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arXiv · 2607.09339

PCPOP.jl: A Julia package for partially commutative polynomial optimization

Moisés Bermejo Morán·Abhishek Mishra
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Abstract

Here we present PCPOP, a Julia package for polynomial optimization that supports non-commutative optimization, tracial polynomial optimization, trace polynomial optimization and state polynomial optimization. PCPOP fully supports exact arithmetic computations and incorporates convenient functionalities such as algebraic reductions based on Gr\"obner basis methods, automatized symmetrization via Wedderburn decompositions, and Jordan algebra reductions. As a distinguished feature, PCPOP implements a specialized framework for polynomial computations in partially commutative variables that provides significant computational advantages for problems appearing in quantum information.

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Moisés Bermejo Morán, Abhishek Mishra. 2026-07-10. PCPOP.jl: A Julia package for partially commutative polynomial optimization. https://arxiv.org/abs/2607.09339

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