symbolic division by h and latexify (#72)

* test symbolic division by h and latexify

* symbolic division by h in tutorial

* set version to v0.1.30

* format

Project.toml

@@ -1,7 +1,7 @@
 name = "BSeries"
 uuid = "ebb8d67c-85b4-416c-b05f-5f409e808f32"
 authors = ["Hendrik Ranocha <[email protected]> and contributors"]
-version = "0.1.29"
+version = "0.1.30"
 
 [deps]
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"

docs/src/tutorials/symbolic_computations.md

@@ -69,6 +69,22 @@ using Latexify
 latexify(series, reduce_order_by=1, dt=SymEngine.symbols("h"), cdot=false) |> println
 ```
 
+The argument `dt=SymEngine.symbols("h")` is not required here.
+
+```@example modified-equation-symengine
+using Latexify
+latexify(series, reduce_order_by=1, cdot=false) |> println
+```
+
+We can obtain basically the same result (up to other notations of the coefficients)
+by dividing the B-series `series` by a symbolic variable for the time step size
+as follows.
+
+```@example modified-equation-symengine
+using Latexify
+h = SymEngine.symbols("h")
+latexify(series / h, cdot=false) |> println
+```
 
 We can also use other packages for the symbolic computations, of course.
 SymPy.jl often provides very clean expressions.
@@ -92,28 +108,46 @@ using Latexify
 latexify(series, reduce_order_by=1, dt=SymPy.symbols("h"), cdot=false) |> println
 ```
 
+We can also use the simplified versions.
+
+```@example modified-equation-sympy
+using Latexify
+latexify(series, reduce_order_by=1, cdot=false) |> println
+```
+
+```@example modified-equation-sympy
+using Latexify
+h = SymPy.symbols("h", real=true)
+latexify(series / h, cdot=false) |> println
+```
 
 Alternatively, we can also use Symbolics.jl.
 
 ```@example modified-equation-symbolics
 using BSeries, Symbolics
 
-Symbolics.@variables α h
+Symbolics.@variables α
 A = [0 0; 1/(2α) 0]
 b = [1-α, α]
 c = [0, 1/(2α)]
 
 series = modified_equation(A, b, c, 3)
 ```
 
+```@example modified-equation-symbolics
+using Latexify
+Symbolics.@variables h
+latexify(series / h, cdot=false) |> println
+```
+
 ## Working with rational coefficients
 
 High-order Runge-Kutta methods are often given in terms of rational coefficients that have large denominators.
-It's often best to use the rational coefficients in calculations, rather than converting to floating-point, since otherwise 
+It's often best to use the rational coefficients in calculations, rather than converting to floating-point, since otherwise
 terms that ought to cancel may not cancel exactly.  Rational coefficients can be entered by using `//` for the division operation.
 
-By default, Julia uses 64-bit integers for the numerator and denominator of a rational on 64-bit systems.  In practical 
-calculations with high-order RK methods, the denominators may become too large to be represented with 64 bits, 
+By default, Julia uses 64-bit integers for the numerator and denominator of a rational on 64-bit systems.  In practical
+calculations with high-order RK methods, the denominators may become too large to be represented with 64 bits,
 leading to overflow.  This can be remedied by specifying higher precision when entering the coefficients:
 
 ```@example int128-coefficients-symbolics

test/runtests.jl

@@ -31,30 +31,81 @@ using Aqua: Aqua
         @test_nowarn latexify(series_integrator, dt = SymEngine.symbols("h"))
 
         @testset "SymEngine.jl" begin
-            α = SymEngine.symbols("α")
-            A = [0 0; 1/(2 * α) 0]
-            b = [1 - α, α]
-            c = [0, 1 / (2 * α)]
-            series_integrator = bseries(A, b, c, 3)
-            @test_nowarn latexify(series_integrator)
+            @testset "Symbolic coefficients" begin
+                α = SymEngine.symbols("α")
+                A = [0 0; 1/(2 * α) 0]
+                b = [1 - α, α]
+                c = [0, 1 / (2 * α)]
+                series_integrator = bseries(A, b, c, 3)
+                @test_nowarn latexify(series_integrator)
+            end
+
+            @testset "Divide by h" begin
+                A = [0 0; 1//2 0]
+                b = [0, 1]
+                c = [0, 1 // 2]
+                series_integrator = bseries(A, b, c, 1)
+                @test_nowarn latexify(series_integrator)
+
+                h = SymEngine.symbols("h")
+                coefficients = modified_equation(series_integrator)
+                val1 = @test_nowarn latexify(coefficients, reduce_order_by = 1,
+                                             cdot = false)
+                val2 = @test_nowarn latexify(coefficients / h, cdot = false)
+                @test val1 == val2
+            end
         end
 
         @testset "SymPy.jl" begin
-            α = SymPy.symbols("α", real = true)
-            A = [0 0; 1/(2 * α) 0]
-            b = [1 - α, α]
-            c = [0, 1 / (2 * α)]
-            series_integrator = bseries(A, b, c, 3)
-            @test_nowarn latexify(series_integrator)
+            @testset "Symbolic coefficients" begin
+                α = SymPy.symbols("α", real = true)
+                A = [0 0; 1/(2 * α) 0]
+                b = [1 - α, α]
+                c = [0, 1 / (2 * α)]
+                series_integrator = bseries(A, b, c, 3)
+                @test_nowarn latexify(series_integrator)
+            end
+
+            @testset "Divide by h" begin
+                A = [0 0; 1//2 0]
+                b = [0, 1]
+                c = [0, 1 // 2]
+                series_integrator = bseries(A, b, c, 1)
+                @test_nowarn latexify(series_integrator)
+
+                h = SymPy.symbols("h", real = true)
+                coefficients = modified_equation(series_integrator)
+                val1 = @test_nowarn latexify(coefficients, reduce_order_by = 1,
+                                             cdot = false)
+                val2 = @test_nowarn latexify(coefficients / h, cdot = false)
+                @test val1 == val2
+            end
         end
 
         @testset "Symbolics.jl" begin
-            Symbolics.@variables α
-            A = [0 0; 1/(2 * α) 0]
-            b = [1 - α, α]
-            c = [0, 1 / (2 * α)]
-            series_integrator = bseries(A, b, c, 3)
-            @test_nowarn latexify(series_integrator)
+            @testset "Symbolic coefficients" begin
+                Symbolics.@variables α
+                A = [0 0; 1/(2 * α) 0]
+                b = [1 - α, α]
+                c = [0, 1 / (2 * α)]
+                series_integrator = bseries(A, b, c, 3)
+                @test_nowarn latexify(series_integrator)
+            end
+
+            @testset "Divide by h" begin
+                A = [0 0; 1//2 0]
+                b = [0, 1]
+                c = [0, 1 // 2]
+                series_integrator = bseries(A, b, c, 1)
+                @test_nowarn latexify(series_integrator)
+
+                Symbolics.@variables h
+                coefficients = modified_equation(series_integrator)
+                val1 = @test_nowarn latexify(coefficients, reduce_order_by = 1,
+                                             cdot = false)
+                val2 = @test_nowarn latexify(coefficients / h, cdot = false)
+                @test val1 == val2
+            end
         end
     end # @testset "latexify"