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Update book example for GenericCharacterTables #4163

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Oct 2, 2024
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Update book example for GenericCharacterTables #4163

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2 changes: 1 addition & 1 deletion test/book/cornerstones/groups/auxiliary_code/main.jl
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
import Pkg
Pkg.add(name="GenericCharacterTables", version="0.2"; io=devnull)
Pkg.add(name="GenericCharacterTables", version="0.4"; io=devnull)
using GenericCharacterTables
# for nicer printing
using GenericCharacterTables: ParameterException
99 changes: 51 additions & 48 deletions test/book/cornerstones/groups/genchar.jlcon
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Original file line number Diff line number Diff line change
@@ -1,63 +1,66 @@
julia> T = genchartab("SL3.n1")
Generic character table
julia> T = generic_character_table("SL3.n1")
Generic character table SL3.n1
of order q^8 - q^6 - q^5 + q^3
with 8 irreducible character types
with 8 class types
with parameters (a, b, m, n)

julia> printval(T,char=4,class=4)
Value of character type 4 on class type
4: (q + 1) * exp(2π𝑖(1//(q - 1)*a*n)) + (1) * exp(2π𝑖(-2//(q - 1)*a*n))

julia> h = tensor!(T,2,2)
9

julia> scalar(T,4,h)
(0, Set(ParameterException{QQPolyRingElem}[(2*n1)//(q - 1) ∈ ℤ]))

julia> print_decomposition(T, h)
Decomposing character 9:
<1,9> = 1
<2,9> = 2
<3,9> = 2
<4,9> = 0 with possible exceptions:
(2*n1)//(q - 1) ∈ ℤ
<5,9> = 0 with possible exceptions:
(2*n1)//(q - 1) ∈ ℤ
<6,9> = 0 with possible exceptions:
(m1 + n1)//(q - 1) ∈ ℤ
(2*m1 - n1)//(q - 1) ∈ ℤ
(m1)//(q - 1) ∈ ℤ
(n1)//(q - 1) ∈ ℤ
(m1 - n1)//(q - 1) ∈ ℤ
(m1 - 2*n1)//(q - 1) ∈ ℤ
<7,9> = 0 with possible exceptions:
(n1)//(q - 1) ∈ ℤ
<8,9> = 0 with possible exceptions:
((q + 1)*n1)//(q^2 + q + 1) ∈ ℤ
(q*n1)//(q^2 + q + 1) ∈ ℤ
(n1)//(q^2 + q + 1) ∈ ℤ
julia> chardeg(T, lincomb!(T,[1,2,2],[1,2,3]))
julia> T[4,4]
(q + 1)*exp(2π𝑖((a*n)//(q - 1))) + exp(2π𝑖((-2*a*n)//(q - 1)))

julia> h = T[2] * T[2];

julia> scalar_product(T[4], h)
0
With exceptions:
2*n1 ∈ (q - 1)ℤ

julia> for i in 1:8 println("<$i, h> = ", scalar_product(T[i], h)) end
<1, h> = 1
<2, h> = 2
<3, h> = 2
<4, h> = 0
With exceptions:
2*n1 ∈ (q - 1)ℤ
<5, h> = 0
With exceptions:
2*n1 ∈ (q - 1)ℤ
<6, h> = 0
With exceptions:
2*m1 - n1 ∈ (q - 1)ℤ
m1 - 2*n1 ∈ (q - 1)ℤ
m1 + n1 ∈ (q - 1)ℤ
m1 ∈ (q - 1)ℤ
m1 - n1 ∈ (q - 1)ℤ
n1 ∈ (q - 1)ℤ
<7, h> = 0
With exceptions:
n1 ∈ (q - 1)ℤ
<8, h> = 0
With exceptions:
q*n1 ∈ (q^2 + q + 1)ℤ
n1 ∈ (q^2 + q + 1)ℤ
q*n1 + n1 ∈ (q^2 + q + 1)ℤ

julia> degree(linear_combination([1,2,2],[T[1],T[2],T[3]]))
2*q^3 + 2*q^2 + 2*q + 1

julia> chardeg(T, h)
julia> degree(h)
q^4 + 2*q^3 + q^2

julia> printcharparam(T,4)
4 n ∈ {1,…, q - 1} except (n)//(q - 1) ∈ ℤ
julia> parameters(T[4])
n ∈ {1,…, q - 1} except n ∈ (q - 1)ℤ

julia> T2 = setcongruence(T, (0,2));
julia> T2 = set_congruence(T; remainder=0, modulus=2);

julia> (q, (a, b, m, n)) = params(T2);
julia> (q, (a, b, m, n)) = parameters(T2);

julia> x = param(T2, "x"); # create an additional "free" variable
julia> x = parameter(T2, "x"); # create an additional "free" variable

julia> speccharparam!(T2, 6, m, -n + (q-1)*x) # force m = -n (mod q-1)
julia> s = specialize(T2[6], m, -n + (q-1)*x); # force m = -n (mod q-1)

julia> s, e = scalar(T2,6,h); s
julia> scalar_product(s, T2(h))
1

julia> e
Set{ParameterException{QQPolyRingElem}} with 2 elements:
(2*n1)//(q - 1) ∈ ℤ
(3*n1)//(q - 1) ∈ ℤ
With exceptions:
3*n1 ∈ (q - 1)ℤ
2*n1 ∈ (q - 1)ℤ
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