Theory2 Symbolic Mathematics

Execute symbolic math operations using the Theory2 CLI.

Available Operations

Lie Algebra Computations

# Compute fine-structure constant from E7
/home/mikeb/theory2/.venv/bin/theory --json symbolic compute-e7-alpha --verify

# Query Lie algebra properties
/home/mikeb/theory2/.venv/bin/theory --json symbolic lie-algebra --type=E7 --query=dimension
/home/mikeb/theory2/.venv/bin/theory --json symbolic lie-algebra --type=E8 --query=fundamental_rep

Expression Evaluation

# Evaluate with substitutions
/home/mikeb/theory2/.venv/bin/theory --json symbolic eval --expr="(x+1)**2" --substitutions='{"x": 3}'

# Simplify expressions
/home/mikeb/theory2/.venv/bin/theory --json symbolic simplify --expr="(x**2-1)/(x-1)"

# Expand expressions
/home/mikeb/theory2/.venv/bin/theory --json symbolic expand --expr="(a+b)**3"

# Factor expressions
/home/mikeb/theory2/.venv/bin/theory --json symbolic factor --expr="x**3 - 1"

Equation Solving

# Solve algebraic equations
/home/mikeb/theory2/.venv/bin/theory --json symbolic solve --expr="x**2 - 4" --symbol=x

Calculus

# Differentiate
/home/mikeb/theory2/.venv/bin/theory --json symbolic diff --expr="x**3 * sin(x)" --symbol=x

# Integrate
/home/mikeb/theory2/.venv/bin/theory --json symbolic integrate --expr="x**2" --symbol=x

Argument Parsing

Parse user arguments to determine the operation:

1. compute-e7-alpha or e7 or alpha: Run E7 alpha computation
2. lie-algebra or lie with --type: Query Lie algebra
3. eval with --expr: Evaluate expression
4. simplify with --expr: Simplify expression
5. solve with --expr: Solve equation
6. diff with --expr: Differentiate
7. integrate with --expr: Integrate

Always use --json flag for structured output. Display results in a readable format.