Multivariable Calculus Lab
Numeric gradient, directional derivative, Jacobian, and Hessian calculations with local visualization.
Open ToolSymbolicComputation.com / Tools
Interactive Tools
These tools are meant to be genuinely useful for students, engineers, developers, and researchers. Some are calculation-heavy, some are visualization-first, and some are miniature symbolic laboratories built to make abstract ideas concrete.
Polynomial Root And Shape Lab
Analyze polynomial curves, real and complex roots, critical points, and overall shape.
Open ToolRecurrence Explorer
Generate and inspect linear recurrences, term growth, and simple closed-form descriptions.
Open ToolSeries And Fourier Lab
Compare a function against its Taylor approximation and Fourier partial sums.
Open ToolSymbolic Rewrite Lab
Experiment with miniature rewrite systems, normal forms, confluence, termination, and toy e-graph clusters.
Open ToolUnification And Matching Lab
See how pattern variables bind in a small first-order symbolic setting.
Open ToolTensor Index Lab
Inspect Einstein-style signatures and compute small tensor contractions directly in the browser.
Open ToolHow These Tools Are Meant To Be Used
Each page is built to be useful in two ways at once: as a practical calculator or visualization, and as a compact lesson in the mathematical structure behind the result. You can usually start with the default example, press the main button, then make one change at a time to see what the outputs are responding to.
- Use the calculus, polynomial, recurrence, and series pages for concrete numerical work.
- Use the rewrite and unification pages to understand structural symbolic ideas step by step.
- Use the tensor page to check index notation and small contractions before moving to larger systems.
The Mathematics Behind The Shelf
The tools cluster follows the same theme as the rest of SymbolicComputation.com: mathematical structure matters. Some tools study local change through derivatives and linearization. Some study algebraic structure through roots, recurrences, and series. Others study symbolic structure through rewriting, unification, and index notation.
That mix is deliberate. It keeps the tools useful for students and engineers while also reinforcing how symbolic and mathematical reasoning connect across the site.