deriveaz

Deriveaz is a fictional open-source software framework described in hypothetical discussions of symbolic mathematics and differentiable programming. It is conceived as a modular platform that combines symbolic differentiation with automatic differentiation to derive expressions, derivatives, and higher-order quantities from user-defined formulas.

Overview

Deriveaz provides a parser for algebraic expressions, a rule-based differentiation engine, and facilities for higher-order derivatives, Jacobians, and Hessians. It supports symbolic differentiation rules such as the product, quotient, and chain rules, as well as directional and mixed derivatives. The system includes expression simplification, common subexpression elimination, and code-generation capabilities to languages like Python, C++, and JavaScript. It is designed to work in interactive environments and scriptable pipelines, enabling users to derive analytic forms, perform derivative-based optimization, or generate derivative code for numerical solvers.

Architecture and design

In the imagined architecture, a core calculus kernel handles differentiation logic, while a rule engine applies transformations to expressions. A modular plugin system allows extensions for nonstandard functions, domain-specific simplifications, and custom differentiation rules. Cross-language bindings and integration points with existing computer algebra systems are envisioned to enhance interoperability. Deriveaz emphasizes reproducibility, with deterministic transformation sequences and traceable derivative outputs.

History and usage

As a hypothetical construct, deriveaz is described in thought experiments and educational scenarios to illustrate how symbolic and automatic differentiation might coexist in a single toolkit. It is commonly cited in discussions about differentiable programming, teaching calculus, and exploring derivative-based optimization concepts, rather than as a real, deployed software project.

See also

Symbolic computation, automatic differentiation, computer algebra system.