On the time-space complexity of geometric elimination procedures

Applicable Algebra in Engineering, Communications and Computing

Volumn 11, Issue 4, 2001, Pages 239-296

  Heintz, Joos ^a,b,c   Matera, Guillermo ^d,e   Waissbein, Ariel ^b  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^c CONICET ^*  (Argentina)

^d FAVALORO UNIVERSITY   (Argentina)

^e INSTITUTO DE CIENCIAS   (Argentina)

Author keywords

Algebraic complexity theory; Algorithmic elimination theory; Computation tree; Polynomial equation solving; Straight line program; Symbolic computation; Time space complexity

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; MATRIX ALGEBRA; POLYNOMIALS; THEOREM PROVING; TREES (MATHEMATICS);

ALGEBRAIC COMPLEXITY THEORY; ALGORITHMIC ELIMINATION THEORY; COMPUTATION TREE; GEOMETRIC ELIMINATION PROCEDURES; STRAIGHT LINE PROGRAM; SYMBOLIC COMPUTATION; TIME SPACE COMPLEXITY;

GEOMETRY;

EID: 0035060036     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002000000046     Document Type: Article

References (72)

1. Algorithmes rapides pour le Calcul du Polynôme Caractéristique
2. Zeroes, multiplicities and idempotents for zerodimensional systems
3. Polar varieties, real equation solving and data structures: The hypersurface case
4. Polar varieties and efficient real elimination
5. Polynomial and matrix computations
6. On relating time and space to size and depth
7. Time space tradeoffs (getting closer to the barrier?)
8. The computational complexity of algebraic and numeric problems
9. Bounds for the degree in the Nullstellensatz
10. Gröbner bases: An algoritmic method in polynomial ideal theory
11. How to compute the Chow Form of an unmixed Polynomial Ideal in Single Exponential Time
12. Some new effectivity bounds in computational geometry
13. Some algebraic and geometric problems in PSPACE
14. Subexponential time solving systems of algebraic equations
15. Subresultants and reduced polynomial sequences
16. The membership problem for unmixed polynomial ideals is solvable in single exponential time
17. Computational methods of linear algebra
18. Nullstellensatz effectif et Conjecture de Serre (Théorème de Quillen-Suslin) pour le calcul formel
19. Sur la complexité du théorème des zéros
20. Lower bounds for diophantine approximation
21. The Projective Noether Maple Package: Computing the dimension of a projective variety
22. La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial
23. Straight-line programs in geometric elimination theory
24. When polynomial equation systems can be solved fast?
25. Le rôle des structures de données dans les problèmes d'élimination
26. On the efficiency of effective Nullstellensätze
27. A Gröbner free alternative for polynomial system solving
28. Algebraic solution of systems of polynomial equations using Gröbner Bases
29. Symbolic recipes for polynomial system solving
30. Intrinsic height estimates for the Nullstellensatz
31. On the intrinsic complexity of the arithmetic Nullstellensatz
32. Definability and fast quantifier elimination in algebraically closed fields
33. On the computational complexity of polynomials and bilinear mappings. A survey
34. Deformation techniques for efficient polynomial equation solving
35. The intrinsic complexity of parametric elimination methods
36. Time-space tradeoffs for some algebraic problems
37. Asymptotically fast solution of Toeplitz-like singular linear systems
38. Solving systems of algebraic equations by general elimination method
39. Une approche informatique pour l' approximation diophantienne
40. A computational method for diophantine approximation
41. Grundzüge einer Arithmetischen Theorie de Algebraischen Grössen
42. Space optimal computation of normal forms of polynomials
43. Exponential space computation of Gröbner bases
44. The algebraic theory of modular systems
45. Sobre la complejidad en espacio y tiempo de la eliminación geométrica
46. Probabilistic algorithms for geometric elimination
47. The space complexity of elimination: Upper bounds
48. Membership in polynomial ideals over Q is exponential space complete
49. The complexity of the word problem for commutative semigroups
50. Resolución eficaz de sistemas de ecuaciones polinomiales
51. How lower and upper complexity bounds meet in elimination theory
52. Solving zero-dimensional systems throught rational univariate representation
53. Bounds for traces in complete intersections and degrees in the Nullstellensatz
54. Fast algorithms: A multitape turing machine implementation
55. Fast probabilistic algorithms for verification of polynomial identities
56. Algoritmos simbólicos de Hankel en álgebra computacional
57. An extended polynomial gcd algorithm using Hankel matrices
58. Basic algebraic geometry
59. An algorithm for division of power series
60. Estimaciones para el Teorema de Ceros de Hilbert
61. Lower bounds for the complexity of polynomials
62. Vermeidung von Divisionen
63. Algebraic complexity theory
64. Parallel arithmetic computations: A survey
65. Parallel linear algebra
66. Deforestation: Transforming programs to eliminate trees
67. Algebraic surfaces. Classics in mathematics
68. Probabilistic algorithms for sparse polynomials
69. Effective polynomial computation