Math Frame

MathFrame is way more than just a chat calculator—it is a comprehensive, highly secure symbolic math engine, data analysis tool, and interactive visualization suite built directly into Discord.

Because it runs on SymPy and a heavily customized parsing engine, it actually "understands" the math you type (whether you write it in plain text, Python syntax, or LaTeX) rather than just crunching numbers.

Here is the deep dive into its full capabilities across different domains:

⚙️ The Core Engine & Step-by-Step Solving

MathFrame doesn't just spit out the final answer; it acts like a tutor. For complex operations like evaluating integrals, calculating derivatives, factoring polynomials, or solving quadratic equations, the bot provides a numbered, step-by-step breakdown of how it reached the solution. It also features a per-user session memory, meaning you can define custom variables (e.g., a = x^2 + 1) and reuse them across multiple commands without retyping them.

📈 Interactive Plotting & Visualization

The bot features a massive 13-mode plotting engine powered by Matplotlib. You don't just type a command and get a static image; you open a full interactive builder inside Discord.

• Supported Plots: 2D/3D parametric curves, vector fields, heatmaps, contour plots, wireframes, polar coordinates, and implicit inequalities.
• Interactivity: You can pan, zoom, tweak the resolution, change the color maps, and adjust axis limits via interactive buttons.
• Interpolation & Animation: You can pass it a set of raw data points, and it will fit a Lagrange polynomial or cubic spline. It can even generate animated GIFs of mathematical functions over time.

🧮 Calculus & Advanced Analysis

MathFrame handles university-level calculus and functional analysis:

• Operations: Computes limits, derivatives (of any order), definite and indefinite integrals, and Taylor/Maclaurin series expansions.
• Vector Calculus: Computes the gradient, divergence, and curl of multi-variable functions.
• Function Analysis: Give it a function, and it will map out its domain, critical points (local max/mins), inflection points, and vertical/horizontal/oblique asymptotes.
• Transforms: Analytically computes Laplace and Fourier transforms.
• ODEs: Solves ordinary differential equations symbolically.

📊 Data Science & CSV Tools

You can upload an actual .csv file (up to 5MB) directly to the chat, and the bot will use Pandas to process it:

• Generate full descriptive statistical tables for the numeric columns.
• Filter the dataset using query strings (e.g., "age > 30").
• Instantly generate scatter, bar, or line plots right from the spreadsheet.
• It also features a unified statistics module for visualizing standard distributions (Normal, Binomial, Poisson), running linear regressions, and calculating z-scores and Pearson correlations.

🔢 Linear Algebra & Matrices

If you are working with matrices and vectors, the bot handles the heavy lifting:

• Computes determinants, exact fractions of inverses, and eigenvalues with algebraic multiplicity.
• Reduces matrices to row-echelon form (RREF).
• Calculates vector dot and cross products.

🧠 Discrete Math & Number Theory

• Boolean Logic: Generates truth tables, simplifies complex boolean expressions, converts them to DNF/CNF forms, and can prove whether two logical statements are strictly equivalent.
• Number Theory: Tests primality for massive numbers, computes prime factorizations, evaluates Euler's totient and the Möbius function, and solves systems using the Chinese Remainder Theorem.

🎓 Educational Tools

Beyond just solving problems, MathFrame includes an interactive, multi-round Quiz Mode that tests users on arithmetic, algebra, and derivative evaluation. It also features a robust unit-conversion system.

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It's essentially a pocket computational algebra system. Which of these mathematical areas do you think you'd end up using the most?