phil

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

Powered by SymPy.

Positioning and Philosophy

• phil is built to be the first-stop calculator for quick terminal math, homework, and symbolic workflows.
• It aims to be the fastest practical choice before opening WolframAlpha, Google, Python REPL, or Calculate84.
• It is not trying to replace Desmos for graphing-first workflows.
• Priorities: speed, correctness, and discoverability.
• Input should be forgiving: when phil makes an assumption, it should make that interpretation visible to the user.

Inspiration

• phil was inspired by chadnauseam.com/coding/random/calculator-app.
• A core motivating example is exact arithmetic on very large expressions:
  • 10^10000 + 1 - 10^10000 = 1

Roadmap

• See ROADMAP.md for planned v0.3.0 and v1.0.0 milestones.

Install

Requires uv.

Install from PyPI (no clone required):

uv tool install philcalc

Then run:

phil

Project links:

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

Local Development Install

From a local clone:

uv tool install .

60-Second Start

uv tool install philcalc
phil --help
phil '1/3 + 1/6'
phil '10^100000 + 1 - 10^100000'
phil '(1 - 25e^5)e^{-5t} + (25e^5 - 1)t e^{-5t} + t e^{-5t} ln(t)'
phil

Then in REPL, try:

1. d(x^3 + 2*x, x)
2. int(sin(x), x)
3. solve(x^2 - 4, x)
4. msolve(Matrix([[2,1],[1,3]]), Matrix([1,2]))

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 auto '<expression>'
phil --color always '<expression>'
phil --color never '<expression>'
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 --latex 'dy/dx = y'
phil 'dsolve(Eq(d(y(x), x), y(x)), y(x))'
phil :examples
phil :tutorial
phil :ode
phil :linalg

Interactive

phil
phil> <expression>

REPL commands:

• :h / :help show strict command reference
• ? / ?? / ??? progressive feature discovery (quick start, speed shortcuts, advanced demos)
• :examples show runnable high-signal expression patterns
• :tutorial / :t / :tour show guided first-run tour
• :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 to next step 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 (for example, [latest] or [vX.Y.Z available]). When an update is available, startup prints uv tool upgrade philcalc on the next line. REPL prints targeted hint: messages on common errors. Unknown : commands return a short correction hint. Evaluation errors also include: hint: try WolframAlpha: <url>. Complex expressions also print a WolframAlpha equivalent hint after successful evaluation. REPL sessions also keep ans (last result) and support assignment such as A = Matrix([[1,2],[3,4]]). REPL also accepts inline CLI options, e.g. --latex d(x^2, x) or phil --latex "d(x^2, x)". For readable ODE solving, use ode ... input (example: ode y' = y).

Help

phil --help

Wolfram helper

• By default, complex expressions print a WolframAlpha equivalent link.
• Links are printed as full URLs for terminal auto-linking (including iTerm2).
• Use --wa to always print the link.
• Use --copy-wa to copy the link to your clipboard when shown.
• Full URLs are usually clickable directly in modern terminals.

Color diagnostics

• Use --color auto|always|never to control ANSI color on diagnostic lines (E: and hint:).
• Default is --color auto (enabled only on TTY stderr, disabled for pipes/non-interactive output).
• NO_COLOR disables auto color.
• --color always forces color even when output is not a TTY.

Interop Output

• --format json prints a compact JSON object with input, parsed, and result.
• --format json keeps diagnostics on stderr, so stdout remains machine-readable.

Clear Input/Output Mode

• Use --format pretty for easier-to-scan rendered output.
• Use --explain-parse to print hint: parsed as: ... on stderr before evaluation.
• Combine with relaxed parsing for shorthand visibility, e.g. phil --explain-parse 'sinx'.
• stdout stays result-only, so pipes/scripts remain predictable.

Updates

From published package (anywhere):

uv tool upgrade philcalc

From a local clone of this repo:

uv tool install --force --reinstall --refresh .

Quick check in CLI:

phil :version
phil :update
phil :check

In REPL:

• Startup (interactive terminals) prints a one-line up-to-date or update-available status.
• :version shows your installed version.
• :update/:check show current version, latest known release, and update command.
• ?, ??, ??? progressively reveal shortcuts and capability demos.

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

Release

Tagged releases are published to PyPI automatically via GitHub Actions trusted publishing. Draft GitHub Release notes live under release-notes/ and should be finalized at tag time. Use scripts/release_notes.sh <version> --body to print copy/paste-ready GitHub Release text.

git pull
git tag -a v0.2.0 -m "Release v0.2.0"
git push origin v0.2.0
# or
scripts/release.sh 0.2.0

Then verify:

• GitHub Actions run: https://github.com/sacchen/phil/actions
• PyPI release page: https://pypi.org/project/philcalc/

Long Expressions (easier input)

phil now uses relaxed parsing by default:

• 2x works like 2*x
• sinx works like sin(x) (with a hint: notice)
• {} works like ()
• ln(t) works like log(t)

So inputs like these work directly:

phil '(1 - 25e^5)e^{-5t} + (25e^5 - 1)t e^{-5t} + t e^{-5t} ln(t)'
phil '(854/2197)e^{8t}+(1343/2197)e^{-5t}+((9/26)t^2 -(9/169)t)e^{8t}'
phil 'dy/dx = y'

Use strict parsing if needed:

phil --strict '2*x'

Reliability and Recovery

phil is optimized to recover quickly on pathological input while keeping exact math behavior where possible.

• Cancellable huge expressions stay fast and exact:
  • 10^10000000000 + 1 - 10^10000000000 -> 1
  • 2^(2^20) + 1 - 2^(2^20) -> 1
• Non-cancellable growth fails fast with local recovery hints:
  • 10^10000000000 + 1
  • 2^(2^(2^20))
  • 100001!
  • factorial(10^10)
• Ambiguous high-risk shorthand is rejected with explicit guidance:
  • sin x^2 -> use sin(x^2) or (sin(x))^2

Precedence note:

• -2^2 is interpreted as -(2^2).
• Use (-2)^2 if you want the negative base squared.

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]

Test

uv run --group dev pytest
# quick local loop (skip process-heavy integration tests)
uv run --group dev pytest -m "not integration"
# full local quality gate
scripts/checks.sh

GitHub

• CI: .github/workflows/ci.yml runs tests on pushes and PRs.
• License: MIT (LICENSE).
• Ignore rules: Python/venv/cache (.gitignore).
• Contribution guide: CONTRIBUTOR.md.

Learn by Doing

Try this sequence in REPL mode:

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 you get stuck, run :examples or :h.

Reference

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([[...]]))
Matrix inverse	inv(Matrix([[...]]))
Matrix rank	rank(Matrix([[...]]))
Matrix eigenvalues	eigvals(Matrix([[...]]))
Matrix RREF	rref(Matrix([[...]]))
Matrix nullspace	nullspace(Matrix([[...]]))
Solve linear system (Ax=b)	msolve(Matrix([[...]]), Matrix([...]))
Symbolic linear solve	linsolve((Eq(...), Eq(...)), (x, y))

Symbols

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

Functions

sin, cos, tan, exp, log, sqrt, abs

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
• In ODE input, prefer explicit multiplication (20*y instead of 20y) for predictable parsing.
• Common LaTeX wrappers and commands are normalized: $...$, \(...\), \sin, \cos, \ln, \sqrt{...}, \frac{a}{b}
• name = expr assigns in REPL session (ans is always last result)
• Undefined symbols raise an error

Safety limits

• Expressions longer than 2000 chars are rejected.
• Inputs containing blocked tokens like __, ;, or newlines are rejected.

See DESIGN.md for implementation details.