring(R)
-(Generic cyclotomic ring over Rational field, Generator of Generic cyclotomic ring over Rational field)
 ```
 """
 mutable struct GenericCycloRing <: Ring
@@ -47,11 +44,7 @@ The type for generic cyclotomic numbers.
 
 # Examples
 ```jldoctest
-julia> R = universal_polynomial_ring(QQ; cached=false);
-
-julia> q = gen(R, "q");
-
-julia> S, E = generic_cyclotomic_ring(R);
+julia> S, E, q = generic_cyclotomic_ring();
 
 julia> S(q; exponent=1//(q-1))
 q*E(q - 1)
@@ -87,11 +80,7 @@ The type for fractions of generic cyclotomic numbers.
 
 # Examples
 ```jldoctest
-julia> R = universal_polynomial_ring(QQ; cached=false);
-
-julia> q = gen(R, "q");
-
-julia> S, E = generic_cyclotomic_ring(R);
+julia> S, E, q = generic_cyclotomic_ring();
 
 julia> a = S(q; exponent=1//(q-1))
 q*E(q - 1)
diff --git a/test/runtests.jl b/test/runtests.jl
index ee0154a..e58900b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -5,25 +5,20 @@ using Test
 include("Aqua.jl")
 
 @testset "Conformance tests" begin
-  R = universal_polynomial_ring(QQ)
-  q, i, j = gens(R, ["q", "i", "j"])
-  S, E = generic_cyclotomic_ring(R)
+  S, E, q = generic_cyclotomic_ring()
+  i, j = params(S, [:i, :j])
   ConformanceTests.test_Ring_interface(S)
 end
 
 @testset "GenericCyclo" begin
-  R = universal_polynomial_ring(QQ)
-  q, i, j = gens(R, [:q, :i, :j])
-  S, E = generic_cyclotomic_ring(R)
-  S1, E = generic_cyclotomic_ring(R)
+  S, E, q = generic_cyclotomic_ring()
+  i, j = params(S, [:i, :j])
+  R = base_ring(S)
 
   a = S(Dict(1//(q - 1) * i + 2//(q - 1) * j + q^2//(q + 1) * i => R(1)))
   b = S(Dict(2 * q//(q^2 - 1) * i + 2//(q - 1) * j => R(1)))
   @test a == b
 
-  b1 = S1(Dict(2 * q//(q^2 - 1) * i + 2//(q - 1) * j => R(1)))
-  @test b != b1
-
   c = S(Dict(1//q * j => R(1)))
   @test (a + c) == (c + a)
   @test iszero(-c + c)

From ca2e5c2d0c0dc6ce5d7165e92355415e58de6f80 Mon Sep 17 00:00:00 2001
From: Martin Wagner <martin.wagner.dev@gmail.com>
Date: Tue, 1 Apr 2025 16:14:53 +0200
Subject: [PATCH 4/4] Update src/GenericCyclotomics.jl

Co-authored-by: Max Horn <max@quendi.de>
---
 src/GenericCyclotomics.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/GenericCyclotomics.jl b/src/GenericCyclotomics.jl
index 1328232..599f95a 100644
--- a/src/GenericCyclotomics.jl
+++ b/src/GenericCyclotomics.jl
@@ -503,7 +503,7 @@ Currently the optional argument `cached` is ignored.
 
 !!! warning
     In the exponents of the generic cyclotomic numbers `q` may only occur in powers which are a multiple of `power`.
-    Otherwise the simplification will return false results.
+    Otherwise the simplification may return incorrect results.
 
 # Examples
 ```jldoctest