references.bib

@book{cardoso1997redes,
	title={Redes de petri},
	author={Cardoso, Janette and Valette, Robert},
	year={1997},
	publisher={Universidade Federal de Santa Catarina}
}

@article{dias2007ferramentas,
	title={Ferramentas para a Integra{\c{c}}{\~a}o de Redes de Petri e VHDL na S{\'\i}ntese de Sistemas Digitais},
	author={Dias, Giorjety Licorini},
	year={2007},
	publisher={Universidade Estadual Paulista (UNESP)}
}

@phdthesis{fidalgotese,
	author		= "Felipe Delfini Caetano Fidalgo",
	title		= "Dividindo e conquistando com simetrias em geometria de distâncias",
	school		= "UNICAMP",
	address		= "Campinas, SP",
	year		= "2015",
	month		= "Fevereiro",
}

@book{carlileBook31Coloquio,
	author    = "C. Lavor and N. Maculan and M. Souza and R. Alves",
	title     = "Álgebra e Geometria no Cálculo de Estrutura Molecular",
	publisher = "IMPA",
	address  = "Rio de Janeiro, RJ",
	edition  = "31º Colóquio Brasileiro de Matemática",
	year      = "2017",
}

@article{RMNproteinWrutrich,
	author    = "K. W{\"{u}}thrich",
	title     = "Protein structure determination in solution by nuclear magnetic resonance spectroscopy",
	journal   = "American Association for the Advancement of Science",
	volume   = "243",
	number   = "4887",
	pages    = "45-50",
	year      = "1989",
	month    = "Jan",
}

@book{GASteinbruch,
	author    = "Alfredo Steinbruch and Paulo Winterle",
	title     = "Geometria Analítica",
	publisher = "Makron Books",
	address  = "São Paulo, SP",
	edition  = "2a",
	year      = "1987",
}

@article{carlileGDandAplications,
	author    = "Leo Liberti and Carlile Lavor and Nelson Maculan and Antonio Mucherino",
	title     = "Euclidean distance geometry and applications",
	journal   = "Society for Industrial and Applied Mathematics",
	volume   = "56",
	number   = "1",
	pages    = "3–69",
	year      = "2014",
	month    = "February",
}

@book{RMNBookIntroduction,
	author    = "Peter A. Rinck",
	title     = "The history of MR imaging",
	publisher = "The Round Table Foundation",
	address  = "Germany",
	edition  = "11th",
	year      = "2017",
}

@book{EstatisticaTratamentoDeDados,
	author    = "Não lembro o autor",
	title     = "Um livro de tratamento de dados estatístico Tenho que verificar certinho o titulo na ufsc, é um livro de lá",
	publisher = "Favor relevar",
	address  = "Germany",
	edition  = "whatever",
	year      = "2017",
}

@book{ComplexidadeComp,
	author    = "Não lembro o autor",
	title     = "Custo computacional, teoria da computação,Tenho que verificar certinho o titulo na ufsc, é um livro de lá",
	publisher = "Favor relevar",
	address  = "Germany",
	edition  = "whatever",
	year      = "2017",
}

@book{BoyerMathHistory,
	author    = "Carl Benjamin Boyer",
	title     = "História da matemática",
	publisher = "Edgard Bl{\"{u}}cher/EDUSP",
	address  = "São Paulo",
	edition  = "3",
	year      = "1974",
}

@book{AlgebraAbstrata2BienalSBM,
	author    = "César Polcino Milies",
	title     = "Breve história da álgebra abstrata",
	publisher = "USP",
	address  = "São Paulo",
	year      = "2014"
}

@book{QuaterniosAndRotationsKuipers,
	author    = "J. B. Kuipers",
	title     = "Quaternions and Rotation Sequences",
	publisher = "Princeton University Press",
	address  = "Princeton, New Jersey",
	year      = "1999",
}

@misc{QuaterniosJucineide,
	author    = "Jucineide Silva Santos and Maurício de Araujo Ferreira",
	title     = "Álgebra de Quatérnios",
	howpublished = "Trabalho de Iniciação cientifica",
	year     = "2011",
	month    = "Agosto",
}

@book{QuaterniosHamilton,
	author    = "William Rowan Hamilton",
	title     = "Elements of Quaternions",
	publisher = "London: Longmans, Green and Co",
	address  = "Dublin",
	edition  = "First",
	year      = "1866",
	note     = "Book II pag 156",
}

@book{AlgebraLinearElon,
	author    = "Elon Lages Lima",
	title     = "Álgebra Linear",
	publisher = "SBM",
	address  = "Rio de Janeiro : IMPA",
	edition  = "1a",
	year      = "2014",
}

@article{carlile:DDGP,
	author    = "Carlile Lavor, Jon Lee, Audrey Lee-St. John, Leo Liberti, Antonio Mucherino and Maxim Sviridenko",
	title     = "Discretization orders for distance geometry problems",
	journal   = "Optimization Letters",
	volume   = "6",
	number   = "Issue 4",
	pages    = "783–796",
	year      = "2012",
	month    = "April",
}

@book{deza2006dictionary,
	title={Dictionary of distances},
	author={Michel-Marie Deza and Elena Deza},
	year={2006},
	publisher={Elsevier}
}

@incollection{deza2009encyclopedia,
	title={Encyclopedia of distances},
	author={Michel-Marie Deza and Elena Deza},
	booktitle={Encyclopedia of distances},
	pages={1--583},
	year={2009},
	publisher={Springer}
}

@inproceedings{savvides2001dynamic,
	title={Dynamic fine-grained localization in ad-hoc networks of sensors},
	author={Savvides, Andreas and Han, Chih-Chieh and Strivastava, Mani B},
	booktitle={Proceedings of the 7th annual international conference on Mobile computing and networking},
	pages={166--179},
	year={2001},
	organization={ACM}
}

@book{Blumenthal:53,
	title={Theory and applications of distance geometry},
	author={Leonard M Blumenthal},
	year={1953},
	publisher={Oxford University Press},
	address  = {Oxford}
}

@article{Cayley:1841,
	title={On a theorem in the geometry of position},
	author={Arthur Cayley},
	journal={Cambridge Mathematical Journal},
	volume={2},
	pages={267--271},
	year={1841}
}

@article{Menger:31,
	title={New foundation of Euclidean geometry},
	author={Karl Menger},
	journal={American Journal of Mathematics},
	volume={53},
	number={4},
	pages={721--745},
	year={1931},
	publisher={JSTOR}
}

@article{Survey:12,
	title={Euclidean distance geometry and applications},
	author={Leo Liberti, Carlile Lavor, Nelson Maculan and Antonio Mucherino},
	journal={Siam Review},
	volume={56},
	number={1},
	pages={3--69},
	year={2014},
	publisher={SIAM}
}

@inproceedings{Yemini:79,
	title={Some theoretical aspects of position-location problems},
	author={Yechiam Yemini},
	booktitle={20th Annual Symposium on Foundations of Computer Science (sfcs 1979)},
	pages={1--8},
	year={1979},
	organization={IEEE}
}

@inproceedings{Saxe:79,
	title={Embeddability of weighted graphs in k-space is strongly NP-hard},
	author={Saxe, James B},
	booktitle={Proc. of 17th Allerton Conference in Communications, Control and Computing, Monticello, IL},
	pages={480--489},
	year={1979}
}

@misc{Havel:95,
	title={Distance Geometry, DM Grant and RK Harris (Eds.), Encyclopedia of Nuclear Magnetic Resonance},
	author={Havel, TF},
	year={1995},
	publisher={Wiley, New York}
}

@article{LavorCNMAC:14,
	title={Um convite {\'a} geometria de dist{\^a}ncias},
	author={Lavor, C and Liberti, L},
	journal={SBMAC, Notas em Matem{\'a}tica Aplicada},
	volume={71},
	year={2014}
}

@article{Crippen:77,
	title={A novel approach to calculation of conformation: distance geometry},
	author={Crippen, Gordon M},
	journal={Journal of Computational Physics},
	volume={24},
	number={1},
	pages={96--107},
	year={1977},
	publisher={Elsevier}
}

@article{iBPCarlile,
	title={The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances},
	author={Lavor, Carlile and Liberti, Leo and Mucherino, Antonio},
	journal={Journal of Global Optimization},
	volume={56},
	number={3},
	pages={855--871},
	year={2013},
	publisher={Springer}
}

@article{carlile:MinimalOrder,
	title={Minimal NMR distance information for rigidity of protein graphs},
	author={Lavor, Carlile and Liberti, Leo and Donald, Bruce and Worley, Bradley and Bardiaux, Benjamin and Malliavin, Th{\'e}r{\`e}se E and Nilges, Michael},
	journal={Discrete Applied Mathematics},
	volume={256},
	pages={91--104},
	year={2019},
	publisher={Elsevier}
}

@article{Liberti:08,
	title={A branch-and-prune algorithm for the molecular distance geometry problem},
	author={Liberti, Leo and Lavor, Carlile and Maculan, Nelson},
	journal={International Transactions in Operational Research},
	volume={15},
	number={1},
	pages={1--17},
	year={2008},
	publisher={Wiley Online Library}
}

@article{carlile:DMDGP,
	title={The discretizable molecular distance geometry problem},
	author={Lavor, Carlile and Liberti, Leo and Maculan, Nelson and Mucherino, Antonio},
	journal={Computational Optimization and Applications},
	volume={52},
	number={1},
	pages={115--146},
	year={2012},
	publisher={Springer}
}

@misc{Pogorelov:87,
	title = {Geometry},
	author={A. Pogorelov},
	publisher={MIR, Moscow},
	year={1987}
}

@article{Philips:96,
	title={ Molecular structure determination by convex underestimation of local energy minima},
	author={A. T. Philips, J. B. Rosen, and V. H. Walke},
	journal={DIMACS Series in Discrete Mathematics and Theoretical Computer Science},
	volume={23},
	pages={181–198},
	year={1996},
	publisher={AMS}
}

@book{bioquimicaLehninger,
	title={Lehninger principles of biochemistry},
	author={Nelson, David L and Cox, Michael M},
	publisher={W.H.Freeman and Company},
	year={2013}
}

@book{crippen:DistancesAndMolecularConformation,
	title={Distance geometry and molecular conformation},
	author={Crippen, Gordon M and Havel, Timothy F and others},
	volume={74},
	year={1988},
	publisher={Research Studies Press Taunton}
}

@article{ramachandran1974MolStructure,
	title={The mean geometry of the peptide unit from crystal structure data},
	author={Ramachandran, GN and Kolaskar, AS and Ramakrishnan, C and Sasisekharan, V},
	journal={Biochimica et Biophysica Acta (BBA)-Protein Structure},
	volume={359},
	number={2},
	pages={298--302},
	year={1974},
	publisher={Elsevier}
}

@phdthesis{carlileTese,
	title={Uma abordagem determin{\'\i}stica para minimiza{\c{c}}{\~a}o global da energia potencial de mol{\'e}culas},
	author={Lavor, Carlile},
	year={2001},
	school={PhD thesis, COPPE/UFRJ, Rio de Janeiro}
}

@misc{wwPDB, 
	title={Worldwide Protein Data Bank}, 
	url={https://www.wwpdb.org/}, 
	journal={wwPDB}, 
	author={wwPDB.org}
}

@misc{emersonMolConf, 
	title={URL = ``https://github.com/evcastelani/MolecularConformation.jl''}, 
	url={https://github.com/evcastelani/MolecularConformation.jl}, 
	journal={GitHub}, 
	author={Emerson Castelani; Repositório da MolecularConformation.jl; Acesso em 11/08/2019}
}

@article{menger1928untersuchungen,
	title={Untersuchungen {\"u}ber allgemeine Metrik},
	author={Menger, Karl},
	journal={Mathematische Annalen},
	volume={100},
	number={1},
	pages={75--163},
	year={1928},
	publisher={Springer}
}

@article{carlile:dvopComplexity,
	title={Discretization vertex orders in distance geometry},
	author={Cassioli, Andrea and G{\"u}nl{\"u}k, Oktay and Lavor, Carlile and Liberti, Leo},
	journal={Discrete Applied Mathematics},
	volume={197},
	pages={27--41},
	year={2015},
	publisher={Elsevier}
}

@article{carlile:BP,
	title={A branch-and-prune algorithm for the molecular distance geometry problem},
	author={Liberti, Leo and Lavor, Carlile and Maculan, Nelson},
	journal={International Transactions in Operational Research},
	volume={15},
	number={1},
	pages={1--17},
	year={2008},
	publisher={Wiley Online Library}
}

@incollection{carlile:instancesMDGP,
	title={On generating instances for the molecular distance geometry problem},
	author={Lavor, Carlile},
	booktitle={Global optimization},
	pages={405--414},
	year={2006},
	publisher={Springer}
}


@book{grafos0,
	Address = {São Paulo},
	Author = {Paulo Oswaldo Boaventura Netto},
	Edition = {5},
	Publisher = {Blucher},
	Title = {Grafos},
	Subtitle = {Grafos: Teoria, Modelos, Algoritmos},
	Year = {2012},
	Pages = {314}
}

@book{graphTheoryApplicationsBondy,
	Address = {New York},
	Author = {J. A. Bondy and U. S. R. Murty},
	Edition = {5},
	Publisher = {Elsevier Science Publishing},
	Title = {Graph Theory With Applications},
	Year = {1982},
	Pages = {264}
}

@article{kruskal1990complexity,
	title={A complexity theory of efficient parallel algorithms},
	author={Kruskal, Clyde P and Rudolph, Larry and Snir, Marc},
	journal={Theoretical Computer Science},
	volume={71},
	number={1},
	pages={95--132},
	year={1990},
	publisher={Elsevier}
}

@article{dijkstra1959note,
	title={A note on two problems in connexion with graphs},
	author={Dijkstra, Edsger W},
	journal={Numerische mathematik},
	volume={1},
	number={1},
	pages={269--271},
	year={1959},
	publisher={Springer}
}

@article{euler:KOENIGSBERG,
	title={Leonhard Euler and the K{\"o}nigsberg bridges},
	author={Euler, Leonhard},
	journal={Scientific American},
	volume={189},
	number={1},
	pages={66--72},
	year={1953},
	publisher={JSTOR}
}

@book{grafosPremioElon,
	title={Teoria computacional de grafos: Os algoritmos},
	author={Szwarcfiter, Jayme Luiz},
	year={2018},
	publisher={Elsevier Brasil}
}

@inproceedings{mucherino:BP,
	title={MD-jeep: an implementation of a branch and prune algorithm for distance geometry problems},
	author={Mucherino, Antonio and Liberti, Leo and Lavor, Carlile},
	booktitle={International Congress on Mathematical Software},
	pages={186--197},
	year={2010},
	organization={Springer}
}

@book{libertiEDG,
	title={Euclidean Distance Geometry},
	author={Liberti, Leo and Lavor, Carlile},
	year={2017},
	publisher={Springer}
}

@book{elementosEuclides,
	title={Os elementos},
	author={Bicudo, Irineu and others},
	year={2009},
	publisher={Unesp}
}

@article{cayley1841HaronGD,
	title={A theorem in the geometry of position},
	author={Cayley, Arthur},
	journal={Cambridge Mathematical Journal},
	volume={2},
	pages={267--271},
	year={1841}
}

@article{mengerDeterminante,
	title={Untersuchungen {\"u}ber allgemeine Metrik},
	author={Menger, Karl},
	journal={Mathematische Annalen},
	volume={100},
	number={1},
	pages={75--163},
	year={1928},
	publisher={Springer}
}

@article{EDMPResolucao,
	title={Cayley-menger coordinates},
	author={Sippl, Manfred J and Scheraga, Harold A},
	journal={Proceedings of the National Academy of Sciences},
	volume={83},
	number={8},
	pages={2283--2287},
	year={1986},
	publisher={National Acad Sciences}
}

@techreport{yemini1978positioning,
	title={The positioning problem-a draft of an intermediate summary},
	author={Yemini, Yechiam},
	year={1978},
	institution={UNIVERSITY OF SOUTHERN CALIFORNIA MARINA DEL REY INFORMATION SCIENCES INST}
}

@article{cinematicaInversa,
	title={Real-time inverse kinematics techniques for anthropomorphic limbs},
	author={Tolani, Deepak and Goswami, Ambarish and Badler, Norman I},
	journal={Graphical models},
	volume={62},
	number={5},
	pages={353--388},
	year={2000},
	publisher={Elsevier}
}

@article{multidimensionalScaling,
	title={13 Theory of multidimensional scaling},
	author={de Leeuw, Jan and Heiser, Willem},
	journal={Handbook of statistics},
	volume={2},
	pages={285--316},
	year={1982},
	publisher={Elsevier}
}

@inproceedings{eren2004rigidity,
	title={Rigidity, computation, and randomization in network localization},
	author={Eren, Tolga and Goldenberg, OK and Whiteley, Walter and Yang, Yang Richard and Morse, A Stephen and Anderson, Brian DO and Belhumeur, Peter N},
	booktitle={IEEE INFOCOM 2004},
	volume={4},
	pages={2673--2684},
	year={2004},
	organization={IEEE}
}

@article{benedettireal,
	title={In Real Algebraic and Semi-algebraic Sets},
	author={Benedetti, Riccardo and Risler, Jean-Jacques},
	journal={Berlin, Hermann, Paris},
	year={1990}
}

@book{carlileIntroductionMDGP,
	title={An Introduction to Distance Geometry applied to Molecular Geometry},
	author={Lavor, Carlile and Liberti, Leo and Lodwick, Weldon A and da Costa, Tiago Mendon{\c{c}}a},
	year={2017},
	publisher={Springer}
}

@book{graphTheoryFHarary,
	Author = {Frank Harary},
	Publisher = {Westview Press},
	Title = {Graph Theory},
	Year = {1969}
}

@article{kirchhoff1847ueber,
	title={Ueber die Aufl{\"o}sung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Str{\"o}me gef{\"u}hrt wird},
	author={Kirchhoff, Gustav},
	journal={Annalen der Physik},
	volume={148},
	number={12},
	pages={497--508},
	year={1847},
	publisher={Wiley Online Library}
}

@misc{cayley1897theory,
	title={On the theory of the analytical forms called trees, Math},
	author={Cayley, A},
	year={1897},
	publisher={Papers Cambridge}
}

@misc{problemsInMath,
	title={HSM Coxeter Mathematical recreations and essays},
	author={Ball, W.W. Rouse},
	year={1956},
	publisher={St Martin’s Press}
}

@book{alfakihEuclideanDistanceMatricesApplicationsRigidity,
	title={Euclidean distance matrices and their applications in rigidity theory},
	author={Alfakih, Abdo Y},
	year={2018},
	publisher={Springer}
}

@article{trilaterationDong,
	title={A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances},
	author={Dong, Qunfeng and Wu, Zhijun},
	journal={Journal of Global Optimization},
	volume={22},
	number={1-4},
	pages={365--375},
	year={2002},
	publisher={Springer}
}

@article{hendrickson1992conditions,
	title={Conditions for unique graph realizations},
	author={Hendrickson, Bruce},
	journal={SIAM journal on computing},
	volume={21},
	number={1},
	pages={65--84},
	year={1992},
	publisher={SIAM}
}

@article{connelly1991generic,
	title={On generic global rigidity, Applied geometry and discrete mathematics, 147--155},
	author={Connelly, Robert},
	journal={DIMACS Ser. Discrete Math. Theoret. Comput. Sci},
	volume={4},
	year={1991}
}

@book{gps,
	title={Global positioning system: theory and practice},
	author={Hofmann-Wellenhof, Bernhard and Lichtenegger, Herbert and Collins, James},
	year={2012},
	publisher={Springer Science \& Business Media}
}

@MastersThesis{rigidezGrafosEAplicacoesAnaCarlile,
	author = {Ana Flávia da Cunha Lima},
	title = {Rigidez de Grafos e Aplicações},
	school = {UNICAMP, IMECC},
	year = {2015},
	address	= "Campinas, SP",
}

@book{mobileRobotsCook,
	title={Mobile Robots: Navigation, Control and Sensing, Surface Robots and AUVs},
	author={Cook, Gerald and Zhang, Feitian},
	year={2020},
	publisher={John Wiley \& Sons}
}

@book{mobileRobotsTzafestas,
	title={Introduction to mobile robot control},
	author={Tzafestas, Spyros G},
	year={2013},
	publisher={Elsevier}
}

@article{dronesAmazon,
	title={Strategic design for delivery with trucks and drones},
	author={Campbell, James F and Sweeney, Don and Zhang, Juan},
	journal={Supply Chain Analytics Report SCMA (04 2017)},
	year={2017}
}

@book{mobileRobotsWheeled,
	title={Wheeled mobile robotics: from fundamentals towards autonomous systems},
	author={Klancar, Gregor and Zdesar, Andrej and Blazic, Saso and Skrjanc, Igor},
	year={2017},
	publisher={Butterworth-Heinemann}
}

@book{sensorsForMobileRobots,
	title={Sensors for mobile robots},
	author={Everett, HR},
	year={1995},
	publisher={CRC Press}
}

@book{bayro2010geometric,
	title={Geometric computing: for wavelet transforms, robot vision, learning, control and action},
	author={Bayro-Corrochano, Eduardo},
	year={2010},
	publisher={Springer Publishing Company, Incorporated}
}

@book{moysesEletromag,
	title={Curso de f{\'\i}sica b{\'a}sica: Eletromagnetismo (vol. 3)},
	author={Nussenzveig, Herch Moys{\'e}s},
	volume={3},
	year={2015},
	publisher={Editora Blucher}
}

@inproceedings{wsnlFewAnchors,
	title={Uniquely localizable networks with few anchors},
	author={Fekete, Zsolt and Jord{\'a}n, Tibor},
	booktitle={International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics},
	pages={176--183},
	year={2006},
	organization={Springer}
}

@article{wsnlSemidefinitePrograming,
	title={Theory of semidefinite programming for sensor network localization},
	author={So, Anthony Man-Cho and Ye, Yinyu},
	journal={Mathematical Programming},
	volume={109},
	number={2-3},
	pages={367--384},
	year={2007},
	publisher={Springer}
}

@book{douglasGD,
	title={Geometria de Distâncias: aspectos teóricos e computacionais},
	author={Gonçalves, Douglas S},
	volume={91},
	year={2020},
	publisher={São Carlos, SP : SBMAC, Notas em Matemática Aplicada}
}

@article{intructionsTableFog,
	title={Instruction tables: Lists of instruction latencies, throughputs and micro-operation breakdowns for Intel, AMD and VIA CPUs},
	author={Fog, Agner and others},
	journal={Copenhagen University College of Engineering},
	volume={93},
	pages={110},
	year={2011}
}

@article{carlileRecentAdvancesMDGP,
	title={Recent advances on the discretizable molecular distance geometry problem},
	author={Lavor, Carlile and Liberti, Leo and Maculan, Nelson and Mucherino, Antonio},
	journal={European Journal of Operational Research},
	volume={219},
	number={3},
	pages={698--706},
	year={2012},
	publisher={Elsevier}
}

@article{libertiMdgpContinousToDiscrete,
	title={Molecular distance geometry methods: from continuous to discrete},
	author={Liberti, Leo and Lavor, Carlile and Mucherino, Antonio and Maculan, Nelson},
	journal={International Transactions in Operational Research},
	volume={18},
	number={1},
	pages={33--51},
	year={2011},
	publisher={Wiley Online Library}
}

@article{libertiSixGemsDGHistory,
	title={Six mathematical gems from the history of distance geometry},
	author={Liberti, Leo and Lavor, Carlile},
	journal={International Transactions in Operational Research},
	volume={23},
	number={5},
	pages={897--920},
	year={2016},
	publisher={Wiley Online Library}
}

@book{linearAlgebraNumericalTrefethen,
	title={Numerical linear algebra},
	author={Trefethen, Lloyd N and Bau III, David},
	volume={50},
	year={1997},
	publisher={Siam}
}

@misc{hanson1994geometry,
	title={Geometry for N-Dimensional Graphics.},
	author={Hanson, Andrew J},
	year={1994}
}

@article{havel1998distance,
	title={Distance geometry: Theory, algorithms, and chemical applications},
	author={Havel, Timothy F},
	journal={Encyclopedia of Computational Chemistry},
	volume={120},
	pages={723--742},
	year={1998},
	publisher={John Wiley \& Sons}
}

@article{correiaCondicoesNecessaESuficiDGPCayleyMenger,
	title={Condi{\c{c}}{\~o}es necess{\'a}rias e suficientes para a realiza{\c{c}}{\~a}o de um conjunto de dist{\^a}ncias atrav{\'e}s de determinantes de Cayley-Menger},
	author={Correia, Fernando and others},
	year={2016}
}

@book{johnAlgebra,
  title={A First Course in Abstract Algebra},
  author={Fraleigh, John B},
  year={2014},
  publisher = {Pearson}
}

@book{michalAlgebra,
	title={Algebra},
	author={Artin, Michael},
	year={1991},
	publisher = {A Simon and Schuster Company}
}

@book{maierAlgebra,
	title={Algebra I (texto de aula)},
	author={Maier, Rudolf R.},
	year={2005},
	publisher = {UFSC}
}

@article{dominguesAlgebra,
	title={{\'A}lgebra moderna},
	author={IEZZI, GELSON and DOMINGUES, Hygino H},
	journal={S{\~a}o Paulo: Atual Editora},
	year={2003}
}

@book{lounestoClifford,
	title={Clifford algebras and spinors},
	author={Lounesto, Pertti},
	volume={286},
	year={2001},
	publisher={Cambridge university press}
}

@book{grassmannLineale,
	title={Die lineale Ausdehnungslehre ein neuer Zweig der Mathematik: dargestellt und durch Anwendungen auf die {\"u}brigen Zweige der Mathematik, wie auch auf die Statik, Mechanik, die Lehre vom Magnetismus und die Krystallonomie erl{\"a}utert},
	author={Grassmann, Hermann},
	volume={1},
	year={1844},
	publisher={O. Wigand}
}

@book{sommerGeometric,
	title={Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics},
	author={Sommer, Gerald},
	year={2013},
	publisher={Springer Science \& Business Media}
}

@article{cliffordApplicationsGrassmannAlgebras,
	title={Applications of Grassmann's extensive algebra},
	author={Clifford, Professor},
	journal={American Journal of Mathematics},
	volume={1},
	number={4},
	pages={350--358},
	year={1878},
	publisher={JSTOR}
}

@article{lundholm2009clifford,
	title={Clifford algebra, geometric algebra, and applications},
	author={Lundholm, Douglas and Svensson, Lars},
	journal={arXiv preprint arXiv:0907.5356},
	year={2009}
}

@article{douglasSideChainOrder,
	title={Discretization orders for protein side chains},
	author={Costa, Virginia and Mucherino, Antonio and Lavor, Carlile and Cassioli, Andrea and Carvalho, Luiz M and Maculan, Nelson},
	journal={Journal of Global Optimization},
	volume={60},
	number={2},
	pages={333--349},
	year={2014},
	publisher={Springer}
}

@article{thompsonBi,
	title={Calculation of cartesian coordinates and their derivatives from internal molecular coordinates},
	author={Thompson, H Bradford},
	journal={The Journal of Chemical Physics},
	volume={47},
	number={9},
	pages={3407--3410},
	year={1967},
	publisher={American Institute of Physics}
}

@book{zillerMicroprocessadores,
	title={Microprocessadores: conceitos importantes},
	author={Ziller, Roberto M},
	year={2000},
	publisher={Ed. do Autor}
}

@article{bezanson2017julia,
	title={Julia: A fresh approach to numerical computing},
	author={Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B},
	journal={SIAM review},
	volume={59},
	number={1},
	pages={65--98},
	year={2017},
	publisher={SIAM},
	url={https://doi.org/10.1137/141000671}
}

@article{bernstein1977protein,
	title={The Protein Data Bank: a computer-based archival file for macromolecular structures},
	author={Bernstein, Frances C and Koetzle, Thomas F and Williams, Graheme JB and Meyer Jr, Edgar F and Brice, Michael D and Rodgers, John R and Kennard, Olga and Shimanouchi, Takehiko and Tasumi, Mitsuo},
	journal={Journal of molecular biology},
	volume={112},
	number={3},
	pages={535--542},
	year={1977},
	publisher={Elsevier}
}


@article{fidalgoAGACSE,
	title={Using quaternion geometric algebra for efficient rotations in the branch-and-prune algorithm to solve the Discretizable Molecular Distance Geometry Problem},
	author={Felipe Fidalgo},
	journal={7th Conference on Applied Geometric Algebra in Computer Science and Engineering (AGACSE 2018)},
	year={2018},
	publisher={ Campinas, Brazil}
}

@article{michaelOrthogonality,
	title={Orthogonality of isometries in the conformal model of the 3D space},
	author={Lavor, Carlile and Souza, Michael and Arag{\'o}n, Jos{\'e} Luis},
	journal={Graphical Models},
	volume={114},
	pages={101100},
	year={2021},
	publisher={Elsevier}
}

@article{phillips1995molecular,
	title={Molecular structure determination by convex, global underestimation of local energy minima.},
	author={Phillips, Andrew T and Rosen, J Ben and Walke, Vann Howard},
	journal={Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding},
	volume={23},
	pages={181--198},
	year={1995},
	publisher={Citeseer}
}

@book{dorst2010geometric,
	title={Geometric algebra for computer science: an object-oriented approach to geometry},
	author={Dorst, Leo and Fontijne, Daniel and Mann, Stephen},
	year={2010},
	publisher={Elsevier}
}

@book{fraleigh2003first,
	title={A first course in abstract algebra},
	author={Fraleigh, John B},
	year={2003},
	publisher={Pearson Education India}
}

@misc{van1949modern,
	title={Modern Algebra, trans. F. Blum, vol. 1},
	author={Van Der Waerden, BL},
	year={1949},
	publisher={New York, Frederick Ungar Publishing Company}
}

@article{artinalgebra,
	title={Algebra, 1991},
	author={Artin, Michael},
	journal={New Jersey}
}

@book{dummit1991abstract,
	title={Abstract algebra},
	author={Dummit, David S and Foote, Richard M},
	volume={1999},
	year={1991},
	publisher={Prentice Hall Englewood Cliffs, NJ}
}