Merge pull request #455 from SciML/zeroone

fix tutorial by covering the other zero/one dispatches

Author: ChrisRackauckas

src/ModelingToolkit.jl

@@ -40,7 +40,11 @@ abstract type AbstractODESystem <: AbstractSystem end
 
 Base.promote_rule(::Type{<:Number},::Type{<:Expression}) = Expression
 Base.zero(::Type{<:Expression}) = Constant(0)
+Base.zero(::Expression) = Constant(0)
 Base.one(::Type{<:Expression}) = Constant(1)
+Base.one(::Expression) = Constant(1)
+Base.oneunit(::Expression) = Constant(1)
+Base.oneunit(::Type{<:Expression}) = Constant(1)
 
 """
 $(TYPEDSIGNATURES)

test/operation_overloads.jl

@@ -32,3 +32,17 @@ C = sparse([1, 2], [2, 1], [c, c])
 D = sparse([1, 2], [2, 1], [d, d])
 
 @test isequal(C * D, sparse([1,2], [1,2], [c * d, c * d]))
+
+@parameters t σ ρ β
+@variables x(t) y(t) z(t)
+@derivatives D'~t Dx'~x Dy'~y Dz'~z
+eqs = [D(x) ~ σ*(y-x),
+       D(y) ~ x*(ρ-z)-y,
+       D(z) ~ x*y - β*z]
+J = [Dx(eqs[1].rhs) Dy(eqs[1].rhs) Dz(eqs[1].rhs)
+ Dx(eqs[2].rhs) Dy(eqs[2].rhs) Dz(eqs[2].rhs)
+ Dx(eqs[3].rhs) Dy(eqs[3].rhs) Dz(eqs[3].rhs)]
+
+J = expand_derivatives.(J)
+using LinearAlgebra
+luJ = lu(J,Val(false))