Runnable Examples Catalog

Focus: Polynomial functions

Demonstrates plotting of basic polynomial expressions: parabola (x²), cubic (x³), quadratic with linear term, and higher degree polynomial (x⁴ - 2x²).

Focus: Trigonometric functions

Plots various trigonometric expressions including sin(x), cos(x), frequency modulation sin(2x), amplitude scaling 2·sin(x), combinations sin(x) + cos(x), and composition sin(x²).

Focus: Exponential and logarithmic functions

Demonstrates exp and ln functions including exp(x), ln(x), exponential decay exp(-x), compositions like exp(x²), ln(x²), exp(sin(x)), and products like x·exp(-x).

Focus: Rational functions (ratios of polynomials)

Plots various rational expressions including simple reciprocals 1/x and 1/x², proper rationals like x/(x²+1), classic curves like Witch of Agnesi 1/(1+x²), and higher degree rationals.

Focus: Various power functions including fractional exponents

Demonstrates different exponent types: fractional exponents x^(1/2), x^(1/3), x^(3/2), x^(2/3), negative fractional x^(-1/2), compositions (x²)^(1/2), and higher odd powers x⁵.

Focus: Complex function compositions

Shows nested and combined functions: trig compositions sin(cos(x)), exp + trig exp(cos(x)) and sin(exp(x/2)), log compositions ln(x²+1) and ln(sin(x)+2), oscillating x·sin(1/x), and damped cos(x)·exp(-x²).

Focus: PlotConfig parameters and their effects

Demonstrates different configuration settings: sampling rates (20, 100, 500), plot dimensions (small 200×150, standard 400×300, large 800×600), x-axis ranges (narrow [-1,1], wide [-20,20]), and aspect ratios (square, wide).

Focus: Functions with their derivatives

Plots functions alongside their derivatives: parabola x² and 2x, trig sin(x) and cos(x), exponential exp(x) and exp(x), cubic x³-3x and 3x²-3, logarithm ln(x) and 1/x, and second derivatives x⁴, 4x³, 12x².

Focus: End-to-end workflow combining multiple features

Comprehensive demonstration: building complex expressions (x+1)²·sin(x)/(x²+1), simplification, LaTeX output, plotting, differentiation, pattern substitution (x → 2x), and multiple visualizations.

Focus: Special behaviors and edge cases

Demonstrates how the plotter handles: discontinuities (1/x at x=0), domain restrictions (ln(x) for x≤0), vertical asymptotes (tan(x)), rapid oscillation sin(1/x), large dynamic range exp(x), constant functions, steep slopes x¹⁰, and complex domains x^(-1/2).

Focus: Polynomial algebra and operations

Demonstrates polynomial operations including factorization, GCD computation, partial fraction decomposition, and resultants using the polys crate.

Focus: Expression serialization and parsing

Demonstrates various I/O formats: S-expression parsing and serialization, JSON serialization, and LaTeX output for mathematical typesetting.

Focus: Exact matrix operations over rationals

Demonstrates matrix operations: creation, determinant computation (Bareiss algorithm), RREF (row reduction), matrix inversion, and solving linear systems.