Fix trigonometric functions with Risch method (Issue #20) #29
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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 JuliaSymbolics#20
Added comprehensive test for Issue JuliaSymbolics#20 to verify that: - sin(x) and cos(x) can be integrated with RischMethod() without errors - Results are properly computed and returned as symbolic expressions - Domain compatibility issues are resolved The test is integrated into the main test suite under the Risch method tests.
Updated tests to verify that integrals produce mathematically correct results: - ∫sin(x)dx derivative should equal sin(x) - ∫cos(x)dx derivative should equal cos(x) - ∫tan(x)dx derivative should equal tan(x) This ensures the Risch method not only runs without errors but produces the correct mathematical results that calculus expects.
Replaced complex domain matching logic with cleaner approach using try-catch for base ring unwrapping. This should be more robust and less prone to compilation issues while still fixing the original domain mismatch error for trigonometric function integration.
Root cause analysis revealed that ComplexExtensionDerivation was using a rigid domain check that didn't account for different nesting levels of derivation domains, similar to how ExtensionDerivation handles multiple constructor patterns. Fixed by: - Following the same pattern as ExtensionDerivation constructors - Checking compatibility at multiple nesting levels - Removing try-catch workarounds in favor of proper domain matching Updated tests to verify mathematical correctness using derivative verification based on the fundamental theorem of calculus.
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Summary
ComplexExtensionDerivationconstructor that prevented trigonometric functions likesin(x)from being integrated using the Risch methodintegrate(sin(x), x, RischMethod())was failing with "base ring of domain must be domain of D" errorChanges Made
Modified the
ComplexExtensionDerivationconstructor in/src/methods/risch/complex_fields.jlto:Test Plan
integrate(sin(x), x, RischMethod())worksTechnical Details
The issue occurred because when
TowerOfDifferentialFieldsprocesses trigonometric functions, it callsComplexify(K, D)which creates a residue fieldkI = residue_field(kz, I^2+1)[1]with nested structureResField{P}whereP<:PolyRingElem{T}. The original checkbase_ring(base_ring(base_ring(domain)))==D.domainwas too strict and didn't account for the various field nesting patterns that can occur.🤖 Generated with Claude Code