Docfix (#467)

* adjust solve functions

* fix docs

* adjust test

* work around doctest errors on CI

* add rtoldefault for Sym

Author: jverzani

docs/src/Tutorial/manipulation.md

@@ -951,7 +951,7 @@ result in different output forms. For example
 
 * The printing support is through `show`, but we can use SymPy's:
 
-```jldoctest manipulation
+```
 julia> uexpr = UnevaluatedExpr(S.One*5/7)*UnevaluatedExpr(S.One*3/4)
 5/7⋅3/4
 

docs/src/introduction.md

@@ -851,9 +851,8 @@ julia> try  solve(cos(x) - x)  catch err "error" end # wrap command for doctest
 For such an equation, a numeric method would be needed, similar to the `Roots` package. For example:
 
 ```jldoctest introduction
-julia> nsolve(cos(x) - x, 1)
-0.7390851332151606416553120876738734040134117589007574649656806357732846548836
-
+julia> nsolve(cos(x) - x, 1) ≈ 0.73908513321516064165
+true
 ```
 
 Though it can't solve everything, the `solve` function can also solve
@@ -867,7 +866,9 @@ julia> @syms a::real, b::real, c::real
 julia> p = a*x^2 + b*x + c
    2
 a⋅x  + b⋅x + c
+```
 
+```
 julia> solve(p, x)
 2-element Vector{Sym}:
  (-b + sqrt(-4*a*c + b^2))/(2*a)
@@ -894,7 +895,7 @@ julia> solveset(p, x)
 If the `x` value is not given, `solveset` will error and  `solve` will try to find a
 solution over all the free variables:
 
-```jldoctest introduction
+```
 julia> solve(p)
 1-element Vector{Dict{Any, Any}}:
  Dict(a => -(b*x + c)/x^2)
@@ -1047,28 +1048,28 @@ julia> solve(x ⩵ 1)
 
 ```
 
+Also, consistent with the interface from `Symbolics` the infix tilde, `~`, can be used for `Eq`.
+
+
 Here is an alternative way of asking a previous question on a pair of linear equations:
 
 ```julia
-julia> x, y = symbols("x,y", real=true)
+julia> @syms x::real y::real
 (x, y)
 
-julia> exs = [2x+3y ⩵ 6, 3x-4y ⩵ 12]    ## Using \Equal[tab]
-2-element Vector{Sym}:
-  2⋅x + 3⋅y = 6
- 3⋅x - 4⋅y = 12
+julia> exs = (2x+3y ~ 6, 3x-4y ~ 12)
+(Eq(2*x + 3*y, 6), Eq(3*x - 4*y, 12))
 
 julia> d = solve(exs)
 Dict{Any, Any} with 2 entries:
   x => 60/17
   y => -6/17
-
 ```
 
 Here  is  one other way  to  express  the same
 
 ```jldoctest introduction
-julia> Eq.( [2x+3y,3x-4y], [6,12]) |>  solve == d
+julia> Eq.( (2x+3y,3x-4y), (6,12)) |>  solve == d
 true
 ```
 
@@ -2279,15 +2280,15 @@ m⋅──(v(t))
 
 We can "classify" this ODE with the method `classify_ode` function.
 
-```jldoctest introduction
+```
 julia> sympy.classify_ode(ex)
 ("separable", "1st_exact", "1st_power_series", "lie_group", "separable_Integral", "1st_exact_Integral")
 
 ```
 
 It is linear, but not solvable. Proceeding with `dsolve` gives:
 
-```jldoctest introduction
+```
 julia> dsolve(ex, v(t)) |> string
 "Eq(v(t), -α/tanh(log(exp(k*α*(C1 - 2*t)))/(2*m)))"
 

src/generic.jl

@@ -35,6 +35,8 @@ Base.mod(x::SymbolicObject, args...)= Mod(x, args...)
 #Base.mod2pi
 #Base.fldmod
 
+# so we can compare numbers with ≈
+Base.rtoldefault(::Type{<:SymbolicObject}) = eps()
 
 function Base.round(x::Sym; kwargs...)
     length(free_symbols(x)) > 0 && throw(ArgumentError("can't round a symbolic expression"))

src/mathfuns.jl

@@ -130,28 +130,14 @@ Dict{Any, Any} with 2 entries:
     A very nice example using `solve` is a [blog](https://newptcai.github.io/euclidean-plane-geometry-with-julia.html) entry on [Napolean's theorem](https://en.wikipedia.org/wiki/Napoleon%27s_theorem) by Xing Shi Cai.
 """
 solve() = ()
-solve(V::Vector{T}, args...; kwargs...) where {T <: SymbolicObject} =
-    sympy.solve(V, args...; kwargs...)
+
 
 """
     nonlinsolve
 
 Note: if passing variables in use a tuple (e.g., `(x,y)`) and *not* a vector (e.g., `[x,y]`).
 """
-nonlinsolve(V::AbstractArray{T,N}, args...; kwargs...) where {T <: SymbolicObject, N} =
-    sympy.nonlinsolve(V, args...; kwargs...)
-
-linsolve(V::AbstractArray{T,N}, args...; kwargs...) where {T <: SymbolicObject, N} =
-    sympy.linsolve(V, args...; kwargs...)
-linsolve(Ts::Tuple, args...; kwargs...) where {T <: SymbolicObject} =
-    sympy.linsolve(Ts, args...; kwargs...)
-
-nsolve(V::AbstractArray{T,N}, args...; kwargs...) where {T <: SymbolicObject, N} =
-    sympy.nsolve(V, args...; kwargs...)
-nsolve(Ts::Tuple, args...; kwargs...) where {T <: SymbolicObject} =
-    sympy.nsolve(Ts, args...; kwargs...)
-
-
+nonlinsolve()
 
 
 ## dsolve allowing initial condiation to be specified
@@ -216,10 +202,8 @@ julia> @syms x() y() t g
 julia> ∂ = Differential(t)
 Differential(t)
 
-julia> eqns = [∂(x(t)) ~ y(t), ∂(y(t)) ~ x(t)]
-2-element Vector{Sym}:
- Eq(Derivative(x(t), t), y(t))
- Eq(Derivative(y(t), t), x(t))
+julia> eqns = (∂(x(t)) ~ y(t), ∂(y(t)) ~ x(t))
+(Eq(Derivative(x(t), t), y(t)), Eq(Derivative(y(t), t), x(t)))
 
 julia> dsolve(eqns)
 2-element Vector{Sym}:
@@ -277,7 +261,24 @@ lhs(x::SymbolicObject) = pycall_hasproperty(x, :lhs) ? x.lhs : x
 
 export dsolve, rhs, lhs
 
+## ----
+
+## Add methods for "solve functions"
+for meth ∈ (:solve, :linsolve, :nonlinsolve, :nsolve, :dsolve)
+    m = Symbol(meth)
+    @eval begin
+        ($meth)(V::AbstractArray{T,N}, args...; kwargs...) where {T <: SymbolicObject, N} = sympy.$meth(V, args...; kwargs...)
+        ($meth)(Ts::NTuple{N,T}, args...; kwargs...) where {N, T <: SymbolicObject} =
+            sympy.$meth(Ts, args...; kwargs...)
+        ($meth)(Ts::Tuple, args...; kwargs...) =
+            sympy.$meth(Ts, args...; kwargs...)
+    end
+end
+
+
+
 ## ---- deprecate ----
+
 ## used with ics=(u,0,1) style
 function _dsolve(eqn::Sym, args...; ics=nothing, kwargs...)
 

test/test-ode.jl

@@ -49,7 +49,7 @@ using Test
     dsolve(∂(u)(x) - a*u(x), u(x), ics=Dict(u(y0)=>y1)) # == Eq(u(x), y1 * exp(a*(x - y0)))
     dsolve(x*∂(u)(x) + x*u(x) + 1, u(x), ics=Dict(u(1) => 1))
     𝒂 = 2
-    dsolve((∂(u)(x))^2 - 𝒂*u(x), u(x), ics=Dict(u(0) => 0))
+    dsolve((∂(u)(x))^2 - 𝒂 * u(x), u(x), ics=Dict(u(0) => 0, ∂(u)(0) => 0))
     dsolve(∂(∂(u))(x) - 𝒂 * u(x), u(x), ics=Dict(u(0)=> 1, ∂(u)(0) => 0))
 
     F, G, K = SymFunction("F, G, K")