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Giac.jl

A Julia wrapper for the GIAC computer algebra system.

Features

  • Dynamic Command Invocation: Access all 2200+ GIAC commands via invoke_cmd(:cmd, args...)
  • Commands Submodule: All ~2000+ commands available via Giac.Commands for clean namespace
  • Expression Evaluation: Parse and evaluate mathematical expressions
  • Command Discovery: Search commands, browse by category, built-in help via ?cmd
  • Arithmetic Operations: +, -, *, /, ^, unary negation, equality
  • Algebra: Factorization, expansion, simplification, equation solving and GCD
  • Calculus: Differentiation, integration, limits, and series expansion
  • Infinity Support: Use Julia's Inf and -Inf directly in limits and improper integrals
  • Linear Algebra: Symbolic matrices with determinant, inverse, trace, transpose operations
  • Base Extensions: Use sin(expr), cos(expr), exp(expr) with GiacExpr
  • Method Syntax: Call commands as methods: expr.factor(), expr.diff(x)
  • Variable Substitution: Symbolics.jl-compatible substitute(expr, Dict(var => value)) interface
  • Laplace Transform: laplace and ilaplace commands for continuous-time signal processing
  • Z-Transform: ztrans and invztrans commands for discrete-time signal processing
  • Type Conversion: Convert results to Julia native types (Int64, Float64, Rational)
  • Symbolics.jl Integration: Bidirectional conversion with Symbolics.jl
  • Tables.jl Compatibility: Convert GiacMatrix and command help to DataFrames, CSV export
  • LaTeX Support: Automatic LaTeX rendering in Pluto notebooks
  • TempApi Submodule: Simplified function names (diff, factor, etc.) via Giac.TempApi

Installation

using Pkg
Pkg.add("Giac")  # when registered to Julia General Registry

For full GIAC integration with C++ library, see the Installation Guide.

Command Access

GIAC commands are available through multiple access patterns:

1. Selective Import from Commands Submodule (Recommended)

using Giac
using Giac.Commands: factor, expand, ifactor

@giac_var x
factor(x^2 - 1)

2. Full Import (Interactive Use)

using Giac
using Giac.Commands

@giac_var x
factor(x^2 - 1)
ifactor(120)  # All ~2000+ commands available

3. Universal Command Invocation

using Giac

# Works for ALL commands, including those conflicting with Julia
invoke_cmd(:factor, giac_eval("x^2-1"))
invoke_cmd(:sin, giac_eval("pi/6"))

Type Conversion and Introspection

Convert GIAC results to native Julia types:

using Giac

# Boolean conversion
to_julia(giac_eval("true"))   # true::Bool
to_julia(giac_eval("1==1"))   # true::Bool (comparison result)
to_julia(giac_eval("1"))      # 1::Int64 (integer, not boolean)

# Use in control flow
if to_julia(giac_eval("2 > 1"))
    println("Works!")
end

# Automatic type conversion
g = giac_eval("[1, 2, 3]")
result = to_julia(g)  # Vector{Int64}

# Boolean detection
is_boolean(giac_eval("true"))  # true
is_boolean(giac_eval("1"))     # false

# Type introspection
using Giac.GenTypes: VECT
giac_type(g) == VECT  # true
is_vector(g)           # true

# Fraction components
frac = giac_eval("3/4")
numer(frac)  # 3
denom(frac)  # 4

# Complex components
z = giac_eval("3+4*i")
real_part(z)  # 3
imag_part(z)  # 4

# Matrix conversion
m = GiacMatrix(giac_eval("[[1, 2], [3, 4]]"))
to_julia(m)  # 2×2 Matrix{Int64}

Vector Indexing and Iteration

Access GIAC vectors with Julia's native indexing:

using Giac

g = giac_eval("[10, 20, 30]")
g[1]  # GiacExpr(10)
g[2]  # GiacExpr(20)

# Iterate over elements
for elem in g
    println(to_julia(elem))
end

# Collect to Julia vector
to_julia(g)  # [10, 20, 30]::Vector{Int64}

Infinity Support

Use Julia's native Inf and -Inf in limits and improper integrals:

using Giac
using Giac.Commands: limit, integrate

@giac_var x

# Limits at infinity
limit(1/x, x, Inf)     # 0
limit(1/x, x, -Inf)    # 0
limit(x^2, x, Inf)     # +infinity

# Improper integrals
integrate(exp(-x), x, 0, Inf)    # 1
integrate(1/x^2, x, 1, Inf)      # 1
integrate(exp(x), x, -Inf, 0)    # 1

Modules

  • Core API: Types, evaluation, and main functions
  • Commands: All GIAC commands as functions
  • Constants: Symbolic mathematical constants (pi, e, i)
  • TempApi: Convenience functions with simple names

Documentation

Getting Started

Mathematics

Physics

API Reference