generalize symbolics (#18)

* generalize symbolic derivative frameworks

* test SymEngine.jl, SymPy.jl, and Symbolics.jl

* use conda for CI

* make default compute_derivative empty

.github/workflows/CI.yml

@@ -27,7 +27,11 @@ jobs:
             ${{ runner.os }}-test-
             ${{ runner.os }}-
       - uses: julia-actions/julia-buildpkg@v1
+        env:
+          PYTHON: ""
       - uses: julia-actions/julia-runtest@v1
+        env:
+          PYTHON: ""
       - uses: julia-actions/julia-processcoverage@v1
       - uses: codecov/codecov-action@v1
         with:

Project.toml

@@ -7,20 +7,22 @@ version = "0.1.5-pre"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 OrderedCollections = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 RootedTrees = "47965b36-3f3e-11e9-0dcf-4570dfd42a8c"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
 [compat]
 OrderedCollections = "1"
 Reexport = "1"
+Requires = "1"
 RootedTrees = "2.1"
-Symbolics = "3"
 julia = "1"
 
 [extras]
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"
+SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["StaticArrays", "Symbolics", "Test"]
+test = ["StaticArrays", "SymEngine", "SymPy", "Symbolics", "Test"]

src/BSeries.jl

@@ -7,8 +7,7 @@ using RootedTrees: RootedTree
 
 @reexport using OrderedCollections: OrderedDict
 
-@reexport using Symbolics: Symbolics, Num
-using Symbolics: Differential, expand_derivatives
+using Requires: @require
 
 
 export bseries, substitute, compose
@@ -26,6 +25,47 @@ export elementary_differentials
 end
 
 
+"""
+    compute_derivative(expression, variable)
+
+Internal function specialized on symbolic variables and expressions from
+
+- [SymEngine.jl](https://github.com/symengine/SymEngine.jl),
+- [SymPy.jl](https://github.com/JuliaPy/SymPy.jl), and
+- [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl)
+
+if these packages are loaded (via Requires.jl).
+"""
+function compute_derivative end
+
+function __init__()
+  @require SymEngine="123dc426-2d89-5057-bbad-38513e3affd8" begin
+    using .SymEngine: SymEngine
+
+    function compute_derivative(expression::SymEngine.Basic, variable::SymEngine.Basic)
+      SymEngine.diff(expression, variable)
+    end
+  end
+
+  @require SymPy="24249f21-da20-56a4-8eb1-6a02cf4ae2e6" begin
+    using .SymPy: SymPy
+
+    function compute_derivative(expression::SymPy.Sym, variable::SymPy.Sym)
+      SymPy.diff(expression, variable)
+    end
+  end
+
+  @require Symbolics="0c5d862f-8b57-4792-8d23-62f2024744c7" begin
+    using .Symbolics: Symbolics
+
+    function compute_derivative(expression::Symbolics.Num, variable::Symbolics.Num)
+      Symbolics.expand_derivatives(Symbolics.Differential(variable)(expression))
+    end
+  end
+end
+
+
+
 """
     substitute(b, a, t::RootedTree)
 
@@ -103,7 +143,7 @@ end
 
 
 """
-    ExactSolution{T}
+    ExactSolution{T}()
 
 Lazy representation of the B-series of the exact solution of an ordinary
 differential equation using coefficients of type at least as representative as
@@ -200,8 +240,15 @@ Butcher coefficients `A, b, c` up to the prescribed `order` with respect to
 the ordinary differential equation ``u'(t) = f(u(t))`` with vector field `f`
 and dependent variables `u` for a time step size `dt`.
 
-Here, `u` is assumed to be a vector of variables from Symbolics.jl (`Symbolics.Num`)
-and `f` is assumed to be a vector of expressions in these variables.
+Here, `u` is assumed to be a vector of symbolic variables and `f` is assumed
+to be a vector of expressions in these variables. Currently, symbolic variables
+from
+
+- [SymEngine.jl](https://github.com/symengine/SymEngine.jl),
+- [SymPy.jl](https://github.com/JuliaPy/SymPy.jl), and
+- [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl)
+
+are supported.
 
 # References
 
@@ -290,8 +337,15 @@ method with Butcher coefficients `A, b, c` up to the prescribed `order` with
 respect to the ordinary differential equation ``u'(t) = f(u(t))`` with vector
 field `f` and dependent variables `u` for a time step size `dt`.
 
-Here, `u` is assumed to be a vector of variables from Symbolics.jl (`Symbolics.Num`)
-and `f` is assumed to be a vector of expressions in these variables.
+Here, `u` is assumed to be a vector of symbolic variables and `f` is assumed
+to be a vector of expressions in these variables. Currently, symbolic variables
+from
+
+- [SymEngine.jl](https://github.com/symengine/SymEngine.jl),
+- [SymPy.jl](https://github.com/JuliaPy/SymPy.jl), and
+- [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl)
+
+are supported.
 
 # References
 
@@ -364,14 +418,14 @@ function _compute_partial_derivatives!(d, f, u, lower_derivatives)
     #   f_idx = first(idx_tuple)
     #   partial_derivative = f[f_idx]
     #   for i in u_idx
-    #     partial_derivative = Differential(u[i])(partial_derivative)
+    #     partial_derivative = compute_derivative(partial_derivative, u[i])
     #   end
     # but we re-use the already computed `lower_derivatives`.
     idx_known = Base.front(idx_tuple)
     idx_new = last(idx_tuple)
-    partial_derivative = Differential(u[idx_new])(lower_derivatives[idx_known...])
+    partial_derivative = compute_derivative(lower_derivatives[idx_known...], u[idx_new])
 
-    d[idx] = expand_derivatives(partial_derivative)
+    d[idx] = partial_derivative
   end
 end