add tests and docs

Author: dlfivefifty

docs/src/index.md

@@ -20,12 +20,35 @@ product of the specified sizes, similar to `plan_fft`.
 5. `plotgrid(::MyBasis, n...)`: return `n` grid points suitable for plotting the basis. The default value for `n` is 10,000. 
 
 
-## Routines
+## Differential Operators
 
 
 ```@docs
 Derivative
 ```
+
+```@docs
+Laplacian
+```
+
+```@docs
+AbsLaplacian
+```
+
+```@docs
+laplacian
+```
+
+```@docs
+abslaplacian
+```
+
+```@docs
+weaklaplacian
+```
+
+## Routines
+
 ```@docs
 transform
 ```

test/test_splines.jl

@@ -45,6 +45,8 @@ import ContinuumArrays: basis, AdjointBasisLayout, ExpansionLayout, BasisLayout,
             @test sum(H/H \ exp.(x)) ≈ ℯ-1 atol=1E-5
             @test last(cumsum(H/H \ exp.(x))) ≈ sum(H/H\exp.(x))
         end
+
+        @test coefficients(H) ≡ Eye(2)
     end
 
     @testset "LinearSpline" begin
@@ -163,6 +165,11 @@ import ContinuumArrays: basis, AdjointBasisLayout, ExpansionLayout, BasisLayout,
         @test typeof(diff(L)) == typeof(diff(L; dims=1)) == typeof(D*L)
         @test_throws ErrorException diff(L; dims=2)
 
+        @test diff(L,0) ≡ L
+        @test diff(f,0) ≡ f
+        @test diff(L,2)[1.1,:] == laplacian(L)[1.1,:] == -abslaplacian(L)[1.1,:]
+        @test diff(f,2)[1.1] == laplacian(f)[1.1] == -abslaplacian(f)[1.1]
+
         M = applied(*, (D*L).args..., [1,2,4])
         @test eltype(materialize(M)) == Float64