Publications

• Lorenzo Baldi, Teresa Krick, Bernard Mourrain:  An Effective Positivstellensatz over the Rational Numbers for Finite Semialgebraic Sets. Preprint October 2024, Arxiv.
  
• Teresa Krick, Bernard Mourrain, Agnes Szanto:  Univariate rational sums of squares. RevUMA 64(2) (2023) 215-237. Diamond Open Access , Arxiv.
  
• Denys Bulavka, Ariel A. Aptekmann, Nicolás A. Méndez, Teresa Krick, Ignacio E. Sánchez: Thousands of protein linear motif classes may still be undiscovered. PLoS ONE 16(5) (2021).
  
• Felipe Cucker, Teresa Krick: On local analysis. J. Complexity 57 (2020).  PDF , Arxiv.
• Alin Bostan,Teresa Krick, Agnes Szanto, Marcelo Valdettaro: Subresultants of (x-a)^m and (x-b)^n, Jacobi polynomials and complexity. J. Symb. Comput. 101 (2020) 330-351.  PDF , Arxiv.
• Carlos D'Andrea, Teresa Krick, Agnes Szanto, Marcelo Valdettaro: Closed formujla for unicariate subresultants in multiple roots.  Linear Algebra and its Applications 565 (2019) 123-155. PDF , Arxiv.
• Felipe Cucker, Teresa Krick, Michael Shub: Computing the homology of real projective sets. Found. Comput. Math. (2018) 18: 929-970.  PDF , Arxiv.
• Alin Bostan, Carlos D'Andrea, Teresa Krick, Agnes Szanto, Marcelo Valdettaro: Subresultants in multiple roots: an extremal case. Linear Algebra and its Applications 529 (2017) 185-198.  PDF , Arxiv.
• Teresa Krick, Agnes Szanto, Marcelo Valdettaro: Symmetric interpolation, exchange lemma and Sylvester sums (former: Understanding Sylvester sums via symmetric Lagrange interpolation). Communications in Algebra 45, Issue 8 (2017) 3231-3250.   PDF , Arxiv.
• Carlos D'Andrea, Teresa Krick, Agnes Szanto: Subresultants, Sylvester sums and the rational interpolation problem. J. Symb. Comput. Vol. 68 (2015) 72–83.  PDF , Arxiv.
• Teresa Krick, Nina Verstraete,  Leonardo G. Alonso, David A. Shub,  Diego U. Ferreiro, Michael Shub, Ignacio E. Sánchez: Amino acid metabolism conflicts with protein diversity. Molecular Biology and Evolution (2014).  PDF
• Carlos D'Andrea, Teresa Krick, Martín Sombra: Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze. Annales Scientifiques de l'Ecole Normale Supérieure 46 (2013) 549-627.  PDF , Arxiv.
• Carlos D'Andrea, Teresa Krick, Agnes Szanto: Subresultants in multiple roots.  Linear Algebra and its Applications 438 (2013) 1969-1989. PDF , Arxiv.
• Teresa Krick, Agnes Szanto: Sylvester's double sums: an inductive proof of the general case.   J. Symb. Comput.  Vol. 47 (2012) 942-953. PDF , Arxiv.
• Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor: A numerical algorithm for zero counting . III: Randomization and Condition.   Adv. in Appl. Math.  Vol. 48 (2012) 215-248.  PDF, Arxiv.
• Martín Avendaño, Teresa Krick: Sharp bounds for the number of roots of unicariate fewnomials.  Journal of Number Theory 131 (2011) 1209–1228. PDF, Arxiv.
• Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor: A numerical algorithm for zero counting . II: Distance to Ill-posedness and Smoothed Analysis   J. fixed point theory appl. 6 (2009) 285-294.  PDF, Arxiv.
• Carlos D'Andrea, Hoon Hong, Teresa Krick, Agnes Szanto: Sylvester's double sums: the general case.  J. Symb. Comput. Vol. 44  (2009) 1164--1175. PDF,  Arxiv. Preliminary version in: Effective Methods in Algebraic Geometry Digital Proceedings, MEGA'07, Strobl, 06.21-27.07.
• Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor: A numerical algorithm for zero counting . I: Complexity and Accuracy.   J. Complexity  Vol. 24 (2008) 582-605. PDF, .Arxiv
• Carlos D'Andrea, Hoon Hong, Teresa Krick, Agnes Szanto: An elementary proof of Sylvester's double sums for subresultants.  J. Symb. Comput. Vol. 42 (2007) 290-297.  PDF,  Arxiv
• Martín Avendaño, Teresa Krick, Martín Sombra: Factoring bivariate sparse (lacunary) polynomials.  J. Complexity Vol. 23  (2007) 193-216. Best Paper Award 2007.  PDF,  Arxiv
• Martín Avendaño, Teresa Krick,  Ariel Pacetti: Newton-Hensel interpolation lifting. Found. Comput. Math. Vol. 6 No. 1 (2006) Special Vol. dedicated to Steve Smale on his 75th birthday. 81-120. MR2198216. PDF,  Arxiv
• Carlos D'Andrea, Teresa Krick, Agnes Szanto:  Multivariate subresultants in roots. J. Alg.  Vol. 302 (2006) 16-36. PDF,  Arxiv. Preliminary version in: Effective Methods in Algebraic Geometry Digital Proceedings, MEGA'05, Porto Cone, Alghero, Sardinia, 05.27.-06.1.05.
• Teresa Krick:  Straight-line programs in polynomial equation solving.  Foundations of Computational Mathematics, Minneapolis 2002 (edited by F. Cucker, R. DeVore, P. Olver and A. Süli). London Mathematical Society  Lecture Notes Series 312, Cambridge University Press  (2004) 96-136. MR2189629. PDF
• Gabriela Jeronimo, Teresa Krick, Juan Sabia, Martín Sombra: The computational complexity of the Chow form. Found. Comput. Math. Vol. 4 No. 1 (2004) 41-117. MR 2005c:14083. PDF,  Arxiv
• Teresa Krick, Luis Pardo, Martín Sombra: Sharp estimates for the arithmetic Nullstellensatz. Duke Math. J. Vol. 109  (2001) no. 3, 521-598. MR 2002h:11060. PDF,  Arxiv
• Joos Heintz, Teresa Krick, Susana Puddu, Juan Sabia, Ariel Waissbein: Deformation techniques for efficient polynomial equation solving. J. Complexity 16 (2000), no. 1, 70--109. MR 2001c:65067. PDF
• Teresa Krick, Juan Sabia, Pablo Solernó:  On intrinsic bounds in the Nullstellensatz. Appl. Algebra Engrg. Comm. Comput. 8 (1997), no. 2, 125--134. MR 98g: 13039. PDF.
  
• Teresa Krick, Luis Pardo: A computational method for diophantine approximation. Algorithms in Algebraic Geometry and Applications (edited by T.Recio and L.Gonzalez Vega), Progr.  Math., 143, Birkhäuser, Basel (1996) 193-254. MR 98h: 13039. Announcement: Une approche informatique pour l'approximation diophantienne. C. R. Acad. Sci. Paris Sér. I Math.318 (1994), no. 5, 407-412. MR 95d:13033.
• Leandro Caniglia, Guillermo Cortiñas, Silvia Danón, Joos Heintz, Teresa Krick, Pablo Solernó: Algorithmic aspects of Suslin's proof of Serre's Conjecture. Comput. Complexity 3 (1993), no. 1, 31-55. MR 94i:13015.
• Bernd Bank, Joos Heintz, Teresa Krick, Reinhard Mandel, Pablo Solernó: Une borne optimale pour la programmation entière quasiconvexe. Bull. Soc. Math. France 12} (1993), no. 2,  299-314. MR 94e:90061. Announcements: Une borne géométrique pour la programmation entière à contraintes polynomiales. C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 6, 475-478. MR 91b:90136. A geometrical bound for integer programming with polynomial constraints. Fundamentals of computation theory (Gosen 1991), 121-125, Lecture Notes in Comput. Sci., 529, Springer, Berlin, 1991. MR 1 136074.
• Bernd Bank, Joos Heintz, Teresa Krick, Reinhard Mandel, Pablo Solernó: Computability and complexity of polynomial optimization problems. Modern Methods of Optimization (W. Krabs and J. Zowe Eds.), LN Econ. and Mathem. Sys. 378, Springer-Verlag (1992) 1-23.
• Teresa Krick, Alessandro Logar: An algorithm for the computation of the radical of an ideal  in the ring of polynomials. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (H.F. Mattson, T. Mora  and T.R.N. Rao Eds.), Lecture Notes in  Comput. Sci. 539. Springer, Berlin (1991) 195-205. MR 94e:68089.
• Joos Heintz, Teresa Krick, Anatol Slissenko, Pablo Solernó: A search for the  shortest path around semi--algebraic obstacles  in the plane.  (In russian)  Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 192 (1991), Teor. Slozhn. Vychisl. 5, 163-173, 176; translation in J. Math. Sci 70 (1994) no. 4, 1944-1949. MR 93b:68088.
• Joos Heintz, Teresa Krick, Marie-Francoise Roy, Pablo Solernó: Geometric problems solvable in single exponential  time.Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (S.Sakata Ed.), Lecture Notes in  Comput. Sci. {\bf 508}, Springer Berlin (1991) 11-23. MR 1 123 942.
• Teresa Krick, Alessandro Logar:  Membership problems, representation problems and the computation of the  radical for one-dimensional ideals. Effective Methods in Algebraic Geometry (Edited by T.Mora and C.Traverso), Progr. Math. 94, Birkhäuser Boston  (1991) 203-216. MR 92d:13016.
• Alicia Dickenstein, Marc Giusti, Noaï Fitchas, Carmen Sessa: The membership problem for unmixed polynomial ideals is solvable in single exponential time. Discrete  Applied Mathematics 33. North--Holland (1991) 73-94. MR 92m:13025.
• Noaï Fitchas, André Galligo: Nullstellensatz effectif et conjecture de Serre (Théorème de Quillen-Suslin) pour le Calcul Formel. Math. Nachr. 149 (1990) 231-253. MR 92i:12002.
• Noaï Fitchas, André Galligo, Jacques Morgenstern: Algorithmes rapides en séquentiel et en parallèle pour l'élimination des quantificateurs en géométrie élémentaire. Publ. Math. Univ. Paris 7, 32, Sélection d'exposés 1986-1987 (1990) 103-145. MR 92h:12010.
• Noaï Fitchas, André Galligo, Jacques Morgenstern: Precise sequential and parallel complexity bounds for the quantifier elimination over algebraically closed fields. Journal of Pure and Applied  Algebra 67. North-Holland (1990)  1-14. MR 91j:03010.

 Conference Abstracts and Manuscripts

• Carlos D'Andrea, Teresa Krick, Agnes Szanto, Marcelo Valdettaro:  Closed formula for univariate subresultants in multiple roots. Accepted for presentation at Effective Methods in Algebraic Geometry, MEGA'17, Nice,  12-16.06.17 (refereed) . PDF.
• Carlos D'Andrea, Teresa Krick, Agnes Szanto:  Subresultants in multiple roots (extended abstract). Presented at Effective Methods in Algebraic Geometry, MEGA'09, Barcelona,  15-19.06.09 (refereed) . PDF.
• Teresa Krick: Enteros. 54 pp. Lecture Notes of part of the regular course on Algebra, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires (2003). PDF
• Gabriela Jeronimo, Teresa Krick, Juan Sabia, Martín Sombra:  Chow forms of algebraic varieties. Extended abstract. Workshop Argentino de Informática Teórica, 30 JAIIO, Buenos Aires (2001) (refereed)
• Teresa Krick, Luis Pardo,  Martín Sombra: Arithmetic Nullstellensätze. Extended abstract. Workshop Argentino de Informática Teórica, 30 JAIIO, Buenos Aires (2001) (refereed) PDF
• Teresa Krick:  Solving Polynomial Equations. Lecture Notes Introductory Workshop of the joint programs  ``Foundations of Computational Mathematics" and ``Symbolic Computation in Geometry & Analysis", Mathematical Science Research Institute, Berkeley (1998) PDF
• Teresa Krick:  Polinomios y Raíces. 40 pp.   Lecture Notes  Reunión de Educación Matemática 1995, UMA, Río Cuarto (1997). PDF
• Joos Heintz, Teresa Krick, Anatol Slissenko,  Pablo Solernó: Une borne inférieure pour la construction de polygonales dans le plan. Publication  Mathématique Univ. Limoges (1993).
• Teresa Krick: Complejidad para problemas de Geometría elemental. PhD Thesis, Universidad de Buenos Aires (1990).
• Noaï Fitchas: Catania Lecture Notes on Complexity in Elementary Geometry. Lecture Notes, Workshop on Computational Real Algebraic Geometry (12.1988).
• Teresa Krick: Ejemplos de anillos de enteros de cuerpos ciclotómicos que no son dominio   de factorización única.  Notas de la Sociedad Matemática de Chile. V Coloquio Latinoamericano de Algebra. Número Especial, vol. V,  No. 1 (1986). MR 89a:11108.
• Teresa Krick:  Infinite families of non--principal cyclotomic rings. Preprint Univ. Buenos Aires (1985).