Update overview.md

Author: ChrisRackauckas

docs/src/methods/overview.md

@@ -29,182 +29,3 @@ integrate(f, x, RischMethod(use_algebraic_closure=true, catch_errors=false))
 **Best for:** Complete symbolic integration with guaranteed correctness
 
 [→ See detailed Risch documentation](risch.md)
-
-## Future Methods
-
-The method dispatch system is designed to support additional integration algorithms:
-
-### Planned Methods
-
-#### HeuristicMethod (Future)
-Fast pattern-matching based integration for common cases.
-```julia
-integrate(f, x, HeuristicMethod())  # Fast heuristic patterns
-```
-
-#### NumericalMethod (Future)  
-Numerical integration with symbolic preprocessing.
-```julia
-integrate(f, x, NumericalMethod(tolerance=1e-10))  # Numerical fallback
-```
-
-#### SymPyMethod (Future)
-Integration using SymPy backend for comparison.
-```julia
-integrate(f, x, SymPyMethod())  # SymPy compatibility
-```
-
-## Method Selection Guide
-
-### Choosing the Right Method
-
-| Use Case | Recommended Method | Reason |
-|----------|-------------------|---------|
-| **Exact symbolic results** | `RischMethod()` | Complete, guaranteed correct |
-| **Research/verification** | `RischMethod(catch_errors=false)` | Strict algorithmic behavior |
-| **Production applications** | `RischMethod(catch_errors=true)` | Robust error handling |
-| **Complex analysis** | `RischMethod(use_algebraic_closure=true)` | Full arctangent terms |
-| **Simple computations** | `RischMethod(use_algebraic_closure=false)` | Faster execution |
-
-### Method Comparison
-
-| Method | Speed | Completeness | Robustness | Use Case |
-|--------|-------|--------------|------------|----------|
-| **RischMethod** | Moderate | Complete | High | Research, exact results |
-| **HeuristicMethod** (future) | Fast | Partial | Moderate | Common patterns |
-| **NumericalMethod** (future) | Variable | Approximate | High | Fallback cases |
-
-## Method Architecture
-
-### Abstract Type Hierarchy
-```julia
-AbstractIntegrationMethod
-├── RischMethod                     # Complete symbolic integration
-├── AbstractRationalIntegration     # Rational function specialists  
-└── AbstractTranscendentalIntegration # Transcendental specialists
-```
-
-### Method Interface
-```julia
-# General interface
-integrate(f, x, method::AbstractIntegrationMethod; kwargs...)
-
-# Method-specific traits
-method_supports_rational(method)      # Check rational function support
-method_supports_transcendental(method) # Check transcendental support
-```
-
-## Configuration Patterns
-
-### Common Configurations
-
-```julia
-# Research configuration (strict, complete)
-research_config = RischMethod(
-    use_algebraic_closure=true,
-    catch_errors=false
-)
-
-# Production configuration (robust, complete)
-production_config = RischMethod(
-    use_algebraic_closure=true, 
-    catch_errors=true
-)
-
-# Performance configuration (fast, simple)
-performance_config = RischMethod(
-    use_algebraic_closure=false,
-    catch_errors=true
-)
-```
-
-### Method Workflows
-
-```julia
-@variables x f
-
-# Try different methods in sequence
-function robust_integrate(f, x)
-    try
-        # First try exact Risch method
-        return integrate(f, x, RischMethod(catch_errors=false))
-    catch NotImplementedError
-        # Fall back to heuristic method (future)
-        return integrate(f, x, HeuristicMethod())
-    catch AlgorithmFailedError
-        # Fall back to numerical method (future)  
-        return integrate(f, x, NumericalMethod())
-    end
-end
-```
-
-## Extending with New Methods
-
-The method system is designed for easy extension:
-
-### Adding a New Method
-
-1. **Define method type**:
-```julia
-struct MyMethod <: AbstractIntegrationMethod
-    option1::Bool
-    option2::Float64
-end
-```
-
-2. **Implement integration**:
-```julia
-function SymbolicIntegration._integrate(f, x, method::MyMethod; kwargs...)
-    # Your algorithm implementation
-    return result
-end
-```
-
-3. **Add method traits**:
-```julia
-method_supports_rational(method::MyMethod) = true
-method_supports_transcendental(method::MyMethod) = false
-```
-
-### Plugin Architecture
-
-The dispatch system supports:
-- **Third-party packages**: Can add new methods
-- **Method composition**: Combining different approaches  
-- **Fallback chains**: Trying multiple methods in sequence
-- **Performance optimization**: Method-specific tuning
-
-## Performance and Benchmarking
-
-### Method Performance Characteristics
-
-- **RischMethod**: Exact results, moderate speed, complete coverage
-- **Future methods**: Will provide different speed/accuracy tradeoffs
-
-### Benchmarking Methods
-
-```julia
-using BenchmarkTools
-
-@variables x
-f = (x^3 + x^2 + x + 2)/(x^4 + 3*x^2 + 2)
-
-# Benchmark different configurations
-@benchmark integrate($f, $x, RischMethod(use_algebraic_closure=true))
-@benchmark integrate($f, $x, RischMethod(use_algebraic_closure=false))
-```
-
-## Migration and Compatibility
-
-### Current Usage Patterns
-
-All existing code continues to work:
-```julia
-# Existing code (still works)
-integrate(f, x)
-
-# New explicit method (equivalent)
-integrate(f, x, RischMethod())
-```
-
-The method system provides a **migration path** for users to gradually adopt new integration methods as they become available, while maintaining full compatibility with existing workflows.