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skills/julia-numerical/SKILL.md

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+---
+name: julia-numerical
+description: Execute numerical calculations and mathematical computations using Julia. Use this skill for matrix operations, linear algebra, numerical integration, optimization, statistics, and scientific computing tasks.
+---
+
+# Julia Numerical Calculation Skill
+
+This skill enables you to execute numerical calculations using Julia, a high-performance programming language designed for numerical and scientific computing.
+
+## When to Use
+
+Use this skill when you need to:
+- Perform matrix operations and linear algebra
+- Solve differential equations
+- Execute numerical integration or optimization
+- Calculate statistical measures
+- Handle large-scale numerical computations
+- Work with complex mathematical operations
+
+## Setup
+
+Before using this skill, ensure Julia is installed on your system:
+
+```bash
+# On macOS (using Homebrew)
+brew install julia
+
+# On Linux (Ubuntu/Debian)
+sudo apt-get install julia
+
+# On Windows (using Chocolatey)
+choco install julia
+
+# Or download from https://julialang.org/downloads/
+```
+
+## Basic Examples
+
+### Linear Algebra
+
+```julia
+using LinearAlgebra
+
+# Create matrices
+A = [1 2; 3 4]
+B = [5 6; 7 8]
+
+# Matrix multiplication
+C = A * B
+
+# Eigenvalues and eigenvectors
+eigenvals, eigenvecs = eigen(A)
+
+# Matrix inverse
+A_inv = inv(A)
+```
+
+### Numerical Integration
+
+```julia
+using QuadGK
+
+# Define a function
+f(x) = sin(x) * exp(-x)
+
+# Integrate from 0 to ∞
+result, error = quadgk(f, 0, Inf)
+```
+
+### Optimization
+
+```julia
+using Optim
+
+# Define objective function
+f(x) = (x[1] - 2)^2 + (x[2] - 3)^2
+
+# Minimize
+result = optimize(f, [0.0, 0.0])
+```
+
+### Statistics
+
+```julia
+using Statistics
+
+data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+
+# Statistical measures
+mean_val = mean(data)
+std_val = std(data)
+var_val = var(data)
+median_val = median(data)
+```
+
+## How to Use This Skill
+
+When you ask me to perform a numerical calculation:
+1. I'll identify the appropriate Julia packages needed
+2. Write Julia code to solve the problem
+3. Execute the code
+4. Return results and explanations
+
+## Common Julia Packages
+
+- **LinearAlgebra**: Matrix operations and linear algebra
+- **Statistics**: Statistical functions
+- **QuadGK**: Numerical integration
+- **Optim**: Optimization algorithms
+- **DifferentialEquations**: Solving differential equations
+- **Plots**: Visualization
+- **Distributions**: Probability distributions
+- **Random**: Random number generation
+
+## Notes
+
+- Julia is JIT-compiled, so first runs may include compilation time
+- Use `.jl` files for organizing longer scripts
+- Install packages with `using Pkg; Pkg.add("PackageName")`
+- Results are returned as Julia objects that are converted to readable format