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Print base rings terse and starting with lowercase #1680

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Apr 25, 2024
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Print base rings terse and starting with lowercase #1680

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28e3275
Print base rings terse and starting with lowercase
fingolfin Apr 24, 2024
a139a12
Align printing of 'quotient space' with 'quotient module'
fingolfin Apr 25, 2024
a6e92a4
Update doctests
fingolfin Apr 24, 2024
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22 changes: 11 additions & 11 deletions docs/src/direct_sum.md
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Original file line number Diff line number Diff line change
Expand Up @@ -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)
Expand All @@ -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)
Expand All @@ -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
Expand All @@ -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)
Expand All @@ -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)
Expand All @@ -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
```


Expand Down
2 changes: 1 addition & 1 deletion docs/src/free_associative_algebra.md
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Expand Up @@ -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
Expand Down
10 changes: 5 additions & 5 deletions docs/src/function_field.md
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Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand All @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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)
Expand Down
12 changes: 6 additions & 6 deletions docs/src/module.md
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Expand Up @@ -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
Expand Down Expand Up @@ -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)
Expand Down
6 changes: 3 additions & 3 deletions docs/src/module_homomorphism.md
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Expand Up @@ -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)

```

Expand Down
2 changes: 1 addition & 1 deletion docs/src/mpolynomial.md
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Expand Up @@ -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]);

Expand Down
40 changes: 20 additions & 20 deletions docs/src/ncpolynomial.md
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Expand Up @@ -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
Expand Down Expand Up @@ -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]
Expand All @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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]
Expand Down Expand Up @@ -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]
Expand Down Expand Up @@ -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]
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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]
Expand Down
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