SymPy
SymPy is an open-source Python library for symbolic mathematics and computer algebra.
Geometry for Programmers
An open-source Python library for symbolic mathematics, including algebraic manipulation, computation, and code generation.
- How it is used
- Automates algebra and equation solving while developing applied-geometry formulas and implementations.
- How deep it goes
- Demonstrates symbolic variables, equation systems, generated formulas, code output, and matrix-based least-squares solving, while deferring solver internals.
- Examples
- Uses train speeds, small linear systems for raytracing, and rowing-time data fitted by a linear polynomial.
- What you can do after
- Apply it via SymPy to solve small equation systems, derive reusable formulas, and extract polynomial coefficients.
Optimization Algorithms: AI techniques for design, planning, and control problems
An open-source Python library for symbolic mathematics, including algebra, calculus, equation solving, and combinatorics.
- How it is used
- Applies symbolic mathematics to combinatorial calculations and constrained optimization in Python.
- How deep it goes
- Demonstrates direct calculations and a worked Lagrange-multiplier implementation, while deferring broader usage to documentation.
- Examples
- Uses binomial coefficients, Stirling numbers, traveling-salesman permutations, and ticket-sales optimization as concrete examples.
- What you can do after
- Apply SymPy to calculate combinatorial expressions, differentiate symbolic objectives, and solve constrained optimization equations.
Build a Reasoning Model (From Scratch)
An open-source Python library for symbolic mathematics used here to parse and compare expressions for equivalence.
- How it is used
- Uses symbolic parsing to verify free-form mathematical answers against reference solutions.
- How deep it goes
- Implements parsing, safeguards, error handling, and difference-based equivalence, stopping short of broader evaluation design.
- Examples
- Demonstrates equivalent forms such as 28/6 and 14/3, plus 0.5 and 1/2.
- What you can do after
- Apply it via SymPy to parse normalized expressions and diagnose malformed or mathematically unequal answers.
Read how Build a Reasoning Model (From Scratch) explains SymPy →
Related concepts
- computer algebra systemkind of · A computer algebra system is software that performs exact or symbolic mathematical manipulation and computation.
- symbolic solverkind of · A symbolic solver is a computational procedure or software component that derives algebraic solutions in symbolic form.
- symbolic solutionproduces · A symbolic solution is an algebraic solution expressed in terms of symbols and parameters rather than only evaluated numbers.
- linear systemaddresses · A linear system is a set of linear relationships among variables, commonly expressed as simultaneous equations or a linear transformation, for which superposition applies.
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