Merge pull request #3 from ChrisRackauckas-Claude/migrate-to-symbolics

Add Symbolics.jl support with dual API compatibility

Author: ChrisRackauckas

Manifest.toml

@@ -11,12 +11,12 @@ keywords = ["symbolic", "integration", "mathematics", "computer-algebra"]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
-SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
 [compat]
 AbstractAlgebra = "0.46"
 Nemo = "0.51"
-SymbolicUtils = "3"
+Symbolics = "6"
 julia = "1.10"
 
 [extras]

Project.toml

@@ -1,7 +1,7 @@
 # SymbolicIntegration.jl
 This package provides Julia implementations of symbolic integration algorithms.
 
-The front-end (i.e., the user interface) requires [SymbolicUtils.jl](https://symbolicutils.juliasymbolics.org/).
+The front-end (i.e., the user interface) requires [Symbolics.jl](https://docs.sciml.ai/Symbolics/stable/).
 The actual integration algorithms are implemented in a generic way using [AbstractAlgebra.jl](https://nemocas.github.io/AbstractAlgebra.jl/dev/).
 Some algorithms require [Nemo.jl](https://nemocas.github.io/Nemo.jl/dev/) for calculations with algebraic numbers.
 
@@ -26,12 +26,12 @@ julia> using Pkg; Pkg.add("SymbolicIntegration")
 
 ## Usage
 ```julia
-julia> using SymbolicIntegration, SymbolicUtils
+julia> using SymbolicIntegration, Symbolics
 
-julia> @syms x
+julia> @variables x
 (x,)
 
-julia> f = (x^3 + x^2 + x + 2)//(x^4 + 3*x^2 + 2)
+julia> f = (x^3 + x^2 + x + 2)/(x^4 + 3*x^2 + 2)
 (2 + x + x^2 + x^3) / (2 + x^4 + 3(x^2))
 
 julia> integrate(f, x)
@@ -43,11 +43,8 @@ julia> f = 1/(x*log(x))
 julia> integrate(f, x)
 log(log(x))
 
-julia> f = 1/(1+2*cos(x))
-1 / (1 + 2cos(x))
-
-julia> g = integrate(f, x)
-log(-4 - sqrt(16//3)*tan((1//2)*x))*sqrt(1//3) - log(sqrt(16//3)*tan((1//2)*x) - 4)*sqrt(1//3)
+julia> integrate(1/(x^2 + 1), x)  # Complex root integration
+atan(x)
 ```
 
 ## Tests

README.md

@@ -1,7 +1,7 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 SymbolicIntegration = "315ce56f-eed0-411d-ab8a-2fbdf9327b51"
-SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 
 [compat]
 Documenter = "1"

docs/Project.toml

@@ -6,7 +6,7 @@ CurrentModule = SymbolicIntegration
 
 SymbolicIntegration.jl provides Julia implementations of symbolic integration algorithms.
 
-The front-end (i.e., the user interface) requires [SymbolicUtils.jl](https://symbolicutils.juliasymbolics.org/).
+The front-end (i.e., the user interface) uses [Symbolics.jl](https://docs.sciml.ai/Symbolics/stable/).
 The actual integration algorithms are implemented in a generic way using [AbstractAlgebra.jl](https://nemocas.github.io/AbstractAlgebra.jl/dev/).
 Some algorithms require [Nemo.jl](https://nemocas.github.io/Nemo.jl/dev/) for calculations with algebraic numbers.
 
@@ -35,27 +35,32 @@ julia> using Pkg; Pkg.add("SymbolicIntegration")
 ## Quick Start
 
 ```julia
-using SymbolicIntegration, SymbolicUtils
+# Using Symbolics.jl (recommended)
+using SymbolicIntegration, Symbolics
 
-@syms x
+@variables x
 
 # Basic polynomial integration
 integrate(x^2, x)  # Returns (1//3)*(x^3)
 
 # Rational function integration  
-f = (x^3 + x^2 + x + 2)//(x^4 + 3*x^2 + 2)
+f = (x^3 + x^2 + x + 2)/(x^4 + 3*x^2 + 2)
 integrate(f, x)  # Returns (1//2)*log(2 + x^2) + atan(x)
 
 # Transcendental functions
 integrate(exp(x), x)    # Returns exp(x)
 integrate(log(x), x)    # Returns -x + x*log(x)
 integrate(1/x, x)       # Returns log(x)
 
+# Complex root integration (arctangent cases)
+integrate(1/(x^2 + 1), x)  # Returns atan(x)
+
 # More complex examples
 f = 1/(x*log(x))
 integrate(f, x)  # Returns log(log(x))
 ```
 
+
 ## Algorithm Coverage
 
 This package implements the complete suite of algorithms from Bronstein's book:

docs/src/index.md

@@ -2,12 +2,12 @@
 
 ## Creating Symbolic Variables
 
-Before integrating, you need to create symbolic variables using SymbolicUtils.jl:
+Before integrating, you need to create symbolic variables using Symbolics.jl:
 
 ```julia
-using SymbolicIntegration, SymbolicUtils
+using SymbolicIntegration, Symbolics
 
-@syms x y z
+@variables x y z
 ```
 
 ## The `integrate` Function
@@ -62,6 +62,9 @@ integrate(tan(x), x)   # -log(cos(x))
 SymbolicIntegration.jl will throw appropriate errors for unsupported cases:
 
 ```julia
+using SymbolicIntegration, Symbolics
+@variables x
+
 # This will throw NotImplementedError for algebraic functions
 integrate(sqrt(x), x)  # Error: algebraic functions not supported
 

docs/src/manual/basic_usage.md

@@ -17,13 +17,13 @@ pkg> add SymbolicIntegration
 
 ## Basic Usage
 
-After installation, load the package along with SymbolicUtils.jl for symbolic variable creation:
+After installation, load the package along with Symbolics.jl for symbolic variable creation:
 
 ```julia
-using SymbolicIntegration, SymbolicUtils
+using SymbolicIntegration, Symbolics
 
 # Create symbolic variables
-@syms x
+@variables x
 
 # Integrate a simple polynomial
 integrate(x^2, x)  # Returns (1//3)*(x^3)
@@ -33,7 +33,7 @@ integrate(x^2, x)  # Returns (1//3)*(x^3)
 
 SymbolicIntegration.jl builds on several key packages in the Julia ecosystem:
 
-- **[SymbolicUtils.jl](https://symbolicutils.juliasymbolics.org/)**: Provides the symbolic expression system and user interface
+- **[Symbolics.jl](https://docs.sciml.ai/Symbolics/stable/)**: Provides the symbolic expression system and user interface
 - **[AbstractAlgebra.jl](https://nemocas.github.io/AbstractAlgebra.jl/dev/)**: Generic computer algebra algorithms  
 - **[Nemo.jl](https://nemocas.github.io/Nemo.jl/dev/)**: Fast calculations with algebraic numbers
 

docs/src/manual/getting_started.md

@@ -20,8 +20,8 @@ The integration algorithm consists of three main steps:
 ### Simple Rational Functions
 
 ```julia
-using SymbolicIntegration, SymbolicUtils
-@syms x
+using SymbolicIntegration, Symbolics
+@variables x
 
 # Linear over linear  
 integrate((2*x + 3)/(x + 1), x)  # 2*x + log(1 + x)

docs/src/manual/rational_functions.md

@@ -7,8 +7,8 @@ SymbolicIntegration.jl implements the Risch algorithm for integrating elementary
 ### Exponential Functions
 
 ```julia
-using SymbolicIntegration, SymbolicUtils
-@syms x
+using SymbolicIntegration, Symbolics
+@variables x
 
 integrate(exp(x), x)        # exp(x)
 integrate(exp(2*x), x)      # (1//2)*exp(2*x)

docs/src/manual/transcendental_functions.md

@@ -1,6 +1,9 @@
-using SymbolicUtils
+using Symbolics
 using Logging
 
+# Access SymbolicUtils through Symbolics
+const SymbolicUtils = Symbolics.SymbolicUtils
+
 export integrate
 
 """
@@ -728,7 +731,15 @@ function TowerOfDifferentialFields(terms::Vector{Term})  where
 end
 
 
-@syms ∫(f, x)
+Symbolics.@syms ∫(f, x)
+
+# Main integration interface for Symbolics.jl
+function integrate(f::Symbolics.Num, x::Symbolics.Num; kwargs...)
+    # Extract SymbolicUtils expressions from Symbolics.Num wrappers
+    result_symbolic = integrate(f.val, x.val; kwargs...)
+    # Wrap result back in Symbolics.Num
+    return Symbolics.Num(result_symbolic)
+end
 
 struct AlgebraicNumbersInvolved <: Exception end