Update doctests

docs/src/direct_sum.md

@@ -45,7 +45,7 @@ julia> m2 = F(BigInt[9, 7, -2, 2, -4])
 (9, 7, -2, 2, -4)
 
 julia> S1, f1 = sub(F, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 5 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 5 over integers)
 
 julia> m1 = F(BigInt[3, 1, 7, 7, -7])
 (3, 1, 7, 7, -7)
@@ -54,7 +54,7 @@ julia> m2 = F(BigInt[-8, 6, 10, -1, 1])
 (-8, 6, 10, -1, 1)
 
 julia> S2, f2 = sub(F, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 5 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 5 over integers)
 
 julia> m1 = F(BigInt[2, 4, 2, -3, -10])
 (2, 4, 2, -3, -10)
@@ -63,10 +63,10 @@ julia> m2 = F(BigInt[5, 7, -6, 9, -5])
 (5, 7, -6, 9, -5)
 
 julia> S3, f3 = sub(F, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 5 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 5 over integers)
 
 julia> D, f = direct_sum(S1, S2, S3)
-(DirectSumModule over integers, AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: submodule over Integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over Integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over Integers with 2 generators and no relations -> DirectSumModule over integers], AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: DirectSumModule over integers -> submodule over Integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over Integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over Integers with 2 generators and no relations])
+(DirectSumModule over integers, AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: submodule over integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over integers with 2 generators and no relations -> DirectSumModule over integers], AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: DirectSumModule over integers -> submodule over integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over integers with 2 generators and no relations])
 ```
 
 ## Functionality for direct sums
@@ -93,7 +93,7 @@ julia> m2 = F(BigInt[9, 7, -2, 2, -4])
 (9, 7, -2, 2, -4)
 
 julia> S1, f1 = sub(F, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 5 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 5 over integers)
 
 julia> m1 = F(BigInt[3, 1, 7, 7, -7])
 (3, 1, 7, 7, -7)
@@ -102,7 +102,7 @@ julia> m2 = F(BigInt[-8, 6, 10, -1, 1])
 (-8, 6, 10, -1, 1)
 
 julia> S2, f2 = sub(F, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 5 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 5 over integers)
 
 julia> m1 = F(BigInt[2, 4, 2, -3, -10])
 (2, 4, 2, -3, -10)
@@ -111,16 +111,16 @@ julia> m2 = F(BigInt[5, 7, -6, 9, -5])
 (5, 7, -6, 9, -5)
 
 julia> S3, f3 = sub(F, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 5 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 5 over integers)
 
 julia> D, f = direct_sum(S1, S2, S3)
-(DirectSumModule over integers, AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: submodule over Integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over Integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over Integers with 2 generators and no relations -> DirectSumModule over integers], AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: DirectSumModule over integers -> submodule over Integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over Integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over Integers with 2 generators and no relations])
+(DirectSumModule over integers, AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: submodule over integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over integers with 2 generators and no relations -> DirectSumModule over integers, Hom: submodule over integers with 2 generators and no relations -> DirectSumModule over integers], AbstractAlgebra.Generic.ModuleHomomorphism{BigInt}[Hom: DirectSumModule over integers -> submodule over integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over integers with 2 generators and no relations, Hom: DirectSumModule over integers -> submodule over integers with 2 generators and no relations])
 
 julia> summands(D)
 3-element Vector{AbstractAlgebra.Generic.Submodule{BigInt}}:
- Submodule over Integers with 2 generators and no relations
- Submodule over Integers with 2 generators and no relations
- Submodule over Integers with 2 generators and no relations
+ Submodule over integers with 2 generators and no relations
+ Submodule over integers with 2 generators and no relations
+ Submodule over integers with 2 generators and no relations
 ```
 
 

docs/src/free_associative_algebra.md

@@ -77,7 +77,7 @@ julia> R, (x, y, z) = free_associative_algebra(ZZ, ["x", "y", "z"])
 (Free associative algebra on 3 indeterminates over integers, AbstractAlgebra.Generic.FreeAssAlgElem{BigInt}[x, y, z])
 
 julia> B = MPolyBuildCtx(R)
-Builder for an element of Free associative algebra on 3 indeterminates over integers
+Builder for an element of free associative algebra
 
 julia> push_term!(B, ZZ(1), [1,2,3,1]); push_term!(B, ZZ(2), [3,3,1]); finish(B)
 x*y*z*x + 2*z^2*x

docs/src/function_field.md

@@ -242,7 +242,7 @@ julia> f = (x1^2 + 1)//(x1 + 1)*z1^3 + 4*z1 + 1//(x1 + 1)
 (x1^2 + 1)//(x1 + 1)*z1^3 + 4*z1 + 1//(x1 + 1)
 
 julia> S1, y1 = function_field(f, "y1")
-(Function Field over Rationals with defining polynomial (x1^2 + 1)*y1^3 + (4*x1 + 4)*y1 + 1, y1)
+(Function Field over rationals with defining polynomial (x1^2 + 1)*y1^3 + (4*x1 + 4)*y1 + 1, y1)
 
 julia> a = S1()
 0
@@ -263,7 +263,7 @@ julia> g = z2^2 + 3z2 + 1
 z2^2 + 3*z2 + 1
 
 julia> S2, y2 = function_field(g, "y2")
-(Function Field over Finite field F_23 with defining polynomial y2^2 + 3*y2 + 1, y2)
+(Function Field over finite field F_23 with defining polynomial y2^2 + 3*y2 + 1, y2)
 
 julia> d = S2(R2(5))
 5
@@ -291,7 +291,7 @@ julia> g = z^2 + 3z + 1
 z^2 + 3*z + 1
 
 julia> S, y = function_field(g, "y")
-(Function Field over Finite field F_23 with defining polynomial y^2 + 3*y + 1, y)
+(Function Field over finite field F_23 with defining polynomial y^2 + 3*y + 1, y)
 
 julia> f = (x + 1)*y + 1
 (x + 1)*y + 1
@@ -367,7 +367,7 @@ julia> g = z^2 + 3*(x + 1)//(x + 2)*z + 1
 z^2 + (3*x + 3)//(x + 2)*z + 1
 
 julia> S, y = function_field(g, "y")
-(Function Field over Rationals with defining polynomial (x + 2)*y^2 + (3*x + 3)*y + x + 2, y)
+(Function Field over rationals with defining polynomial (x + 2)*y^2 + (3*x + 3)*y + x + 2, y)
 
 julia> base_field(S)
 Rational function field
@@ -430,7 +430,7 @@ julia> g = z^2 + 3*(x + 1)//(x + 2)*z + 1
 z^2 + (3*x + 3)//(x + 2)*z + 1
 
 julia> S, y = function_field(g, "y")
-(Function Field over Rationals with defining polynomial (x + 2)*y^2 + (3*x + 3)*y + x + 2, y)
+(Function Field over rationals with defining polynomial (x + 2)*y^2 + (3*x + 3)*y + x + 2, y)
 
 julia> f = (-3*x - 5//3)//(x - 2)*y + (x^3 + 1//9*x^2 + 5)//(x - 2)
 ((-3*x - 5//3)*y + x^3 + 1//9*x^2 + 5)//(x - 2)

docs/src/module.md

@@ -226,10 +226,10 @@ julia> m2 = rand(M, -10:10)
 (4, 4, -7)
 
 julia> S, f = sub(M, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 3 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 3 over integers)
 
 julia> I, g = image(f)
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 3 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 3 over integers)
 
 julia> is_isomorphic(S, I)
 true
@@ -261,15 +261,15 @@ julia> m2 = rand(M, -10:10)
 (4, 4, -7)
 
 julia> S, f = sub(M, [m1, m2])
-(Submodule over Integers with 2 generators and no relations, Hom: submodule over Integers with 2 generators and no relations -> free module of rank 3 over integers)
+(Submodule over integers with 2 generators and no relations, Hom: submodule over integers with 2 generators and no relations -> free module of rank 3 over integers)
 
 julia> Q, g = quo(M, S)
-(Quotient module over Integers with 2 generators and relations:
-[16 -21], Hom: free module of rank 3 over integers -> quotient module over Integers with 2 generators and relations:
+(Quotient module over integers with 2 generators and relations:
+[16 -21], Hom: free module of rank 3 over integers -> quotient module over integers with 2 generators and relations:
 [16 -21])
 
 julia> I, f = snf(Q)
-(Invariant factor decomposed module over Integers with invariant factors BigInt[0], Hom: invariant factor decomposed module over Integers with invariant factors BigInt[0] -> quotient module over Integers with 2 generators and relations:
+(Invariant factor decomposed module over integers with invariant factors BigInt[0], Hom: invariant factor decomposed module over integers with invariant factors BigInt[0] -> quotient module over integers with 2 generators and relations:
 [16 -21])
 
 julia> invs = invariant_factors(Q)

docs/src/module_homomorphism.md

@@ -77,13 +77,13 @@ julia> m = M([ZZ(1), ZZ(2), ZZ(3)])
 (1, 2, 3)
 
 julia> S, f = sub(M, [m])
-(Submodule over Integers with 1 generator and no relations, Hom: submodule over Integers with 1 generator and no relations -> free module of rank 3 over integers)
+(Submodule over integers with 1 generator and no relations, Hom: submodule over integers with 1 generator and no relations -> free module of rank 3 over integers)
 
 julia> Q, g = quo(M, S)
-(Quotient module over Integers with 2 generators and no relations, Hom: free module of rank 3 over integers -> quotient module over Integers with 2 generators and no relations)
+(Quotient module over integers with 2 generators and no relations, Hom: free module of rank 3 over integers -> quotient module over integers with 2 generators and no relations)
 
 julia> kernel(g)
-(Submodule over Integers with 1 generator and no relations, Hom: submodule over Integers with 1 generator and no relations -> free module of rank 3 over integers)
+(Submodule over integers with 1 generator and no relations, Hom: submodule over integers with 1 generator and no relations -> free module of rank 3 over integers)
 
 ```
 

docs/src/mpolynomial.md

@@ -153,7 +153,7 @@ julia> R, (x, y) = polynomial_ring(ZZ, ["x", "y"])
 (Multivariate polynomial ring in 2 variables over integers, AbstractAlgebra.Generic.MPoly{BigInt}[x, y])
 
 julia> C = MPolyBuildCtx(R)
-Builder for an element of Multivariate polynomial ring in 2 variables over integers
+Builder for an element of multivariate polynomial ring
 
 julia> push_term!(C, ZZ(3), [1, 2]);
 

docs/src/ncpolynomial.md

@@ -69,13 +69,13 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 julia> U, z = R["z"]
-(Univariate polynomial ring in z over matrix ring of degree 2 over integers, z)
+(Univariate polynomial ring in z over matrix ring, z)
 
 julia> f = S()
 0
@@ -123,10 +123,10 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 julia> f = x^3 + 3x + 21
 x^3 + [3 0; 0 3]*x + [21 0; 0 21]
@@ -150,16 +150,16 @@ julia> n = length(g)
 3
 
 julia> U = base_ring(T)
-Univariate polynomial ring in x over matrix ring of degree 2 over integers
+Univariate polynomial ring in x over matrix ring
 
 julia> V = base_ring(y + 1)
-Univariate polynomial ring in x over matrix ring of degree 2 over integers
+Univariate polynomial ring in x over matrix ring
 
 julia> v = var(T)
 :y
 
 julia> U = parent(y + 1)
-Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers
+Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring
 
 julia> g == deepcopy(g)
 true
@@ -210,10 +210,10 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 julia> a = zero(T)
 0
@@ -268,10 +268,10 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 julia> f = x*y^2 + (x + 1)*y + 3
 x*y^2 + (x + 1)*y + [3 0; 0 3]
@@ -302,10 +302,10 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 julia> f = x*y^2 + (x + 1)*y + 3
 x*y^2 + (x + 1)*y + [3 0; 0 3]
@@ -336,10 +336,10 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 julia> f = x*y^2 + (x + 1)*y + 3
 x*y^2 + (x + 1)*y + [3 0; 0 3]
@@ -370,10 +370,10 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 
 julia> f = x*y^2 + (x + 1)*y + 3
@@ -404,10 +404,10 @@ Matrix ring of degree 2
   over integers
 
 julia> S, x = polynomial_ring(R, "x")
-(Univariate polynomial ring in x over matrix ring of degree 2 over integers, x)
+(Univariate polynomial ring in x over matrix ring, x)
 
 julia> T, y = polynomial_ring(S, "y")
-(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring of degree 2 over integers, y)
+(Univariate polynomial ring in y over univariate polynomial ring in x over matrix ring, y)
 
 julia> f = x*y^2 + (x + 1)*y + 3
 x*y^2 + (x + 1)*y + [3 0; 0 3]