Factorizationmake

Factorizationmake is a term used in computational number theory to describe a modular workflow that applies build-system ideas to integer and polynomial factorization tasks. Conceptually, it treats factorization experiments as targets in a dependency graph, enabling reproducible runs, parameter experiments, and result caching within a Make-like framework.

Originating from the analogy between factorization processes and software build processes, the name fuses factorization with Make, a widely used build automation tool. It is not a widely standardized standard, but appears in niche discussions and experimental projects that seek to automate factorization pipelines.

Implementation typically involves a configuration file modeled on Makefiles, with rules for running specific algorithms (trial division, Pollard's rho, ECM, GNFS, SNFS) and for selecting parameters. It can orchestrate external tools (GMP, MPIR, yafu, CADO-NFS) and provide hooks for data management, logging, and caching of intermediate results. A factorization task can depend on precomputed data, such as partial factorizations or smooth numbers, so that the workflow is incremental.

Common use cases include benchmarking and reproducibility of factorization experiments, educational demonstrations of methods, and automated testing of new algorithms against standard datasets. Benefits include improved repeatability, structured experimentation, and easier integration of diverse software components; drawbacks include the overhead of maintaining Makefile-like configurations, potential fragility of long-running tasks, and dependence on external software with varying licenses and interfaces.

Related concepts include the Make build tool, integer factorization algorithms, and automated scientific workflows. Factorizationmake remains a niche concept rather than a mainstream tool.