[1.0] Update book examples

.github/workflows/CI.yml

@@ -73,7 +73,8 @@ jobs:
           # be able to properly deal with PRs / merges
           fetch-depth: 2
       - name: "Set up Julia"
-        uses: julia-actions/setup-julia@v1
+        id: setup-julia
+        uses: julia-actions/setup-julia@v2
         with:
           version: ${{ matrix.julia-version }}
       - uses: julia-actions/cache@v1
@@ -89,6 +90,9 @@ jobs:
       - name: "set test subgroup"
         if: ${{ matrix.group }} != ''
         run: echo "OSCAR_TEST_SUBSET=${{matrix.group}}" >> $GITHUB_ENV
+      - name: "workaround libstdc++ issue for julia 1.6"
+        if: matrix.julia-version == '1.6' && runner.os == 'Linux'
+        run: rm -f ${{ steps.setup-julia.outputs.julia-bindir }}/../lib/julia/libstdc++.so.6
       - name: "Run tests"
         uses: julia-actions/julia-runtest@latest
         with:

test/book/cornerstones/algebraic-geometry/exres.jlcon

@@ -1,25 +1,25 @@
-julia> R, (w, x, y, z) = graded_polynomial_ring(QQ, ["w", "x", "y", "z"]);
+julia> S, (w, x, y, z) = graded_polynomial_ring(QQ, ["w", "x", "y", "z"]);
 
-julia> I = ideal([w^2-x*z,w*x-y*z,x^2-w*y,x*y-z^2,y^2-w*z]);
+julia> J = ideal([w^2-x*z,w*x-y*z,x^2-w*y,x*y-z^2,y^2-w*z]);
 
-julia> A, _ = quo(R, I);
+julia> A, _ = quo(S, J);
 
 julia> FA = free_resolution(A)
 Free resolution of A
-R^1 <---- R^5 <---- R^6 <---- R^2 <---- 0
+S^1 <---- S^5 <---- S^6 <---- S^2 <---- 0
 0         1         2         3         4
 
 julia> FA[1]
-Graded free module R^5([-2]) of rank 5 over R
+Graded free module S^5([-2]) of rank 5 over S
 
 julia> FA[2]
-Graded free module R^5([-3]) + R^1([-4]) of rank 6 over R
+Graded free module S^5([-3]) + S^1([-4]) of rank 6 over S
 
 julia> FA[3]
-Graded free module R^1([-4]) + R^1([-5]) of rank 2 over R
+Graded free module S^1([-4]) + S^1([-5]) of rank 2 over S
 
 julia> map(FA,1)
-R^5 -> R^1
+S^5 -> S^1
 e[1] -> (-w*z + y^2)*e[1]
 e[2] -> (x*y - z^2)*e[1]
 e[3] -> (-w*y + x^2)*e[1]
@@ -28,7 +28,7 @@ e[5] -> (w^2 - x*z)*e[1]
 Homogeneous module homomorphism
 
 julia> map(FA,2)
-R^6 -> R^5
+S^6 -> S^5
 e[1] -> -x*e[1] + y*e[2] - z*e[4]
 e[2] -> w*e[1] - x*e[2] + y*e[3] + z*e[5]
 e[3] -> -w*e[3] + x*e[4] - y*e[5]
@@ -38,7 +38,7 @@ e[6] -> (-w^2 + x*z)*e[1] + (-w*z + y^2)*e[5]
 Homogeneous module homomorphism
 
 julia> map(FA,3)
-R^2 -> R^6
+S^2 -> S^6
 e[1] -> -w*e[2] - y*e[3] + x*e[4] - e[6]
 e[2] -> (-w^2 + x*z)*e[1] + y*z*e[2] + z^2*e[3] - w*y*e[4] + (w*z - y^2)*e[5] + x*e[6]
 Homogeneous module homomorphism

test/book/cornerstones/algebraic-geometry/hilbert-polynomial.jlcon

@@ -1,6 +1,6 @@
-julia> R, (w,x,y,z) = graded_polynomial_ring(QQ, ["w", "x", "y", "z"]);
+julia> S, (w,x,y,z) = graded_polynomial_ring(QQ, ["w", "x", "y", "z"]);
 
-julia> I = ideal(R, [x*w-y*z, y*w-(x-z)*(x-2*z)]);
+julia> I = ideal(S, [x*w-y*z, y*w-(x-z)*(x-2*z)]);
 
 julia> Q = projective_scheme(I);
 

test/book/cornerstones/groups/actions.jlcon

@@ -3,8 +3,7 @@ G-set of
   Alt(4)
   with seeds 1:4
 
-julia> G = dihedral_group(6)
-Pc group of order 6
+julia> G = dihedral_group(6);
 
 julia> U = sub(G, [g for g in gens(G) if order(g) == 2])[1]
 Pc group of order 2
@@ -37,7 +36,7 @@ Group homomorphism
 julia> phi(G[1]), phi(G[2])
 ((2,3), (1,2,3))
 
-julia> function optimal_perm_rep(G)
+julia> function optimal_transitive_perm_rep(G)
          is_natural_symmetric_group(G) && return hom(G,G,gens(G))
          is_natural_alternating_group(G) && return hom(G,G,gens(G))
          cand = []  # pairs (U,h) with U ≤ G and h a map G -> Sym(G/U)
@@ -52,7 +51,7 @@ julia> function optimal_perm_rep(G)
 julia> U = dihedral_group(8)
 Pc group of order 8
 
-julia> optimal_perm_rep(U)
+julia> optimal_transitive_perm_rep(U)
 Group homomorphism
   from pc group of order 8
   to permutation group of degree 4 and order 8
@@ -65,8 +64,8 @@ Group homomorphism
 julia> permutation_group(U)
 Permutation group of degree 8 and order 8
 
-julia> for g in all_transitive_groups(degree => 3:9, !is_primitive)
-         h = image(optimal_perm_rep(g))[1]
+julia> for g in all_transitive_groups(degree => 3:8, !is_primitive)
+         h = image(optimal_transitive_perm_rep(g))[1]
          if degree(h) < degree(g)
            id = transitive_group_identification(g)
            id_new = transitive_group_identification(h)
@@ -81,5 +80,3 @@ julia> for g in all_transitive_groups(degree => 3:9, !is_primitive)
 (8, 13) => (6, 6)
 (8, 14) => (4, 5)
 (8, 24) => (6, 11)
-(9, 4) => (6, 5)
-(9, 8) => (6, 9)

test/book/cornerstones/groups/auxiliary_code/main.jl

@@ -1,5 +1,3 @@
 import Pkg
-Pkg.add(name="GenericCharacterTables", version=v"0.2"; io=devnull)
+Pkg.add(name="GenericCharacterTables", version="0.4"; io=devnull)
 using GenericCharacterTables
-# for nicer printing
-using GenericCharacterTables: ParameterException

test/book/cornerstones/groups/genchar.jlcon

@@ -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

test/book/cornerstones/groups/intro.jlcon

@@ -62,13 +62,7 @@ julia> pts = collect(orb)
 
 julia> visualize(convex_hull(pts))
 
-julia> R2 = free_module(K, 2) # the "euclidean" plane over K
-Vector space of dimension 2 over field of algebraic numbers
-
-julia> A = R2([0,1])
-(Root 0 of x, Root 1.00000 of x - 1)
-
-julia> pts = [A*mat_rot^i for i in 0:4];
+julia> R2 = vector_space(K, 2); # the "euclidean" plane over K
 
 julia> sigma_1 = hom(R2, R2, [-R2[1], R2[2]])
 Module homomorphism

test/book/cornerstones/number-theory/galoismod.jlcon

@@ -52,9 +52,9 @@ true
 
 julia> V, f = galois_module(K); OK = ring_of_integers(K); M = f(OK);
 
-julia> fl, c = is_free_with_basis(M); # the elements of c are a basis
+julia> fl, c = is_free_with_basis(M); # the elements of c form a basis
 
-julia> b = preimage(f, c[1]) # the element might different per session
+julia> b = preimage(f, c[1]) # the element may be different per session
 a
 
 julia> A, mA = automorphism_group(K);

test/book/cornerstones/number-theory/intro.jlcon

@@ -94,4 +94,4 @@ julia> preimage(mU, -214841715*a - 3293461126)
 Abelian group element [1, 5]
 
 julia> -214841715*a - 3293461126 == (-1)^1 * (3a + 46)^5
-true
+true

test/book/cornerstones/polyhedral-geometry/GKZ_orbits.jlcon

@@ -15,8 +15,7 @@ julia> OrbitRepresentatives=
 julia> OrbitSizes = 
         [length(
           filter(x->minimum(gset(G,permuted,[x]))==u,
-          GKZ_Vectors)
-         ) for u in OrbitRepresentatives];
+          GKZ_Vectors)) for u in OrbitRepresentatives];
 
 julia> show(OrbitSizes)
 [12, 24, 24, 8, 2, 4]

test/book/cornerstones/polyhedral-geometry/platonic.jlcon

@@ -1,4 +1,5 @@
-julia> [ f_vector(P) for P in [T, cube(3), cross_polytope(3), dodecahedron(), icosahedron()] ]
+julia> [ f_vector(P) for P in [T, cube(3), cross_polytope(3),
+                               dodecahedron(), icosahedron()] ]
 5-element Vector{Vector{ZZRingElem}}:
  [4, 6, 4]
  [8, 12, 6]