Adjust doctests

docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases_integers.md

@@ -56,7 +56,9 @@ julia> R, (x,y) = polynomial_ring(ZZ, ["x","y"])
 (Multivariate polynomial ring in 2 variables over ZZ, ZZMPolyRingElem[x, y])
 
 julia> I = ideal(R, [3*x^2*y+7*y, 4*x*y^2-5*x])
-ideal(3*x^2*y + 7*y, 4*x*y^2 - 5*x)
+Ideal generated by
+  3*x^2*y + 7*y
+  4*x*y^2 - 5*x
 
 julia> G = groebner_basis(I, ordering = lex(R))
 Gröbner basis with elements

docs/src/CommutativeAlgebra/Miscellaneous/binomial_ideals.md

@@ -62,7 +62,9 @@ julia> is_binomial(f)
 true
 
 julia> J = ideal(R, [x^2-y^3, z^2])
-ideal(x^2 - y^3, z^2)
+Ideal generated by
+  x^2 - y^3
+  z^2
 
 julia> is_binomial(J)
 true

docs/src/CommutativeAlgebra/affine_algebras.md

@@ -77,7 +77,9 @@ Multivariate polynomial ring in 3 variables x, y, z
   over rational field
 
 julia> modulus(A)
-ideal(-x^2 + y, -x^3 + z)
+Ideal generated by
+  -x^2 + y
+  -x^3 + z
 
 julia> gens(A)
 3-element Vector{MPolyQuoRingElem{QQMPolyRingElem}}:
@@ -231,7 +233,7 @@ julia> base_ring(a)
 Quotient
   of multivariate polynomial ring in 3 variables x, y, z
     over rational field
-  by ideal(-x^2 + y, -x^3 + z)
+  by ideal (-x^2 + y, -x^3 + z)
 
 julia> gens(a)
 2-element Vector{MPolyQuoRingElem{QQMPolyRingElem}}:
@@ -369,7 +371,10 @@ defined by
   z -> t^3
 
 julia> twistedCubic = kernel(para)
-ideal(-x*z + y^2, -w*z + x*y, -w*y + x^2)
+Ideal generated by
+  -x*z + y^2
+  -w*z + x*y
+  -w*y + x^2
 
 julia> C2, p2 = quo(D1, twistedCubic);
 
@@ -380,14 +385,15 @@ julia> V2 = [p2(w-y), p2(x), p2(z)];
 julia> proj = hom(D2, C2, V2)
 Ring homomorphism
   from graded multivariate polynomial ring in 3 variables over QQ
-  to quotient of multivariate polynomial ring by ideal(-x*z + y^2, -w*z + x*y, -w*y + x^2)
+  to quotient of multivariate polynomial ring by ideal (-x*z + y^2, -w*z + x*y, -w*y + x^2)
 defined by
   a -> w - y
   b -> x
   c -> z
 
 julia> nodalCubic = kernel(proj)
-ideal(-a^2*c + b^3 - 2*b^2*c + b*c^2)
+Ideal generated by
+  -a^2*c + b^3 - 2*b^2*c + b*c^2
 
 ```
 
@@ -408,10 +414,12 @@ defined by
   y[3] -> x[2]*x[3]
 
 julia> sphere = ideal(C3, [x[1]^3 + x[2]^3  + x[3]^3 - 1])
-ideal(x[1]^3 + x[2]^3 + x[3]^3 - 1)
+Ideal generated by
+  x[1]^3 + x[2]^3 + x[3]^3 - 1
 
 julia> steinerRomanSurface = preimage(F3, sphere)
-ideal(y[1]^6*y[2]^6 + 2*y[1]^6*y[2]^3*y[3]^3 + y[1]^6*y[3]^6 + 2*y[1]^3*y[2]^6*y[3]^3 + 2*y[1]^3*y[2]^3*y[3]^6 - y[1]^3*y[2]^3*y[3]^3 + y[2]^6*y[3]^6)
+Ideal generated by
+  y[1]^6*y[2]^6 + 2*y[1]^6*y[2]^3*y[3]^3 + y[1]^6*y[3]^6 + 2*y[1]^3*y[2]^6*y[3]^3 + 2*y[1]^3*y[2]^3*y[3]^6 - y[1]^3*y[2]^3*y[3]^3 + y[2]^6*y[3]^6
 
 ```
 
@@ -439,7 +447,7 @@ julia> V = [p(2*a + b^6), p(7*b - a^2), p(c^2)];
 julia> F = hom(D, C, V)
 Ring homomorphism
   from multivariate polynomial ring in 3 variables over QQ
-  to quotient of multivariate polynomial ring by ideal(-b^3 + c)
+  to quotient of multivariate polynomial ring by ideal (-b^3 + c)
 defined by
   x -> 2*a + c^2
   y -> -a^2 + 7*b
@@ -528,17 +536,17 @@ julia> L[1]
 
 julia> L[2]
 Ring homomorphism
-  from quotient of multivariate polynomial ring by ideal(x*y, x*z)
-  to quotient of multivariate polynomial ring by ideal(2*x^2 + x*y, 10*x^2 + 5*x*y + x*z)
+  from quotient of multivariate polynomial ring by ideal (x*y, x*z)
+  to quotient of multivariate polynomial ring by ideal (2*x^2 + x*y, 10*x^2 + 5*x*y + x*z)
 defined by
   x -> x
   y -> 2*x + y
   z -> 10*x + 5*y + z
 
 julia> L[3]
 Ring homomorphism
-  from quotient of multivariate polynomial ring by ideal(2*x^2 + x*y, 10*x^2 + 5*x*y + x*z)
-  to quotient of multivariate polynomial ring by ideal(x*y, x*z)
+  from quotient of multivariate polynomial ring by ideal (2*x^2 + x*y, 10*x^2 + 5*x*y + x*z)
+  to quotient of multivariate polynomial ring by ideal (x*y, x*z)
 defined by
   x -> x
   y -> -2*x + y

docs/src/CommutativeAlgebra/ideals.md

@@ -36,7 +36,10 @@ julia> R, (x, y) = polynomial_ring(QQ, ["x", "y"])
 (Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])
 
 julia> I = ideal(R, [x, y])^2
-ideal(x^2, x*y, y^2)
+Ideal generated by
+  x^2
+  x*y
+  y^2
 
 julia> base_ring(I)
 Multivariate polynomial ring in 2 variables x, y

docs/src/CommutativeAlgebra/localizations.md

@@ -111,11 +111,12 @@ This reflects the way of creating localizations of quotients of multivariate pol
 julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> P = ideal(R, [x])
-ideal(x)
+Ideal generated by
+  x
 
 julia> U = complement_of_prime_ideal(P)
 Complement
-  of prime ideal(x)
+  of prime ideal (x)
   in multivariate polynomial ring in 3 variables over QQ
 
 julia> Rloc, _ = localization(U);
@@ -135,14 +136,18 @@ julia> K, a =  number_field(2*t^2-1, "a");
 julia> R, (x, y) = polynomial_ring(K, ["x", "y"]);
 
 julia> I = ideal(R, [2*x^2-y^3, 2*x^2-y^5])
-ideal(2*x^2 - y^3, 2*x^2 - y^5)
+Ideal generated by
+  2*x^2 - y^3
+  2*x^2 - y^5
 
 julia> P = ideal(R, [y-1, x-a])
-ideal(y - 1, x - a)
+Ideal generated by
+  y - 1
+  x - a
 
 julia> U = complement_of_prime_ideal(P)
 Complement
-  of prime ideal(y - 1, x - a)
+  of prime ideal (y - 1, x - a)
   in multivariate polynomial ring in 2 variables over number field
 
 julia> RQ, _ = quo(R, I);
@@ -181,11 +186,12 @@ julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> P = ideal(R, [x])
-ideal(x)
+Ideal generated by
+  x
 
 julia> U = complement_of_prime_ideal(P)
 Complement
-  of prime ideal(x)
+  of prime ideal (x)
   in multivariate polynomial ring in 3 variables over QQ
 
 julia> Rloc, iota = localization(U);
@@ -225,14 +231,18 @@ julia> K, a =  number_field(2*t^2-1, "a");
 julia> R, (x, y) = polynomial_ring(K, ["x", "y"]);
 
 julia> I = ideal(R, [2*x^2-y^3, 2*x^2-y^5])
-ideal(2*x^2 - y^3, 2*x^2 - y^5)
+Ideal generated by
+  2*x^2 - y^3
+  2*x^2 - y^5
 
 julia> P = ideal(R, [y-1, x-a])
-ideal(y - 1, x - a)
+Ideal generated by
+  y - 1
+  x - a
 
 julia> U = complement_of_prime_ideal(P)
 Complement
-  of prime ideal(y - 1, x - a)
+  of prime ideal (y - 1, x - a)
   in multivariate polynomial ring in 2 variables over number field
 
 julia> RQ, p = quo(R, I);
@@ -289,11 +299,12 @@ of representing `f` by pairs of elements of `RQ` and not the internal representa
 julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
 
 julia> P = ideal(R, [x])
-ideal(x)
+Ideal generated by
+  x
 
 julia> U = complement_of_prime_ideal(P)
 Complement
-  of prime ideal(x)
+  of prime ideal (x)
   in multivariate polynomial ring in 3 variables over QQ
 
 julia> Rloc, iota = localization(U);
@@ -305,7 +316,7 @@ julia> parent(f)
 Localization
   of multivariate polynomial ring in 3 variables x, y, z
     over rational field
-  at complement of prime ideal(x)
+  at complement of prime ideal (x)
 
 julia> g = iota(y)/iota(z)
 y/z
@@ -328,14 +339,18 @@ julia> K, a =  number_field(2*t^2-1, "a");
 julia> R, (x, y) = polynomial_ring(K, ["x", "y"]);
 
 julia> I = ideal(R, [2*x^2-y^3, 2*x^2-y^5])
-ideal(2*x^2 - y^3, 2*x^2 - y^5)
+Ideal generated by
+  2*x^2 - y^3
+  2*x^2 - y^5
 
 julia> P = ideal(R, [y-1, x-a])
-ideal(y - 1, x - a)
+Ideal generated by
+  y - 1
+  x - a
 
 julia> U = complement_of_prime_ideal(P)
 Complement
-  of prime ideal(y - 1, x - a)
+  of prime ideal (y - 1, x - a)
   in multivariate polynomial ring in 2 variables over number field
 
 julia> RQ, p = quo(R, I);
@@ -352,8 +367,8 @@ Localization
   of quotient
     of multivariate polynomial ring in 2 variables x, y
       over number field of degree 2 over QQ
-    by ideal(2*x^2 - y^3, 2*x^2 - y^5)
-  at complement of prime ideal(y - 1, x - a)
+    by ideal (2*x^2 - y^3, 2*x^2 - y^5)
+  at complement of prime ideal (y - 1, x - a)
 
 julia> g = f/phi(y)
 x/y
@@ -441,9 +456,7 @@ julia> U = complement_of_point_ideal(R, [0, 0]);
 julia> Rloc, _ = localization(R, U);
 
 julia> MI = ideal(Rloc, V)
-Ideal
-  of localized ring
-with 2 generators
+Ideal generated by
   3*x^2
   4*y^3
 ```

docs/src/InvariantTheory/finite_groups.md

@@ -93,10 +93,8 @@ Matrix group of degree 3
   over cyclotomic field of order 3
 
 julia> IR = invariant_ring(G)
-Invariant ring of
-  Matrix group of degree 3 over cyclotomic field of order 3
-with generators
-  AbstractAlgebra.Generic.MatSpaceElem{nf_elem}[[0 0 1; 1 0 0; 0 1 0], [1 0 0; 0 a 0; 0 0 -a-1]]
+Invariant ring
+  of matrix group of degree 3 over cyclotomic field of order 3
 
 julia> group(IR)
 Matrix group of degree 3

experimental/FTheoryTools/src/FamilyOfSpaces/attributes.jl

@@ -115,7 +115,8 @@ julia> f = family_of_spaces(coord_ring, grading, d)
 A family of spaces of dimension d = 3
 
 julia> stanley_reisner_ideal(f)
-ideal(f*g*Kbar*u)
+Ideal generated by
+  f*g*Kbar*u
 ```
 """
 @attr MPolyIdeal{QQMPolyRingElem} function stanley_reisner_ideal(f::FamilyOfSpaces)
@@ -149,7 +150,11 @@ julia> f = family_of_spaces(coord_ring, grading, d)
 A family of spaces of dimension d = 3
 
 julia> irrelevant_ideal(f)
-ideal(u, Kbar, g, f)
+Ideal generated by
+  u
+  Kbar
+  g
+  f
 ```
 """
 @attr MPolyIdeal{QQMPolyRingElem} function irrelevant_ideal(f::FamilyOfSpaces)
@@ -182,7 +187,9 @@ julia> f = family_of_spaces(coord_ring, grading, 3)
 A family of spaces of dimension d = 3
 
 julia> ideal_of_linear_relations(f)
-ideal(-5*f + 3*g + 2*Kbar, -3*f + 2*g)
+Ideal generated by
+  -5*f + 3*g + 2*Kbar
+  -3*f + 2*g
 ```
 """
 @attr MPolyIdeal{QQMPolyRingElem} function ideal_of_linear_relations(f::FamilyOfSpaces)

experimental/FTheoryTools/src/TateModels/attributes.jl

@@ -352,7 +352,7 @@ julia> length(singular_loci(t))
 2
 
 julia> singular_loci(t)[2]
-(ideal(w), (1, 2, 3), "III")
+(Ideal (w), (1, 2, 3), "III")
 ```
 """
 @attr Vector{<:Tuple{<:MPolyIdeal{<:MPolyRingElem}, Tuple{Int64, Int64, Int64}, String}} function singular_loci(t::GlobalTateModel)

experimental/MatroidRealizationSpaces/src/realization_space.jl

@@ -506,7 +506,7 @@ One realization is given by
   [0   0   0   1   x1 + 1       x1    1   x1   x1 + 1]
 in the multivariate polynomial ring in 1 variable over GF(2)
 within the vanishing set of the ideal
-ideal(x1^2 + x1 + 1)
+Ideal (x1^2 + x1 + 1)
 
 julia> realization(uniform_matroid(3,6), char=5)
 One realization is given by

experimental/Schemes/BlowupMorphism.jl

@@ -204,14 +204,17 @@ Spectrum
     over rational field
 
 julia> I = ideal(R, [x,y,z])
-ideal(x, y, z)
+Ideal generated by
+  x
+  y
+  z
 
 julia> bl = blow_up(A3, I)
 Blowup
   of scheme over QQ covered with 1 patch
     1b: [x, y, z]   affine 3-space
   in sheaf of ideals with restriction
-    1b: ideal(x, y, z)
+    1b: Ideal (x, y, z)
 with domain
   scheme over QQ covered with 3 patches
     1a: [(s1//s0), (s2//s0), x]   V(0, 0, 0)
@@ -241,7 +244,7 @@ Sheaf of ideals
   on scheme over QQ covered with 1 patch
     1: [x, y, z]   affine 3-space
 with restriction
-  1: ideal(x, y, z)
+  1: Ideal (x, y, z)
 ```
 """
 @attributes mutable struct BlowupMorphism{

experimental/Schemes/CartierDivisor.jl

@@ -161,9 +161,9 @@ Effective cartier divisor
     3: [(x//z), (y//z)]   affine 2-space
 defined by
   sheaf of ideals with restrictions
-    1: ideal(-(y//x)^2*(z//x) + 1)
-    2: ideal((x//y)^3 - (z//y))
-    3: ideal((x//z)^3 - (y//z)^2)
+    1: Ideal (-(y//x)^2*(z//x) + 1)
+    2: Ideal ((x//y)^3 - (z//y))
+    3: Ideal ((x//z)^3 - (y//z)^2)
 
 julia> cartier_divisor(E)
 Cartier divisor
@@ -227,9 +227,9 @@ Effective cartier divisor
     3: [(x//z), (y//z)]   affine 2-space
 defined by
   sheaf of ideals with restrictions
-    1: ideal(-(y//x)^2*(z//x) + 1)
-    2: ideal((x//y)^3 - (z//y))
-    3: ideal((x//z)^3 - (y//z)^2)
+    1: Ideal (-(y//x)^2*(z//x) + 1)
+    2: Ideal ((x//y)^3 - (z//y))
+    3: Ideal ((x//z)^3 - (y//z)^2)
 ```
 """
 effective_cartier_divisor(I::IdealSheaf; trivializing_covering::Covering = default_covering(scheme(I)), check::Bool = true) = EffectiveCartierDivisor(I, trivializing_covering=trivializing_covering, check=check)