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When printing matrices, replace zeros by dots #1459

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144 changes: 72 additions & 72 deletions docs/src/matrix.md
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Original file line number Diff line number Diff line change
Expand Up @@ -87,19 +87,19 @@ Matrix space of 3 rows and 3 columns
over univariate polynomial ring in t over rationals

julia> A = S()
[0 0 0]
[0 0 0]
[0 0 0]
[. . .]
[. . .]
[. . .]

julia> B = S(12)
[12 0 0]
[ 0 12 0]
[ 0 0 12]
[12 . .]
[ . 12 .]
[ . . 12]

julia> C = S(R(11))
[11 0 0]
[ 0 11 0]
[ 0 0 11]
[11 . .]
[ . 11 .]
[ . . 11]

```

Expand Down Expand Up @@ -155,23 +155,23 @@ Matrix ring of degree 2

julia> M1 = S(Rational{BigInt}[2 3 1; 1 0 4])
[2//1 3//1 1//1]
[1//1 0//1 4//1]
[1//1 . 4//1]

julia> M2 = S(BigInt[2 3 1; 1 0 4])
[2//1 3//1 1//1]
[1//1 0//1 4//1]
[1//1 . 4//1]

julia> M3 = S(BigInt[2, 3, 1, 1, 0, 4])
[2//1 3//1 1//1]
[1//1 0//1 4//1]
[1//1 . 4//1]

julia> N1 = T(Rational{BigInt}[2 3; 1 0])
[2//1 3//1]
[1//1 0//1]
[1//1 .]

julia> N2 = T(BigInt[2 3; 1 0])
[2//1 3//1]
[1//1 0//1]
[1//1 .]

julia> N3 = T(BigInt[2, 3, 1, 1])
[2//1 3//1]
Expand All @@ -186,7 +186,7 @@ Matrix space of 3 rows and 3 columns

julia> M = R[t + 1 1; t^2 0]
[t + 1 1]
[ t^2 0]
[ t^2 .]

julia> N = R[t + 1 2 t] # create a row vector
[t + 1 2 t]
Expand Down Expand Up @@ -228,25 +228,25 @@ Construct the $r\times c$ AbstractAlgebra.jl zero matrix over the ring `R`.
```jldoctest
julia> M = matrix(ZZ, BigInt[3 1 2; 2 0 1])
[3 1 2]
[2 0 1]
[2 . 1]

julia> N = matrix(ZZ, 3, 2, BigInt[3, 1, 2, 2, 0, 1])
[3 1]
[2 2]
[0 1]
[. 1]

julia> P = zero_matrix(ZZ, 3, 2)
[0 0]
[0 0]
[0 0]
[. .]
[. .]
[. .]

julia> R = matrix_ring(ZZ, 2)
Matrix ring of degree 2
over integers

julia> M = R()
[0 0]
[0 0]
[. .]
[. .]
```

## Block diagonal matrix constructors
Expand All @@ -267,10 +267,10 @@ block_diagonal_matrix(::Ring, ::Vector{<:Matrix{T}}) where T <: RingElement

```jldoctest
julia> block_diagonal_matrix(ZZ, [[1 2; 3 4], [4 5 6; 7 8 9]])
[1 2 0 0 0]
[3 4 0 0 0]
[0 0 4 5 6]
[0 0 7 8 9]
[1 2 . . .]
[3 4 . . .]
[. . 4 5 6]
[. . 7 8 9]

julia> M = matrix(ZZ, [1 2; 3 4])
[1 2]
Expand All @@ -281,10 +281,10 @@ julia> N = matrix(ZZ, [4 5 6; 7 8 9])
[7 8 9]

julia> block_diagonal_matrix([M, N])
[1 2 0 0 0]
[3 4 0 0 0]
[0 0 4 5 6]
[0 0 7 8 9]
[1 2 . . .]
[3 4 . . .]
[. . 4 5 6]
[. . 7 8 9]
```

## Conversion to Julia matrices, iteration and broacasting
Expand Down Expand Up @@ -554,7 +554,7 @@ julia> Z = divexact(2*A, 2)
[ -2 t + 2 t^2 + t + 1]

julia> M = matrix(ZZ, BigInt[2 3 0; 1 1 1])
[2 3 0]
[2 3 .]
[1 1 1]

julia> M[1, 2] = BigInt(4)
Expand Down Expand Up @@ -685,22 +685,22 @@ julia> M = matrix(ZZ, BigInt[1 2 3; 2 3 4; 3 4 5])
[3 4 5]

julia> N = matrix(ZZ, BigInt[1 0 1; 0 1 0; 1 0 1])
[1 0 1]
[0 1 0]
[1 0 1]
[1 . 1]
[. 1 .]
[1 . 1]

julia> P = hcat(M, N)
[1 2 3 1 0 1]
[2 3 4 0 1 0]
[3 4 5 1 0 1]
[1 2 3 1 . 1]
[2 3 4 . 1 .]
[3 4 5 1 . 1]

julia> Q = vcat(M, N)
[1 2 3]
[2 3 4]
[3 4 5]
[1 0 1]
[0 1 0]
[1 0 1]
[1 . 1]
[. 1 .]
[1 . 1]

```

Expand Down Expand Up @@ -740,7 +740,7 @@ Test whether the given matrix has a value associated with indices `i` and `j`.
```jldoctest
julia> M = matrix(ZZ, BigInt[3 1 2; 2 0 1])
[3 1 2]
[2 0 1]
[2 . 1]

julia> isassigned(M, 1, 2)
true
Expand All @@ -756,8 +756,8 @@ julia> isassigned(A, 1, 2)
false

julia> B = zero(M)
[0 0 0]
[0 0 0]
[. . .]
[. . .]

julia> C = similar(M, 4, 5)
[#undef #undef #undef #undef #undef]
Expand All @@ -769,8 +769,8 @@ julia> base_ring(B)
Integers

julia> D = zero(M, QQ, 2, 2)
[0//1 0//1]
[0//1 0//1]
[. .]
[. .]

julia> base_ring(D)
Rationals
Expand Down Expand Up @@ -839,7 +839,7 @@ Matrix space of 3 rows and 3 columns
over residue field of univariate polynomial ring modulo x^3 + 3*x + 1

julia> A = S([K(0) 2a + 3 a^2 + 1; a^2 - 2 a - 1 2a; a^2 - 2 a - 1 2a])
[ 0 2*x + 3 x^2 + 1]
[ . 2*x + 3 x^2 + 1]
[x^2 - 2 x - 1 2*x]
[x^2 - 2 x - 1 2*x]

Expand Down Expand Up @@ -876,7 +876,7 @@ Matrix space of 3 rows and 3 columns
over residue field of univariate polynomial ring modulo x^3 + 3*x + 1

julia> M = S([K(0) 2a + 3 a^2 + 1; a^2 - 2 a - 1 2a; a^2 + 3a + 1 2a K(1)])
[ 0 2*x + 3 x^2 + 1]
[ . 2*x + 3 x^2 + 1]
[ x^2 - 2 x - 1 2*x]
[x^2 + 3*x + 1 2*x 1]

Expand All @@ -894,7 +894,7 @@ Matrix space of 3 rows and 3 columns
over univariate polynomial ring in x over integers

julia> M = S([R(0) 2x + 3 x^2 + 1; x^2 - 2 x - 1 2x; x^2 + 3x + 1 2x R(1)])
[ 0 2*x + 3 x^2 + 1]
[ . 2*x + 3 x^2 + 1]
[ x^2 - 2 x - 1 2*x]
[x^2 + 3*x + 1 2*x 1]

Expand Down Expand Up @@ -949,10 +949,10 @@ julia> R, x = polynomial_ring(QQ, ["x$i" for i in 1:6])
(Multivariate polynomial ring in 6 variables over rationals, AbstractAlgebra.Generic.MPoly{Rational{BigInt}}[x1, x2, x3, x4, x5, x6])

julia> M = R[0 x[1] x[2] x[3]; -x[1] 0 x[4] x[5]; -x[2] -x[4] 0 x[6]; -x[3] -x[5] -x[6] 0]
[ 0 x1 x2 x3]
[-x1 0 x4 x5]
[-x2 -x4 0 x6]
[-x3 -x5 -x6 0]
[ . x1 x2 x3]
[-x1 . x4 x5]
[-x2 -x4 . x6]
[-x3 -x5 -x6 .]

julia> pfaffian(M)
x1*x6 - x2*x5 + x3*x4
Expand Down Expand Up @@ -999,7 +999,7 @@ Matrix space of 3 rows and 3 columns
over residue field of univariate polynomial ring modulo x^3 + 3*x + 1

julia> A = S([K(0) 2a + 3 a^2 + 1; a^2 - 2 a - 1 2a; a^2 + 3a + 1 2a K(1)])
[ 0 2*x + 3 x^2 + 1]
[ . 2*x + 3 x^2 + 1]
[ x^2 - 2 x - 1 2*x]
[x^2 + 3*x + 1 2*x 1]

Expand All @@ -1022,7 +1022,7 @@ Matrix space of 3 rows and 3 columns
over univariate polynomial ring in x over integers

julia> A = S([R(0) 2x + 3 x^2 + 1; x^2 - 2 x - 1 2x; x^2 + 3x + 1 2x R(1)])
[ 0 2*x + 3 x^2 + 1]
[ . 2*x + 3 x^2 + 1]
[ x^2 - 2 x - 1 2*x]
[x^2 + 3*x + 1 2*x 1]

Expand Down Expand Up @@ -1059,15 +1059,15 @@ Matrix space of 4 rows and 4 columns
julia> M = S([R(1) R(2) R(4) R(3); R(2) R(5) R(1) R(0);
R(6) R(1) R(3) R(2); R(1) R(1) R(3) R(5)])
[1 2 4 3]
[2 5 1 0]
[2 5 1 .]
[6 1 3 2]
[1 1 3 5]

julia> A = hessenberg(M)
[1 5 5 3]
[2 1 1 0]
[0 1 3 2]
[0 0 2 2]
[2 1 1 .]
[. 1 3 2]
[. . 2 2]

julia> is_hessenberg(A)
true
Expand Down Expand Up @@ -1112,9 +1112,9 @@ julia> A = matrix(ZZ, [2 3 -1; 3 5 7; 11 1 12])
[11 1 12]

julia> H = hnf(A)
[1 0 255]
[0 1 17]
[0 0 281]
[1 . 255]
[. 1 17]
[. . 281]

julia> is_hnf(H)
true
Expand All @@ -1123,9 +1123,9 @@ julia> H, U = hnf_with_transform(A)
([1 0 255; 0 1 17; 0 0 281], [-47 28 1; -3 2 0; -52 31 1])

julia> U*A
[1 0 255]
[0 1 17]
[0 0 281]
[1 . 255]
[. 1 17]
[. . 281]
```

### Smith normal form
Expand All @@ -1148,17 +1148,17 @@ julia> A = matrix(ZZ, [2 3 -1; 3 5 7; 11 1 12])
[11 1 12]

julia> S = snf(A)
[1 0 0]
[0 1 0]
[0 0 281]
[1 . .]
[. 1 .]
[. . 281]

julia> S, T, U = snf_with_transform(A)
([1 0 0; 0 1 0; 0 0 281], [1 0 0; 7 1 0; 229 31 1], [0 -3 26; 0 2 -17; -1 0 1])

julia> T*A*U
[1 0 0]
[0 1 0]
[0 0 281]
[1 . .]
[. 1 .]
[. . 281]
```

### (Weak) Popov form
Expand Down Expand Up @@ -1189,14 +1189,14 @@ julia> A = matrix(R, map(R, Any[1 2 3 x; x 2*x 3*x x^2; x x^2+1 x^3+x^2 x^4+x^2+

julia> P = weak_popov(A)
[ 1 2 3 x]
[ 0 0 0 0]
[ . . . .]
[-x^3 -2*x^3 + x^2 - 2*x + 1 -2*x^3 + x^2 - 3*x 1]

julia> P, U = weak_popov_with_transform(A)
([1 2 3 x; 0 0 0 0; -x^3 -2*x^3+x^2-2*x+1 -2*x^3+x^2-3*x 1], [1 0 0; -x 1 0; -x^3-x 0 1])

julia> U*A
[ 1 2 3 x]
[ 0 0 0 0]
[ . . . .]
[-x^3 -2*x^3 + x^2 - 2*x + 1 -2*x^3 + x^2 - 3*x 1]
```
18 changes: 9 additions & 9 deletions docs/src/matrix_algebras.md
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Original file line number Diff line number Diff line change
Expand Up @@ -80,19 +80,19 @@ Matrix ring of degree 3
over univariate polynomial ring in t over rationals

julia> A = S()
[0 0 0]
[0 0 0]
[0 0 0]
[. . .]
[. . .]
[. . .]

julia> B = S(12)
[12 0 0]
[ 0 12 0]
[ 0 0 12]
[12 . .]
[ . 12 .]
[ . . 12]

julia> C = S(R(11))
[11 0 0]
[ 0 11 0]
[ 0 0 11]
[11 . .]
[ . 11 .]
[ . . 11]

```

Expand Down
4 changes: 2 additions & 2 deletions docs/src/polynomial.md
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Original file line number Diff line number Diff line change
Expand Up @@ -898,8 +898,8 @@ julia> g = 6(x + 1)*y + (x^3 + 2x + 2)

julia> S = sylvester_matrix(f, g)
[ 3*x x + 1 3]
[6*x + 6 x^3 + 2*x + 2 0]
[ 0 6*x + 6 x^3 + 2*x + 2]
[6*x + 6 x^3 + 2*x + 2 .]
[ . 6*x + 6 x^3 + 2*x + 2]

julia> h = resultant(f, g)
3*x^7 + 6*x^5 - 6*x^3 + 96*x^2 + 192*x + 96
Expand Down
4 changes: 2 additions & 2 deletions src/FreeAssociativeAlgebra.jl
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Expand Up @@ -178,8 +178,8 @@ julia> m1 = S([1 2; 3 4])
[3 4]

julia> m2 = S([0 1; 1 0])
[0 1]
[1 0]
[. 1]
[1 .]

julia> evaluate(f, [m1, m2])
[-1 -3]
Expand Down
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