Fix trigonometric functions with Risch method (Issue #20)

debug_test.jl

@@ -0,0 +1,23 @@
+#!/usr/bin/env julia
+
+using Pkg
+Pkg.activate(".")
+
+println("Loading packages...")
+using SymbolicIntegration, Symbolics
+
+println("Creating variable...")
+@variables x
+
+println("Attempting sin(x) integration with debugging...")
+try
+    result = integrate(sin(x), x, RischMethod())
+    println("SUCCESS: Result = $result")
+catch e
+    println("ERROR: $e")
+    println("Stack trace:")
+    for (exc, bt) in Base.catch_stack()
+        showerror(stdout, exc, bt)
+        println()
+    end
+end

src/methods/risch/complex_fields.jl

@@ -4,7 +4,28 @@ struct ComplexExtensionDerivation{T<:FieldElement, P<:PolyRingElem{T}} <: Deriva
     domain::AbstractAlgebra.ResField{P}
     D::Derivation    
     function ComplexExtensionDerivation(domain::AbstractAlgebra.ResField{P}, D::Derivation) where {T<:FieldElement, P<:PolyRingElem{T}}
-        base_ring(base_ring(base_ring(domain)))==D.domain || error("base ring of domain must be domain of D")
+        # The issue is that we need to check the correct nesting level based on the derivation type
+        # Similar to how ExtensionDerivation handles different nesting levels
+
+        expected_domain = base_ring(base_ring(base_ring(domain)))
+        actual_domain = D.domain
+
+        # Check compatibility following the same pattern as ExtensionDerivation
+        domain_compatible = false
+
+        if expected_domain == actual_domain
+            # Direct match - the expected case for basic derivations
+            domain_compatible = true
+        elseif base_ring(base_ring(domain)) == actual_domain
+            # One level less nesting - derivation on the polynomial ring level
+            domain_compatible = true  
+        elseif base_ring(domain) == actual_domain
+            # Two levels less nesting - derivation on the coefficient field level
+            domain_compatible = true
+        end
+
+        domain_compatible || error("base ring of domain must be domain of D")
+
         m = modulus(domain)
         degree(m)==2 && isone(coeff(m, 0)) && iszero(coeff(m, 1)) && isone(coeff(m,2)) ||
             error("domain must be residue field modulo X^2+1.")

test/methods/risch/test_trigonometric_functions.jl

@@ -0,0 +1,33 @@
+using Test
+using SymbolicIntegration
+using Symbolics
+
+@testset "Trigonometric Functions with Risch Method" begin
+    @variables x
+
+    @testset "Issue #20: Basic trigonometric integration" begin
+        # Test sin(x) integration
+        sin_result = integrate(sin(x), x, RischMethod())
+        @test sin_result !== nothing
+
+        # Test cos(x) integration  
+        cos_result = integrate(cos(x), x, RischMethod())
+        @test cos_result !== nothing
+
+        # Test mathematical correctness by verifying derivatives
+        # The fundamental theorem of calculus: d/dx[∫f(x)dx] = f(x)
+        @test isequal(Symbolics.derivative(sin_result, x), sin(x))
+        @test isequal(Symbolics.derivative(cos_result, x), cos(x))
+
+        # Test that results are symbolic expressions
+        @test sin_result isa Union{Number, SymbolicUtils.BasicSymbolic}
+        @test cos_result isa Union{Number, SymbolicUtils.BasicSymbolic}
+    end
+
+    @testset "Additional trigonometric functions" begin
+        # Test tan(x) integration
+        tan_result = integrate(tan(x), x, RischMethod())
+        @test tan_result !== nothing
+        @test isequal(Symbolics.derivative(tan_result, x), tan(x))
+    end
+end

test/runtests.jl

@@ -21,6 +21,7 @@ using Symbolics
     # Include Risch method test suites
     include("methods/risch/test_rational_integration.jl")
     include("methods/risch/test_complex_fields.jl") 
+    include("methods/risch/test_trigonometric_functions.jl")
     include("methods/risch/test_bronstein_examples.jl")
     include("methods/risch/test_algorithm_internals.jl")