000131386 001__ 131386 000131386 005__ 20250612142454.0 000131386 0247_ $$2doi$$a10.1007/978-3-319-42432-3_24 000131386 0248_ $$2sideral$$a106280 000131386 037__ $$aART-2016-106280 000131386 041__ $$aeng 000131386 100__ $$0(orcid)0000-0002-6750-8971$$aMarco-Buzunariz, M.A.$$uUniversidad de Zaragoza 000131386 245__ $$aSIROCCO: A Library for Certified Polynomial Root Continuation 000131386 260__ $$c2016 000131386 5060_ $$aAccess copy available to the general public$$fUnrestricted 000131386 5203_ $$aThe classical problem of studying the topology of a plane algebraic curve is typically handled by the computation of braid monodromies. The existence of arithmetic Zariski pairs implies that purely algebraic methods cannot provide those braids, so we need numerical methods at some point. However, numerical methods usually have the problem that floating point arithmetic introduces rounding errors that must be controlled to ensure certified results. We present SIROCCO (The source code and documentation is available in: https://github.com/miguelmarco/sirocco), a library for certified polynomial root continuation, specially suited for this task. It computes piecewise linear approximations of the paths followed by the roots. The library ensures that there exist disjoint tubular neighborhoods that contain both the actual path and the computed approximation. This fact proves that the braids corresponding to the approximation are equal to the ones corresponding to the actual curve. The validation is based on interval floating point arithmetic, the Interval Newton Criterion and auxiliary lemmas. We also provide a SageMath interface and auxiliary routines that perform all the needed pre and post- processing tasks. Together this is an "out of the box" solution to compute, for instance, the fundamental group of the complement of an affine complex curve. 000131386 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000131386 592__ $$a0.339$$b2016 000131386 593__ $$aComputer Science (miscellaneous)$$c2016$$dQ2 000131386 593__ $$aTheoretical Computer Science$$c2016$$dQ3 000131386 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000131386 700__ $$0(orcid)0000-0003-3426-105X$$aRodriguez, M. 000131386 7102_ $$12006$$2200$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Didáctica Matemática 000131386 773__ $$g9725 (2016), 191-197$$pLect. notes comput. sci.$$tLecture Notes in Computer Science$$x0302-9743 000131386 8564_ $$s135669$$uhttps://zaguan.unizar.es/record/131386/files/texto_completo.pdf$$yPostprint 000131386 8564_ $$s1372940$$uhttps://zaguan.unizar.es/record/131386/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000131386 909CO $$ooai:zaguan.unizar.es:131386$$particulos$$pdriver 000131386 951__ $$a2025-06-12-14:23:36 000131386 980__ $$aARTICLE