# using IJulia
# notebook()

push!(LOAD_PATH, pwd())
using MaxPlus

set_tropical_display(0)

Base.show(io::IO, ::MIME"text/latex", x::MI) = show(io, MIME"text/plain", x)
Base.show(io::IO, ::MIME"text/latex", A::MIAbstractVecOrMat) = show(io, MIME"text/plain", A)

a = MI(1.0);  b = MI(3.5);  c = MI(5)
typeof(a), typeof(b), typeof(c)

a,   a.λ,   typeof(a),   typeof(a.λ)

c,   c.λ,   typeof(c),   typeof(c.λ)

a,   plustimes(a),   typeof(a),   typeof(plustimes(a))

a + a,   plustimes(a) + plustimes(a)

d = 1.0
typeof(d),   typeof(c),   typeof(c + d),   typeof((c + d).λ),   c + d

f = 1
typeof(f), typeof(c), typeof(c + f), typeof((c + f).λ),   c + f

MP(MI(4))

MI(MP(4))

MI(MP([4 5]))

# MI(4) + MP(4); as well as MI(4) * MP(4);

mi0, mi1, mitop, zero(MI), one(MI)

# Classic Julia-style display
set_tropical_display(0)

J = MI([+Inf 0; 0 +Inf])

# Display 0 as e
set_tropical_display(2)

J

# Display +Inf as ε
set_tropical_display(3)

J

# Display +Inf as ε and 0 as e
set_tropical_display(4)

J

# Display +Inf as a .
set_tropical_display(1)

J

a = MI(1); b = MI(3); c = MI(5);
(a, b, c)

a + b

a + b == b + a

a + b + c == (a + b) + c == a + (b + c)

a + b + c # ≜ min(a, b, c) == min(1, 3, 5)

a + mi0 == mi0 + a == a

a + mi0 == mi0 + a == a

(a, mi0), (a + mi0), (mi0 + a)

a + 0 == 0 + a == a

a, 0, a + 0

a + a    # ≜ min(a, a) == min(1, 1) == 1

a * b    # ≜ a + b == 1 + 3 == 4

a * b == b * a

a * b * c == (a * b) * c == a * (b * c)

a * b * c

a * mie == mie * a == a

a * mi1 == mi1 * a == a

a * mi0 == mi0 * a == mi0

a * mi0 == mi0 * a == mi0

mitop * mi0

a * a    # ≜ a + a == 1 + 1 == 2

(a + b) * c == (a * c) + (b * c)     # => min(a, b) + c == min(a + c, b + c) 

(a * c) + (b * c)

MI(2)^5   # ==> 2 * 5

MI(2)^0   # ==> 2 * 0

MI(2)^-1   # ==> 2 * -1

inv(MI(2))

MI(1:5)

MI(1:0.5:3)

[MI(1) 2; 3.5 4.0]

MI([1 2; 3 4])

f = 3; a = MI(1)
[f       a
 f + f   a + a]

[mi0 2; 3.5 4]

using SparseArrays;
set_tropical_display(0);

S = MI(sparse([1 2; 0 4]))

S = sparse(MI([1 2; +Inf 4]))

i,j,d = findnz(S)

S = MI(sparse([1; 2; 3], [1; 2; 3], [42; 0; 5]))

S = sparse([1; 2; 3], [1; 2; 3], MI([42; +Inf; 5]))

S = MI([1; 2; 3], [1; 2; 3], MI([0; +Inf; 5]))

A = MI([4 0; 7 +Inf])
plustimes(A)

Z = spzeros(MI,2,2)

plustimes(Z)

Matrix(plustimes(Z))

full(Z),  dense(Z),   Matrix(Z)

sparsevec([1, 3], MI([0, -Inf]))

MI(sparsevec([1, 3], [0, -Inf]))

MI([1, 3], [0, -Inf])

using LinearAlgebra
I

Matrix{MI}(I, 2, 2)

miI

Matrix(miI, 2, 2)

Matrix(miI, 2, 2) == eye(MI,2,2),   Matrix{MI}(I, 2, 2) == eye(MI,2,2)

J = eye(MI,2,2)

J = eye(MI,2) # Equivalent to eye(MI, 2,2)

J = eye(MI,3,2)

A = MI([1.0 -Inf; 0.0 4])
J = eye(A)

O = ones(MI,2,2)

O = ones(MI,2) # /!\ N'est pas équivalent à ones(MI,2,2) /!\

A = MI([1.0 -Inf; 0.0 4])
J = ones(A)

Z = zeros(MI,2,2)

Z = zeros(MI,2,3)

Z = zeros(MI,2)

Z = spzeros(MI,2,2)

Z = spzeros(MI,2,3)

Z = spzeros(MI,2)

Z = full(zeros(MI,2,2))

diagm(MP([1,2,3]))

spdiagm(MP([1,2,3]))

A = MI([2; 8])

4 .+ A

A .+ 4.0

4 .* A

A .* 4.0

MI([1 6; 8 3]) + MI([2 5; 3 3])

A = MI([4 3; 7 +Inf])
A * A

A * A == A^2

A = MI([4 3; 7 +Inf])
sparse(A)

A * sparse(A) == sparse(A) * A == sparse(A) * sparse(A)

A^5

A^0

MI([2 0; mi0 5]) * MI([2; 8])

MI([2 8]) * MI([2 0; mi0 5])

A = MI([4 3; 7 +Inf])
A * eye(MI, 2,2) == eye(MI, 2,2) * A == A

A * zeros(MI, 2,2) == zeros(MI, 2,2) * A == zeros(MI, 2,2)

A + zeros(MI, 2,2) == zeros(MI, 2,2) + A == A

set_tropical_display(0)
LaTeX(stdout, eye(MI, 2,2))

set_tropical_display(2)
LaTeX(stdout, eye(MI, 2,2))

set_tropical_display(1)
LaTeX(stdout, zeros(MI, 2,2))