phil

A minimal command-line calculator for exact arithmetic, symbolic differentiation, integration, algebraic equation solving, and ordinary differential equations.

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Why phil

phil is designed to be the first-stop calculator for quick terminal math, homework, and symbolic workflows — before reaching for WolframAlpha, a Python REPL, or a graphing calculator.

It prioritizes exactness, speed, and discoverability. When it rewrites your input, it says so.

Install

Requires uv.

uv tool install philcalc

• PyPI: https://pypi.org/project/philcalc/
• Source: https://github.com/sacchen/phil
• Tutorial: TUTORIAL.md
• Roadmap: ROADMAP.md

Quick Start

phil '1/3 + 1/6'
phil '10^100000 + 1 - 10^100000'
phil 'd(x^3 + 2*x, x)'
phil 'int(sin(x), x)'
phil "ode y' = y, y(0)=1"
phil '(1 - 25e^5)e^{-5t} + (25e^5 - 1)t e^{-5t} + t e^{-5t} ln(t)'

Or open the REPL (phil) and try these in order:

1. 1/3 + 1/6
2. d(x^3 + 2*x, x)
3. int(sin(x), x)
4. solve(x^2 - 4, x)
5. N(pi, 20)

If stuck, run :examples or :h.

Usage

One-shot

phil '<expression>'
phil --format pretty '<expression>'
phil --format json '<expression>'
phil --no-simplify '<expression>'
phil --explain-parse '<expression>'
phil --latex '<expression>'
phil --latex-inline '<expression>'
phil --latex-block '<expression>'
phil --wa '<expression>'
phil --wa --copy-wa '<expression>'
phil --color always '<expression>'   # also: auto (default), never
phil "ode y' = y"
phil "ode y' = y, y(0)=1"
phil "linalg solve A=[[2,1],[1,3]] b=[1,2]"
phil "linalg rref A=[[1,2],[2,4]]"
phil "linalg det A=[[1,2],[3,4]]"
phil "linalg inv A=[[1,2],[3,4]]"
phil "linalg eig A=[[1,2],[3,4]]"
phil "linalg nullspace A=[[1,2],[2,4]]"
phil :examples
phil :tutorial
phil :ode
phil :linalg

Interactive REPL

phil
phil> <expression>

REPL commands:

• :h / :help show strict command reference
• ?, ??, ??? progressive feature discovery (quick start, speed shortcuts, advanced demos)
• :examples show runnable expression patterns
• :tutorial / :t / :tour start interactive tutorial mode
• :ode show ODE cheat sheet and templates
• :linalg / :la show linear algebra cheat sheet and templates
• :next / :repeat / :done control interactive tutorial mode (Enter advances while tutorial is active)
• :v / :version show current version
• :update / :check compare current vs latest version and print update command
• :q / :quit / :x exit

The REPL starts with phil vX.Y.Z REPL [status] (:h help, :t tutorial) on interactive terminals. When an update is available, startup prints uv tool upgrade philcalc on the next line. Errors are prefixed with E: followed by a hint: line. Most evaluation errors also include hint: try WolframAlpha: <url> (suppressed for some local guardrail failures). Session keeps ans (last result) and supports assignment: A = Matrix([[1,2],[3,4]]). Inline CLI options work per-expression: --latex d(x^2, x). For readable ODE solving, prefer ode ... input: ode y' = y.

Parsing and Input Style

These normalizations apply in all modes (including --strict):

• {} -> ()
• ln(t) -> log(t)
• ! factorial
• sin^2(x) accepted
• Leibniz shorthand accepted (d(sin(x))/dx, df(t)/dt)
• ODE shorthand accepted (dy/dx = y, y' = y, y'' + y = 0, y'(0)=0)
• LaTeX-style ODE accepted (\frac{dy}{dx} = y, \frac{d^2y}{dx^2} + y = 0)
• Common LaTeX wrappers and commands are normalized: $...$, \(...\), \sin, \cos, \ln, \sqrt{...}, \frac{a}{b}

Relaxed parsing (default) also enables implicit multiplication:

• 2x -> 2*x
• sinx -> sin(x) (with a hint: notice)

Use --strict to require explicit multiplication:

phil --strict '2*x'

Undefined symbols raise errors. Built-in helper names are reserved for evaluation and cannot be reassigned. In ODE input, prefer explicit multiplication (20*y instead of 20y) for predictable parsing.

Exact Arithmetic and Reliability

phil defaults to exact symbolic arithmetic.

Cancellable huge expressions stay fast and exact:

10^10000000000 + 1 - 10^10000000000  ->  1
2^(2^20) + 1 - 2^(2^20)  ->  1

Non-cancellable explosive growth fails fast with a recovery hint rather than hanging:

10^10000000000 + 1
2^(2^(2^20))
100001!
factorial(10^10)

Ambiguous shorthand is rejected with explicit guidance:

sin x^2

Precedence note:

• -2^2 -> -(2^2)
• Use (-2)^2 for a negative base squared.

Output and Interop

• --format json prints a compact JSON object with input, parsed, and result; diagnostics stay on stderr
• --format pretty improves matrix readability
• --explain-parse prints hint: parsed as: ... on stderr
• --color auto|always|never controls ANSI output on diagnostic lines; NO_COLOR also respected
• stdout stays result-only, so pipes and scripts remain predictable
• Complex expressions print a WolframAlpha equivalent link by default; --wa forces it, --copy-wa copies it to the clipboard

Updates

uv tool upgrade philcalc

In REPL:

• Startup prints a status badge on interactive terminals; when an update is available a second line prints the upgrade command
• :version shows your installed version
• :update / :check show current version, latest known release, and update command

For release notifications on GitHub, use "Watch" -> "Custom" -> "Releases only" on the repo page.

Examples

$ phil '1/3 + 1/6'
1/2

$ phil 'd(x^3 + 2*x, x)'
3*x**2 + 2

$ phil 'int(sin(x), x)'
-cos(x)

$ phil 'solve(x^2 - 4, x)'
[-2, 2]

$ phil 'N(pi, 30)'
3.14159265358979323846264338328

$ phil --latex 'd(x^2, x)'
2 x

$ phil --latex-inline 'd(x^2, x)'
$2 x$

$ phil --latex-block 'd(x^2, x)'
$$
2 x
$$

$ phil --format pretty 'Matrix([[1,2],[3,4]])'
[1  2]
[3  4]

Reference

Core operations

Operation	Syntax
Derivative	d(expr, var)
Integral	int(expr, var)
Solve equation	solve(expr, var)
Solve ODE	dsolve(Eq(...), func)
Equation	Eq(lhs, rhs)
Numeric eval	N(expr, digits)
Integer GCD/LCM	gcd(a, b), lcm(a, b)
Primality / factorization	isprime(n), factorint(n)
Rational parts	num(expr), den(expr)
Matrix determinant	det(Matrix([[...]])) or linalg det A=[[...]]
Matrix inverse	inv(Matrix([[...]])) or linalg inv A=[[...]]
Matrix rank	rank(Matrix([[...]])) or linalg rank A=[[...]]
Matrix eigenvalues	eigvals(Matrix([[...]])) or linalg eig A=[[...]]
Matrix RREF	rref(Matrix([[...]])) or linalg rref A=[[...]]
Matrix nullspace	nullspace(Matrix([[...]])) or linalg nullspace A=[[...]]
Solve linear system (Ax=b)	msolve(Matrix([[...]]), Matrix([...])) or linalg solve A=[[...]] b=[...]
Symbolic linear solve	linsolve((Eq(...), Eq(...)), (x, y))

Notes: For Ax=b, use linalg solve A=[[...]] b=[...] or msolve(A, b) instead of solve(A=..., b=...).

Common symbols

x, y, z, t, pi, e, f

Functions

sin, cos, tan, exp, log, sqrt, abs, gamma, atan2, binomial, limit, series, factor, expand

Exact arithmetic helpers

gcd, lcm, isprime, factorint, num, den

Symbol helpers

• symbols("A B C") returns a tuple of symbols
• S("A") is shorthand for Symbol("A")

Matrix helpers

Matrix, eye, zeros, ones, det, inv, rank, eigvals, rref, nullspace, msolve, linsolve

Syntax notes

• ^ is exponentiation (x^2)
• Function exponent notation is accepted (sin^2(x), cos^2(x))
• ! is factorial (5!)
• Relaxed mode (default) allows implicit multiplication (2x); use --strict to require 2*x
• d(expr) / int(expr) infer the variable when exactly one symbol is present
• Leibniz shorthand is accepted: d(sin(x))/dx, df(t)/dt
• ODE shorthand is accepted: dy/dx = y, y' = y, y'' + y = 0, y'(0)=0
• LaTeX-style ODE shorthand is accepted: \frac{dy}{dx} = y, \frac{d^2y}{dx^2} + y = 0
• name = expr assigns in the REPL session (ans is always the last result)
• Built-in helper names are reserved and cannot be reassigned
• Undefined symbols raise an error

Development

From a local clone:

uv tool install .                               # install locally
uv run --group dev pytest                       # run tests
uv run --group dev pytest -m "not integration" # fast local loop
scripts/checks.sh                              # full quality gate

CI runs via GitHub Actions. License is MIT. See CONTRIBUTOR.md for contribution guide and release process.