Merge pull request #4 from ChrisRackauckas-Claude/polish-and-docs

Polish package: fix integration symbol, add .gitignore, fix docs

Author: ChrisRackauckas

.gitignore

@@ -0,0 +1,30 @@
+# Julia
+Manifest.toml
+docs/Manifest.toml
+
+# Documentation build artifacts
+docs/build/
+
+# Julia compiled files
+*.ji
+*.o
+*.so
+
+# Backup files
+*~
+*.bak
+
+# Editor files
+.vscode/
+.idea/
+*.swp
+*.tmp
+
+# OS generated files
+.DS_Store
+.DS_Store?
+._*
+.Spotlight-V100
+.Trashes
+ehthumbs.db
+Thumbs.db

docs/Project.toml

@@ -1,7 +1,8 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 SymbolicIntegration = "315ce56f-eed0-411d-ab8a-2fbdf9327b51"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
 [compat]
-Documenter = "1"
+Documenter = "1"
+Symbolics = "6"

docs/make.jl

@@ -1,4 +1,4 @@
-using Documenter, SymbolicIntegration
+using Documenter, SymbolicIntegration, Symbolics
 
 makedocs(
     sitename="SymbolicIntegration.jl",

docs/src/api.md

@@ -10,49 +10,42 @@ CurrentModule = SymbolicIntegration
 integrate
 ```
 
-## Internal Types and Functions
+## Algorithm Overview
 
-```@docs
-Term
-IdTerm
-FunctionTerm
-Result
-```
+SymbolicIntegration.jl implements the complete symbolic integration algorithms from Manuel Bronstein's book "Symbolic Integration I: Transcendental Functions".
 
-## Algorithm Functions
+### Supported Function Classes
 
-### Rational Function Integration
+- **Polynomial functions**: ∫xⁿ dx
+- **Rational functions**: ∫P(x)/Q(x) dx using Rothstein-Trager method
+- **Exponential functions**: ∫exp(f(x)) dx using Risch algorithm
+- **Logarithmic functions**: ∫log(f(x)) dx using integration by parts
+- **Trigonometric functions**: Transformed to exponential form
 
-```@docs
-IntegrateRationalFunction
-HermiteReduce
-IntRationalLogPart
-```
+### Algorithm Components
 
-### Transcendental Function Integration
+The package includes implementations of:
+- Hermite reduction for rational functions
+- Rothstein-Trager method for logarithmic parts
+- Risch algorithm for transcendental functions
+- Differential field tower construction
+- Complex root finding for arctangent terms
 
-```@docs
-Integrate
-HermiteReduce
-ResidueReduce
-PolynomialReduce
-```
+## Internal Structure
 
-### Differential Field Operations
+The package is organized into several algorithm modules:
+- `rational_functions.jl`: Rational function integration algorithms
+- `transcendental_functions.jl`: Risch algorithm implementation  
+- `differential_fields.jl`: Differential field operations
+- `complex_fields.jl`: Complex number field handling
+- `frontend.jl`: User interface and expression conversion
 
-```@docs
-BasicDerivation
-ExtensionDerivation
-AlgebraicExtensionDerivation
-```
-
-## Utility Functions
+## Error Handling
 
-```@docs
-isrational
-rationalize
-constant_roots
-```
+The package defines custom exception types:
+- `NotImplementedError`: For unsupported function types
+- `AlgorithmFailedError`: When no elementary antiderivative exists
+- `AlgebraicNumbersInvolved`: When algebraic numbers complicate the result
 
 ## Index
 

src/frontend.jl

@@ -731,9 +731,41 @@ function TowerOfDifferentialFields(terms::Vector{Term})  where
 end
 
 
-Symbolics.@syms ∫(f, x)
+@variables ∫(.., ..)
 
-# Main integration interface for Symbolics.jl
+"""
+    integrate(f, x; kwargs...)
+
+Compute the symbolic integral of expression `f` with respect to variable `x`.
+
+# Arguments
+- `f`: Symbolic expression to integrate (Symbolics.Num)
+- `x`: Integration variable (Symbolics.Num)
+
+# Keyword Arguments  
+- `useQQBar::Bool=false`: Use algebraic closure for root finding
+- `catchNotImplementedError::Bool=true`: Catch implementation errors gracefully
+- `catchAlgorithmFailedError::Bool=true`: Catch algorithm failures gracefully
+
+# Returns
+- Symbolic expression representing the antiderivative (Symbolics.Num)
+
+# Examples
+```julia
+using SymbolicIntegration, Symbolics
+@variables x
+
+# Basic polynomial integration
+integrate(x^2, x)  # (1//3)*(x^3)
+
+# Rational function integration
+integrate(1/(x^2 + 1), x)  # atan(x)
+
+# Transcendental functions  
+integrate(exp(x), x)  # exp(x)
+integrate(log(x), x)  # -x + x*log(x)
+```
+"""
 function integrate(f::Symbolics.Num, x::Symbolics.Num; kwargs...)
     # Extract SymbolicUtils expressions from Symbolics.Num wrappers
     result_symbolic = integrate(f.val, x.val; kwargs...)