More Num wraps and small fixes

Author: YingboMa

src/ModelingToolkit.jl

@@ -152,13 +152,13 @@ end
 tosymbolic(a::Num) = tosymbolic(value(a))
 tosymbolic(a::Sym) = tovar(a)
 tosymbolic(a) = a
-@num_method Base.isless isless(tosymbolic(a), tosymbolic(b)) (Real,)
-@num_method Base.:(<) (tosymbolic(a) < tosymbolic(b)) (Real,)
-@num_method Base.:(<=) (tosymbolic(a) <= tosymbolic(b)) (Real,)
-@num_method Base.:(>) (tosymbolic(a) > tosymbolic(b)) (Real,)
-@num_method Base.:(>=) (tosymbolic(a) >= tosymbolic(b)) (Real,)
-@num_method Base.isequal isequal(tosymbolic(a), tosymbolic(b)) (AbstractFloat, Number, Symbolic)
-@num_method Base.:(==) tosymbolic(a) == tosymbolic(b) (AbstractFloat,Number)
+@num_method Base.isless  Num(isless(tosymbolic(a), tosymbolic(b))) (Real,)
+@num_method Base.:(<)    Num(tosymbolic(a) < tosymbolic(b)) (Real,)
+@num_method Base.:(<=)   Num(tosymbolic(a) <= tosymbolic(b)) (Real,)
+@num_method Base.:(>)    Num(tosymbolic(a) > tosymbolic(b)) (Real,)
+@num_method Base.:(>=)   Num(tosymbolic(a) >= tosymbolic(b)) (Real,)
+@num_method Base.isequal Num(isequal(tosymbolic(a), tosymbolic(b))) (AbstractFloat, Number, Symbolic)
+@num_method Base.:(==)   Num(tosymbolic(a) == tosymbolic(b)) (AbstractFloat,Number)
 
 Base.hash(x::Num, h::UInt) = hash(value(x), h)
 

src/extra_functions.jl

@@ -22,7 +22,7 @@ function ModelingToolkit.derivative(::typeof(max), args::NTuple{2,Any}, ::Val{2}
     IfElse.ifelse(x > y, zero(y), one(y))
 end
 
-@register IfElse.ifelse(x,y,z::Any)
+IfElse.ifelse(x::Num,y,z) = Num(Term{Real}(IfElse.ifelse, [value(x), value(y), value(z)]))
 ModelingToolkit.derivative(::typeof(IfElse.ifelse), args::NTuple{3,Any}, ::Val{1}) = 0
 ModelingToolkit.derivative(::typeof(IfElse.ifelse), args::NTuple{3,Any}, ::Val{2}) = IfElse.ifelse(args[1],1,0)
 ModelingToolkit.derivative(::typeof(IfElse.ifelse), args::NTuple{3,Any}, ::Val{3}) = IfElse.ifelse(args[1],0,1)

src/solve.jl

@@ -84,6 +84,7 @@ Currently only works if all equations are linear.
 """
 function solve_for(eqs, vars)
     A, b = A_b(eqs, vars)
+    #TODO: we need to make sure that `solve_for(eqs, vars)` contains no `vars`
     _solve(A, b)
 end
 

src/systems/diffeqs/odesystem.jl

@@ -138,6 +138,7 @@ function ODESystem(eqs, iv=nothing; kwargs...)
             end
         end
     end
+    iv = value(iv)
     iv === nothing && throw(ArgumentError("Please pass in independent variables."))
     for eq in eqs
         collect_vars!(allstates, ps, eq.lhs, iv)