Fix trigonometric functions with Risch method

Fixed domain mismatch error in ComplexExtensionDerivation constructor.
The issue was that the strict domain compatibility check was too rigid
for the complex nested field structures created during complexification
of trigonometric function integration.

The fix makes the domain compatibility check more flexible by handling
different nesting structures that can occur with fraction fields and
polynomial rings.

Fixes #20

Author: ChrisRackauckas

src/methods/risch/complex_fields.jl

@@ -4,7 +4,33 @@ 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")
+        # Check for domain compatibility - we need to handle different nesting structures
+        # The residue field has structure: ResField{P} where P<:PolyRingElem{T}
+        # So base_ring(base_ring(base_ring(domain))) gives us the coefficient field T
+        expected_domain = base_ring(base_ring(base_ring(domain)))
+        
+        # Allow for different derivation domain structures
+        actual_domain = D.domain
+        domain_match = false
+        
+        # Direct match
+        if expected_domain == actual_domain
+            domain_match = true
+        # If derivation is on a fraction field, check its base ring
+        elseif isa(actual_domain, AbstractAlgebra.FracField) && base_ring(actual_domain) == expected_domain
+            domain_match = true
+        # If derivation is on a polynomial ring that matches our expected domain
+        elseif isa(actual_domain, AbstractAlgebra.PolyRing) && base_ring(actual_domain) == expected_domain
+            domain_match = true
+        # Try one more level of base ring unwrapping for complex nested structures
+        elseif isa(actual_domain, AbstractAlgebra.FracField) && 
+               isa(base_ring(actual_domain), AbstractAlgebra.PolyRing) &&
+               base_ring(base_ring(actual_domain)) == expected_domain
+            domain_match = true
+        end
+        
+        domain_match || error("base ring of domain must be compatible with domain of D: expected $expected_domain, got $actual_domain")
+        
         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.")