Table Of ContentFrançois Boulier
Matthew England
Timur M. Sadykov
Evgenii V. Vorozhtsov (Eds.)
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Computer Algebra
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C in Scientific Computing
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24th International Workshop, CASC 2022
Gebze, Turkey, August 22–26, 2022
Proceedings
Lecture Notes in Computer Science 13366
FoundingEditors
GerhardGoos
KarlsruheInstituteofTechnology,Karlsruhe,Germany
JurisHartmanis
CornellUniversity,Ithaca,NY,USA
EditorialBoardMembers
ElisaBertino
PurdueUniversity,WestLafayette,IN,USA
WenGao
PekingUniversity,Beijing,China
BernhardSteffen
TUDortmundUniversity,Dortmund,Germany
MotiYung
ColumbiaUniversity,NewYork,NY,USA
Moreinformationaboutthisseriesathttps://link.springer.com/bookseries/558
· ·
François Boulier Matthew England
·
Timur M. Sadykov Evgenii V. Vorozhtsov (Eds.)
Computer Algebra
in Scientific Computing
24th International Workshop, CASC 2022
Gebze, Turkey, August 22–26, 2022
Proceedings
Editors
FrançoisBoulier MatthewEngland
UniversitédeLille CoventryUniversity
Villeneuved’Ascq,France Coventry,UK
TimurM.Sadykov EvgeniiV.Vorozhtsov
PlekhanovRussianUniversityofEconomics InstituteofTheoreticalandApplied
Moscow,Russia Mechanics
Novosibirsk,Russia
ISSN 0302-9743 ISSN 1611-3349 (electronic)
LectureNotesinComputerScience
ISBN 978-3-031-14787-6 ISBN 978-3-031-14788-3 (eBook)
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Preface
The International Workshop on Computer Algebra in Scientific Computing (CASC)
is an annual forum which aims to bring together the leading scientists, scholars, and
engineersfromthevariousdisciplinesincludingcomputeralgebraandtoattractoriginal
research papers of high quality. This workshop provides a platform for the delegates
toexchangenewideasandapplicationexperiences,shareresearchresults,anddiscuss
existingissuesandchallenges.
Thisyear,CASCwashostednearIstanbul,thelargestcityinTurkeyandthefinancial
andculturalcenterofthecountry.GebzeTechnicalUniversity(GTU)issituatedcloseto
theborderoftheprovincesofIstanbulandKocaeli.GTU(previouslytheGebzeInstitute
ofAdvancedTechnologies–GYTE)isoneoftheleadingresearchinstitutesandoneof
10researchuniversitiesinTurkey.
During the two years of the COVID-19 pandemic, many conferences were either
canceledortookplacefullyonline.Thisimpactedourcommunityandespeciallytheearly
careerresearchers.Adecisionwasmadetogathermanysymboliccomputation/computer
algebra events together in the same place, driven by the need to restore ties in the
community.SCALE(SymbolicComputation:Algorithms,Learning,andEngineering),
athree-weeklongevent,wastheresultofthiseffort.CASC2022wastheconcluding
eventofSCALE.
The choice of Istanbul/Gebze for CASC 2022 was made because Turkey has an
increasing number of symbolic computation researchers. Some years ago, symbolic
computationandcomputeralgebrawerealmostnonexistentinTurkey,buttodaymany
researcherswhoobtainedtheirPh.D.orspenttimeaspost-doctoralresearchersabroad
arebasedinTurkey,togetherwithanumberofforeignresearchers.
The ALCYON lab (Institute of Information Technologies, GTU) was started by
Zafeirakis Zafeirakopoulos six years ago. Its main focus is symbolic computation.
During this period, three nationally and internationally funded research projects
werecarriedout,morethan10researcherswereemployed,andmorethan30students
supervised.Inthelastthreeyears,afurtherthreeresearchprojectsrelatedtocomputer
algebra were granted to researchers based around Istanbul and a joint effort between
computer algebra researchers from different universities was initiated. This led to the
SymbolicComputationIstanbulMeetings(organizedbyTülayAyyıldızAkog˘lu,Türkü
Özlüm Çelik, and Zafeirakis Zafeirakopoulos): a biweekly seminar and social event
series that has successfully ran for a year with local and international speakers and
participants. In addition, the International Mathematics Union approved a grant for
computation in Turkey. In this context there are monthly workshops (organized by
Tülay Ayyıldız Akog˘lu, Can Ozan Og˘uz, and Zafeirakis Zafeirakopoulos) related to
computational mathematics (focused on computer algebra). The first event was the
SagedaysWorkshop,heldaspartofSCALE(twoweeksbeforeCASC2022).
This year, the CASC International Workshop had two categories of participation:
(1) talks with accompanying papers to appear in these proceedings and (2) talks with
accompanyingextendedabstractsfordistributionattheconferenceonly.Thelatterwas
vi Preface
forworkeitheralreadypublishedornotyetreadyforpublication,butineithercasestill
newandofinteresttotheCASCaudience.Theformerwasstrictlyfornewandoriginal
researchresultsorreviewarticles,readyforpublication.
AllpaperssubmittedtotheLNCSproceedingsreceivedaminimumofthreereviews.
Inaddition,thewholeProgramCommittee(PC)wasinvitedtocommentonanddebate
allpapers.Intotalthisvolumecontains20contributedpapers.Alongwiththecontributed
talks,CASC2022hadtwoinvitedspeakers.
The invited talk of Michael Nikitas Vrahatis was devoted to the generalizations
of the intermediate value theorem in several variables. This theorem is very useful in
variousapproachesincludingtheexistenceofsolutionsofsystemsofnonlinearalgebraic
and/ortranscendentalequations,theexistenceoffixedpointsofcontinuousfunctions,
thelocalizationofextremaofobjectivefunctions,andthelocalizationofperiodicorbits
ofnonlinearmappingsandperiodicorbits(fixedpoints)onPoincaré’ssurfaceofsection
(thePoincarémap).
Methods emanating from the theorem are of major importance for studying and
tacklingproblemswithimprecise(notexactlyknown)informationbecause,inalarge
varietyofapplications,precisefunctionvaluesareeitherimpossibleortime-consuming
and computationally expensive to obtain. Furthermore, these methods are particularly
useful for investigating various problems where the corresponding functions assume
verylargeand/orverysmallvalues.
Applications related to systems of nonlinear algebraic and/or transcendental
equations, as well as fixed points of continuous functions, were presented. Further-
more,anapplicationwaspresentedwhichconcernsthecomputationofalltheperiodic
orbits(stableandunstable)ofanyperiodandaccuracywhichoccur,amongothers,in
thestudyofbeamdynamicsincircularparticleaccelerators,suchastheLargeHadron
CollidermachineattheEuropeanOrganizationforNuclearResearch.
TheinvitedtalkofMarcMorenoMazawasonthetopicofimplementationtechniques
forpower,Laurent,andPuiseuxseriesinseveralvariables.Thisthemewasmotivated
bythefactthatlimitsofmultivariatefunctionsandmoreadvancednotionsoflimits,like
topological closures, are almost absent from such general-purpose computer algebra
systemsasMapleandMathematica.
The discussion of the application of above-mentioned implementation techniques
started with the implementation of arithmetic operations which are sometimes easier
thanonemaythink(forinstance,thesubstitutionofunitformalpowerseriesintoformal
powerseries)andsometimesharder(forinstance,theinversionofmultivariateLaurent
series). The impact of the implementation environment on the implementation tech-
niques,consideringbothinterpretedandcompiledcode,wasalsodiscussed.Themain
points of the talk were illustrated with Maple’s MultivariatePowerSeries package and
the Basic Polynomial Algebra Subroutines Library. In that latter environment, it was
shownhowdifferentparallelprogrammingpatternscanbeusedtoobtainefficientmulti-
threadedimplementationofarithmeticoperationsonpowerseriesandfactorizationof
univariatepolynomialsoversuchseries.
The CASC 2022 program covered a wide range of topics. Polynomial algebra,
which is at the computer algebra core, was represented by contributions devoted to
the development of a new accelerated subdivision algorithm for finding the complex
Preface vii
roots of univariate polynomials, the use of Gröbner bases and invariant manifolds for
findingtheequilibriumpositionsintheproblemofthemotionofasystemoftwobodies
inauniformgravityfield,theapplicationofthequaternionFouriertransformforlocating
thenearestsingularityinapolynomialhomotopy,anewinterpolationalgorithmforthe
solutionofpolynomialequationswithparametersbyusingtheDixonresultant,andthe
computationsinthecomputeralgebrasystem(CAS)MapleandintheCprogramming
language.Polynomialcomputeralgebraisalsothefoundationofthecontributionstothe
presentproceedingsthatexposeanewspeculativealgorithmforcomputingsub-resultant
chains over rings of multivariate polynomials with the aid of the Bézout matrix, new
chordality-preservingtop-downalgorithmsfortriangulardecompositionofpolynomial
sets,newheuristicsforchoosingacylindricalalgebraicdecompositionvariableordering
motivatedbycomplexityanalysis,acomparisonofseveralalgorithmsimplementedinthe
CASsSageMathandMathematicaforprovingpositivityoflinearlyrecurrentsequences
with polynomial coefficients, and the derivation with the aid of Gröbner bases and
Sylvester resultants of new optimal symplectic fourth-order partitioned Runge–Kutta
methodsforthenumericalsolutionofHamiltonianmechanicsproblems.
Two papers deal with the application of symbolic manipulations for obtaining
the solutions of both ordinary and partial differential equations. These are the
contributions devoted to finding the solutions to linear ordinary differential equations
undertheconditionofincompleteinformationaboutthecoefficientsandtheuseofthe
parametrizationofboundaryconditionsatthesolutionofboundary-valueproblemsfor
partialdifferentialequationstoensurewell-posedness.
Two papers are devoted to the applications of symbolic-numerical algorithms
developed in the language of the CAS Mathematica for the calculation of energy
spectrumandeigenfunctionsinthegeometriccollectivemodelofatomicnucleusandthe
analysisofgyroscopicstabilizationofequilibriumsofagyrostat,respectively.Afurther
applicationofCASsinmechanicsisincluded,specificallyforthestabilityanalysisof
periodicmotionoftheswingingAtwoodmachine.
The remaining topics include a new algorithm for finding the Frobenius distance
from a given matrix to the set of matrices possessing multiple eigenvalues, the
parallelimplementationofthefastFouriertransforminaringandafinitefieldthatcan
be used for homomorphic encryption and polynomial multiplication, a new symbolic
computation method for constructing a small neighborhood around a known local
optimal point of a given multivariate function that contains radical or rational expres-
sions,newalgorithmsimplementedinMapleandintheC/C++programminglanguage
forcomputingtheintegerhullofaconvexpolyhedralset,anewalgorithmimplemented
in the CAS SageMath for computing the equivalent Hilbert series of automorphisms
actingoncanonicalringsofprojectivecurveswiththeapplicationtoFermatcurves,and
asurveyofthestateoftheartandofthefutureofcomputerscienceforcontinuousdata
as a bridge between pure and applied mathematics and as an expansion of computer
algebratoanalyticdatatypes.
WewanttothankallthemembersoftheCASC2022ProgramCommitteefortheir
thorough work in selecting and preparing the technical program. We also thank the
externalrefereeswhoprovidedreviewsaspartofthisprocess.
viii Preface
We are grateful to the members of the group headed by Timur Sadykov for their
technical help in the preparation of the camera-ready manuscript for this volume.
We are grateful to the CASC publicity chair Dmitry Lyakhov for the management of
the conference web page (http://www.casc-conference.org) and for the design of the
conferenceposter.
The local organization of the CASC 2022 at Gebze Technical University was
conducted as part of the larger SCALE event. Our particular thanks are due to the
members of the CASC 2022 local organizing committee at the GTU, in particular
Zafeirakis Zafeirakopoulos (chair), Tülay Ayyıldız Akog˘lu, Hadi Alizadeh, Hülya
Öztürk, and Ali Kemal Uncu, who ably handled the local arrangements. In addition,
Zafeirakis Zafeirakopoulos kindly provided us with the information above about
computeralgebraactivitiesatGTU.
SCALE would not have been possible without the enormous help of a large
local team. This includes members of the Institute of Information Technologies and
the Department of Mathematics of Gebze Technical University, members of other
universitiesinIstanbul,andthe(student)MathematicsClubofTurkey(TMK).Among
them, Hadi Alizadeh and Bas¸ak Karakas¸ especially worked tirelessly to deal with the
manyproblemsapost-pandemicconferencehadtoface.Intotalthereweremorethan
20peoplevolunteeringworktoensurethesuccessoftheevent.
Finally,weacknowledgethatthesuccessofCASCandSCALEhasbeenfinancially
supported by the sponsors: the Scientific and Technological Research Institution
of Turkey (TÜBITAK), the Turkish Mathematics Society (TMD), the European
Mathematics Society (EMS), the International Mathematics Union (IMU), the ACM
Special Interest Group on Symbolic and Algebraic Manipulation (SIGSAM), the
MATRISlabofSBAResearch(Austria),theCARGOlabofWilfridLaurierUniversity
(Canada),andMaplesoft.
July2022 FrançoisBoulier
MatthewEngland
TimurM.Sadykov
EvgeniiV.Vorozhtsov
Organization
CASC2022washostedbyGebzeTechnicalUniversity,Gebze,Turkey.
GeneralChairs
FrançoisBoulier UniversitédeLille,France
TimurM.Sadykov PlekhanovRussianUniversityofEconomics,
Russia
ProgramCommitteeChairs
MatthewEngland CoventryUniversity,UK
EvgeniiV.Vorozhtsov KhristianovichInstituteofTheoreticaland
AppliedMechanics,Russia
ProgramCommittee
FrançoisBoulier UniversityofLille,France
ChangboChen ChineseAcademyofSciences,China
Jin-SanCheng AcademyofMathematicsandSystemsScience,
China
TürküÖzlümÇelik Bog˘aziçiUniversity,Turkey
VictorF.Edneral LomonosovMoscowStateUniversity,Russia
JaimeGutierrez UniversityofCantabria,Spain
SergeyGutnik MoscowStateInstituteofInternationalRelations,
Russia
AmirHashemi IsfahanUniversityofTechnology,Iran
GabrielaJeronimo UniversidaddeBuenosAires,Argentina
Rui-JuanJing JinagsuUniversity,China
Wen-ShinLee UniversityofStirling,UK
FrançoisLemaire UniversityofLille,France
ViktorLevandovskyy UniversityofKassel,Germany
MarcMorenoMaza UniversityofWesternOntario,Canada
DominikL.Michels KAUST,SaudiArabia
ChenqiMou BeihangUniversity,China
SoniaPerez-Diaz UniversidaddeAlcalá,Spain
VeronikaPillwein JKULinz,Austria
AlexanderProkopenya WarsawUniversityofLifeSciences,Poland
