pydisks 0.1.0

Volumes and surface areas of solids of revolution (disc, washer, shell) via SymPy.

pydisks

Compute volumes and surface areas of solids of revolution — the disc, washer, and shell methods plus surface area of revolution — symbolically, using SymPy. Built for checking calculus homework: you get an exact answer, and mistakes (wrong variable, self-intersecting solids, curves in the wrong order) raise clear errors instead of silently returning a wrong number.

Install

pip install pydisks

Quick start

from pydisks import disc, washer, shell, surface_area, revolve, x, y
import sympy as sp

# Volume of a sphere of radius 2: revolve y = sqrt(4 - x^2) about the x-axis
disc(sp.sqrt(4 - x**2), -2, 2)          # -> 32*pi/3

# Washer: region between y = x and y = x^2 on [0, 1], about the x-axis
washer(x, x**2, 0, 1)                    # -> 2*pi/15

# Shell: revolve y = x^2 on [0, 2] about the y-axis
shell(x**2, 0, 2)                        # -> 8*pi

# Dispatcher: disc if no inner curve, else washer; also gives a float check
revolve(x, 0, 3)                         # -> {'method': 'disc', 'volume': 9*pi, 'approx': 28.27...}

The axis of rotation

The axis is written as a string — either a named axis or a line equation:

You write	Means	Line
"x"	the x-axis	y = 0
"y"	the y-axis	x = 0
"x=2"	vertical line	x = 2
"y=-1"	horizontal line	y = -1

A bare letter names an axis; an equation is a literal line. Note the asymmetry this creates: "x" is the x-axis (y = 0), but "x=0" is the line x = 0 (the y-axis).

The variable you write your curve in is derived from the axis and method:

• disc / washer / surface_area: horizontal axis → f(x); vertical axis → f(y)
• shell: horizontal axis → f(y); vertical axis → f(x)

If you pass a curve in the wrong variable, pydisks raises VariableMismatchError rather than trying to invert it for you — solving for the right variable is part of the problem.

Functions

Function	Method
disc(f, a, b, axis="x")	region between f and the axis
washer(outer, inner, a, b, axis="x")	region between two curves; outer stays farther from the axis
shell(f, a, b, axis="y", bottom=0)	cylindrical shells; pass bottom for a two-curve region
surface_area(f, a, b, axis="x")	surface area of revolution
revolve(f, a, b, axis="x", inner=None)	disc/washer dispatcher; returns {method, volume, approx}

Errors

Every error subclasses RevolutionError, and messages name the likely fix. Validation runs before integration:

Exception	When
AxisError	malformed axis string/pair
VariableMismatchError	curve or bound in the wrong variable
BoundsError	non-constant bounds, or a >= b
SelfIntersectingSolidError	the axis passes through the region
CurveCrossingError	two boundary curves cross or are given in the wrong order
DomainError	curve discontinuous on [a, b]
UnevaluatedIntegralError	SymPy found no closed form

Caveat: the geometric and domain checks use sp.solve / continuous_domain, which quietly no-op when the bounds are symbolic or SymPy can't solve. They catch common concrete-number mistakes, not every symbolic edge case — treat a returned volume as validated only for numeric bounds.

Tests

python3 -m pytest test_main.py -v                  # all tests
python3 -m pytest test_main.py::test_disc_sphere   # a single test

License

MIT — see LICENSE.