Equation Visualizer

A desktop app that shows you what a math equation does — from basic arithmetic up to 3D surfaces, systems, and differential equations. Type any equation or function and it plots it, marks its roots, draws its derivative and tangent line, shades the area under the curve, and shows real step-by-step solving. Works fully offline on a PC — no account, no internet needed after install.

What it does

• 2D plots of any function with labeled axes, grid, and the equation on the plot — e.g. y = x^2, y = sin(x), y = e^x, y = |x|
• Roots marked on the plot: where the curve crosses y = 0, plus the solution values of equations like 2x + 3 = 7 and x^2 - 5x + 6 = 0
• Derivative view: plots f(x) and f'(x) together, plus the tangent line at any x you choose
• Integral view: shades the area under the curve between two bounds and shows the computed area value
• Step-by-step solving for linear, quadratic, and cubic equations, plus systems — computed from real coefficients (not canned text): discriminant, quadratic formula, factored form where it applies
• Complex roots: equations with a negative discriminant show their complex roots, clearly labeled as complex
• Interactive sliders: functions with parameters a, b, c (e.g. y = a*x^2 + b*x + c) update live as you drag the sliders
• Multiple functions on one plot, each with its own color and legend
• 3D surface plots for two-variable functions, e.g. z = x^2 + y^2
• Systems of equations: two equations in two unknowns, solved and plotted with the intersection point marked
• Implicit plots: curves like the circle x^2 + y^2 = 25 and the ellipse x^2/9 + y^2/4 = 1
• Parametric curves: x = cos(t), y = sin(t), Lissajous figures
• Polar plots: r = 2*sin(3*theta) rose curves
• Basic math, exact: arithmetic and fractions stay exact (1/2 + 1/3 = 5/6), trigonometry evaluated exactly (sin(pi/3) = sqrt(3)/2), and limits (sin(x)/x at 0 = 1)
• Simple ODEs: first-order equations like dy/dx = y solved with sympy and plotted as solution curves for several constants
• Matrices: determinant, trace, inverse (when it exists), eigenvalues, and +, -, * between two matrices
• 32 one-click presets covering every area above, so a first-time user sees it work instantly
• Plain-language errors: invalid input shows a message, never a crash
• Save plot as PNG from the app

How to run

Windows

pip install -r requirements.txt
python main.py

Linux / macOS

pip install -r requirements.txt
python3 main.py

Tkinter ships with most Python installs. On Debian/Ubuntu, if it is missing: sudo apt install python3-tk.

Try it

Then click Derivative (tangent at your chosen x) or Integral (shaded area between your chosen bounds). For calc:, limit:, matrix: and ode: inputs, Compute shows the text answer.

How it works

• main.py — Tkinter GUI, the app entry point
• equation_engine.py — all math: parsing (sympy), roots, derivative, integral, step-by-step solving, and matplotlib plots
• test_engine.py — headless verification (see below)

Input accepts ^ for powers, implicit multiplication (2x), ln(x), and |x|. Only x is the variable; anything else is reported as an unknown name instead of silently mis-parsing.

Tests (verified)

python3 test_engine.py

All 115 checks pass: all 32 presets parse/plot/compute, quadratic roots 2 and 3, linear root 2, derivative of x² is 2x with tangent slope 2 at x = 1, integral of x² from 0 to 3 is 9, a real sine PNG is saved (27,137 bytes), and bad input ("", y =, x^^2, hello world) is rejected with a plain error. v2 checks: slider substitution gives roots 2 and 3, 3D surface f(1, 2) = 5, system solves to (3, 2), complex roots of x² + 1 are ±i, cubic roots 1, 2 and 3, parametric circle starts at (1, 0), polar rose r(pi/6) = 2. Breadth checks: 1/2 + 1/3 = 5/6 exactly, sin(pi/3) = sqrt(3)/2, limits sin(x)/x at 0 = 1 and (x²−1)/(x−1) at 1 = 2, ODE dy/dx = y gives C1·e^x with the C = 1 curve equal to 1 at x = 0, matrix [[1,2],[3,4]] has det −2, inverse [[−2, 1], [3/2, −1/2]] and eigenvalues (5 ± sqrt(33))/2, and a singular matrix is reported as having no inverse instead of crashing. Sample plots are in screenshots/.

Known limitations (honest gaps)

• The GUI window itself was not opened in this Linux VM (no display available headlessly). The math/plotting engine is fully verified via test_engine.py and main.py compiles cleanly, but the Tk window has not been clicked through on a real desktop yet — please run python main.py on a PC with a display to confirm the window.

Still not supported (not claimed, not faked)

• Partial differential equations (PDEs) and systems of ODEs — only single first-order ODEs that sympy's dsolve can actually solve. Anything else shows an error, not an invented solution.
• Matrix decompositions (LU, QR, SVD) and matrix calculus.
• 3D implicit surfaces (e.g. a sphere as x² + y² + z² = 25) — 3D covers explicit surfaces z = f(x, y) only.
• Statistics, probability, and number theory (distributions, hypothesis tests, prime factorization beyond sympy's basic factoring).
• Multi-variable calculus beyond 3D surfaces: no partial-derivative or double-integral views yet.
• Step-by-step working for limits, ODEs, and matrices — those show the verified answer, not a full worked derivation.
• The default x-range is −10 to 10 (adjustable in the app); very large values can make the y-axis hard to read.

License

MIT — see LICENSE.

Built With

• python