Math Frame

MathFrame

MathFrame is a powerful Discord math bot built for students, educators, and anyone who loves mathematics. It brings a full symbolic and numeric computation engine directly into your server through clean, intuitive slash commands — no setup, no external tools, just type and get answers.

What It Can Do

Algebra & Arithmetic
Simplify, expand, factor, and solve equations step by step. Verify if two expressions are equivalent, divide polynomials, or generate value tables for any function. MathFrame accepts plain notation like x^2 + 2x, Python-style x2, natural language like x squared plus 2x, or full LaTeX — it detects the format automatically.

Calculus
Differentiate and integrate symbolically with full step-by-step working. Evaluate limits, compute Taylor series, summations, products, and solve ordinary differential equations. Laplace, Inverse Laplace, Fourier, and Inverse Fourier transforms are also supported.

Linear Algebra
Compute determinants, matrix inverses, eigenvalues, dot products, cross products, and reduced row-echelon form — all with exact rational arithmetic, no floating-point rounding.

Statistics & Probability
Descriptive statistics (mean, median, mode, standard deviation, variance), Pearson correlation, linear regression with a plotted chart, and a unified probability distribution command covering Normal, Binomial, and Poisson distributions with visual PDF/CDF plots.

Number Theory
GCD, LCM, primality testing up to 10¹², prime factorization up to 10¹⁵, Euler's totient, Möbius function, divisors, perfect number checking, and the Chinese Remainder Theorem.

Geometry
Circle area and circumference, triangle area (base-height or Heron's formula), the Pythagorean theorem, trigonometric evaluation with exact and decimal results, and Euclidean distance in 2D or 3D.

Discrete Math & Logic
Permutations, combinations, full truth tables, set operations, Boolean simplification (Simplified / DNF / CNF), and logical equivalence checking with counterexample witnesses — built on a custom parser that never calls eval().

Symbolic Tools
Partial fraction decomposition, root finding with multiplicity, expression substitution, and an expression classifier that identifies whether an expression is polynomial, rational, trigonometric, exponential, even/odd, periodic, or constant.

Complex Numbers
Evaluate complex expressions, convert between rectangular and polar form, and display results as a + bi or r·e^(iθ).

Base-N Arithmetic
Convert numbers between any bases from 2 to 36, evaluate arithmetic in a custom base, and run bitwise logic operations.

Interactive Plotting
The plot builder supports 13 plot types: standard functions, contour plots, vector fields, parametric curves (2D and 3D), surfaces, wireframes, scatter plots, polar plots, implicit curves, inequality regions, and heatmaps. Build and refine your plot through a modal-based UI with pan, zoom, style controls, and animation support. Export your session as a shareable string and recreate it anywhere with /plot_import. For quick results, /quickplot renders a function instantly with no UI at all.

Rendering
Convert any expression or LaTeX string into a clean PNG image using matplotlib's math typesetting engine.

Unit Conversion
Convert between units across 10 categories: length, mass, temperature, time, area, volume, speed, force, energy, and power.

Wikipedia
Browse Wikipedia articles paragraph by paragraph and search for topics without leaving Discord.

Smart Inputs, Safe Computation**
MathFrame automatically detects whether you're typing plain math, Python-style notation, natural language, or LaTeX — no mode-switching required. All expressions are validated before parsing: inputs are length-capped, screened for dangerous keywords, and executed under a hard 3-second timeout so no pathological expression can stall the bot. Results are cached for 5 minutes so repeated queries return instantly.