Reimport examples from OSCAR book

test/book/cornerstones/algebraic-geometry/alexander-surface.jlcon

@@ -7,7 +7,7 @@ julia> degree(X)
 9
 
 julia> S = ambient_coordinate_ring(X)
-Multivariate polynomial ring in 5 variables over GF(31991) graded by
+Multivariate polynomial ring in 5 variables over GF(31991) graded by 
   x -> [1]
   y -> [1]
   z -> [1]

test/book/cornerstones/algebraic-geometry/ex21a.jlcon

@@ -1,4 +1,4 @@
-julia> J1 = ideal([H(I[1]), H(I[2])])
+julia> J1 = ideal([H(I[1]), H(I[2])]) 
 Ideal generated by
   x0*x2 - x1^2
   x0*x3 - x1*x2

test/book/cornerstones/algebraic-geometry/ex23a.jlcon

@@ -12,11 +12,10 @@ julia> other_pos_abs = pos_abs == 1 ? 2 : 1
 julia> cI2 = cIabs[other_pos_abs][3]
 Ideal generated by
   648*y + (-160*_a^3 - 1269*_a^2 + 22446*_a + 972)*z
-  184147758075888*x + (2850969000960*_a^3 + 22611747888864*_a^2 - 399955313722176*_a - 17319636680832)*y + (2884707374400*_a^3 + 2
-  2782606070410*_a^2 - 405172045313820*_a - 57843867366864)*z
+  184147758075888*x + (2850969000960*_a^3 + 22611747888864*_a^2 - 399955313722176*_a - 17319636680832)*y + (2884707374400*_a^3 + 22782606070410*_a^2 - 405172045313820*_a - 57843867366864)*z
 
 julia> R2 = base_ring(cI2)
-Multivariate polynomial ring in 3 variables over number field graded by
+Multivariate polynomial ring in 3 variables over number field graded by 
   x -> [1]
   y -> [1]
   z -> [1]

test/book/cornerstones/algebraic-geometry/ex314.jlcon

@@ -68,13 +68,11 @@ M1 -> M
 e[1] -> (-x_0*x_3 + x_1*x_2)*e[1]
 Graded module homomorphism of degree [2]
 
-
 julia> phi2 = psi(tohomM1M(hom1[2]))
 M1 -> M
 e[1] -> (-x_0*x_2 + x_1^2)*e[1]
 Graded module homomorphism of degree [2]
 
-
 julia> kerphi2, _ = kernel(phi2);
 
 julia> iszero(kerphi2)

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/algebraic-geometry/param.jlcon

@@ -4,8 +4,7 @@ julia> f = x^5 + 10*x^4*y + 20*x^3*y^2 + 130*x^2*y^3 - 20*x*y^4 + 20*y^5 - 2*x^4
 
 julia> C = plane_curve(f)
 Projective plane curve
-  defined by 0 = x^5 + 10*x^4*y - 2*x^4*z + 20*x^3*y^2 - 40*x^3*y*z + x^3*z^2 + 130*x^2*y^3 - 150*x^2*y^2*z + 30*x^2*y*z^2 - 20*x*
-  y^4 - 90*x*y^3*z + 110*x*y^2*z^2 + 20*y^5 - 40*y^4*z + 20*y^3*z^2
+  defined by 0 = x^5 + 10*x^4*y - 2*x^4*z + 20*x^3*y^2 - 40*x^3*y*z + x^3*z^2 + 130*x^2*y^3 - 150*x^2*y^2*z + 30*x^2*y*z^2 - 20*x*y^4 - 90*x*y^3*z + 110*x*y^2*z^2 + 20*y^5 - 40*y^4*z + 20*y^3*z^2
 
 julia> conics = [x^2-x*z, y^2-y*z];
 

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="0.4"; io=devnull)
 using GenericCharacterTables
-# for nicer printing
-using GenericCharacterTables: ParameterException

test/book/cornerstones/groups/explSL25.jlcon

@@ -4,21 +4,37 @@ SL(2,5)
 julia> T = character_table(G)
 Character table of SL(2,5)
 
-  2  3                 1                 1  3                  1                  1  1  1  2
-  3  1                 .                 .  1                  .                  .  1  1  .
-  5  1                 1                 1  1                  1                  1  .  .  .
-
-    1a               10a               10b 2a                 5a                 5b 3a 6a 4a
-
-X_1  1                 1                 1  1                  1                  1  1  1  1
-X_2  2 z_5^3 + z_5^2 + 1    -z_5^3 - z_5^2 -2 -z_5^3 - z_5^2 - 1      z_5^3 + z_5^2 -1  1  .
-X_3  2    -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1 -2      z_5^3 + z_5^2 -z_5^3 - z_5^2 - 1 -1  1  .
-X_4  3    -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1  3     -z_5^3 - z_5^2  z_5^3 + z_5^2 + 1  .  . -1
-X_5  3 z_5^3 + z_5^2 + 1    -z_5^3 - z_5^2  3  z_5^3 + z_5^2 + 1     -z_5^3 - z_5^2  .  . -1
-X_6  4                -1                -1  4                 -1                 -1  1  1  .
-X_7  4                 1                 1 -4                 -1                 -1  1 -1  .
-X_8  5                 .                 .  5                  .                  . -1 -1  1
-X_9  6                -1                -1 -6                  1                  1  .  .  .
+  2  3                 1                 1  3                  1
+  3  1                 .                 .  1                  .
+  5  1                 1                 1  1                  1
+
+    1a               10a               10b 2a                 5a
+
+X_1  1                 1                 1  1                  1
+X_2  2 z_5^3 + z_5^2 + 1    -z_5^3 - z_5^2 -2 -z_5^3 - z_5^2 - 1
+X_3  2    -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1 -2      z_5^3 + z_5^2
+X_4  3    -z_5^3 - z_5^2 z_5^3 + z_5^2 + 1  3     -z_5^3 - z_5^2
+X_5  3 z_5^3 + z_5^2 + 1    -z_5^3 - z_5^2  3  z_5^3 + z_5^2 + 1
+X_6  4                -1                -1  4                 -1
+X_7  4                 1                 1 -4                 -1
+X_8  5                 .                 .  5                  .
+X_9  6                -1                -1 -6                  1
+
+  2                  1  1  1  2
+  3                  .  1  1  .
+  5                  1  .  .  .
+
+                    5b 3a 6a 4a
+
+X_1                  1  1  1  1
+X_2      z_5^3 + z_5^2 -1  1  .
+X_3 -z_5^3 - z_5^2 - 1 -1  1  .
+X_4  z_5^3 + z_5^2 + 1  .  . -1
+X_5     -z_5^3 - z_5^2  .  . -1
+X_6                 -1  1  1  .
+X_7                 -1  1 -1  .
+X_8                  . -1 -1  1
+X_9                  1  .  .  .
 
 julia> R = gmodule(T[end])
 G-module for G acting on vector space of dimension 6 over abelian closure of Q

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

@@ -1,4 +1,4 @@
-julia> Oscar.randseed!(7360734);
+julia> Oscar.randseed!(3371100);
 
 julia> Qx, x = QQ["x"];
 
@@ -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);