메뉴 건너뛰기




Volumn 51, Issue 5, 2000, Pages 497-528

On the data structure straight-line program and its implementation in symbolic computation

Author keywords

Arithmetic boolean circuit; Directed acyclic graph; Evaluation; Greatest common divisor of multivariate polynomials; Linear recurring sequence; Mixed representation; Multivariate polynomial; Straight line program

Indexed keywords


EID: 0010634078     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(99)00140-8     Document Type: Article
Times cited : (5)

References (44)
  • 1
    • 0031097237 scopus 로고    scopus 로고
    • Polar varieties and efficient real equation solving: The hypersurface case
    • B. Bank, M. Giusti, J. Heintz, G. Mbakop, Polar varieties and efficient real equation solving: the hypersurface case, J. Complexity 13(1) (1997) 5-27.
    • (1997) J. Complexity , vol.13 , Issue.1 , pp. 5-27
    • Bank, B.1    Giusti, M.2    Heintz, J.3    Mbakop, G.4
  • 2
    • 0021388907 scopus 로고
    • On computing the determinant in small parallel time using a small number of processors
    • S.J. Berkowitz, On computing the determinant in small parallel time using a small number of processors, Information Processing Letters 18 (1984) 147-150.
    • (1984) Information Processing Letters , vol.18 , pp. 147-150
    • Berkowitz, S.J.1
  • 3
    • 0000797215 scopus 로고
    • Time space tradeoffs (getting closer to the barrier?)
    • ISSAC, LNCS, Springer, Berlin
    • A. Borodin, Time space tradeoffs (getting closer to the barrier?), Algorithms and Computation, Proceedings 4, ISSAC, LNCS, vol. 762, Springer, Berlin, 1993, pp. 209-220.
    • (1993) Algorithms and Computation, Proceedings 4 , vol.762 , pp. 209-220
    • Borodin, A.1
  • 6
    • 84945709818 scopus 로고
    • Subresultants and related polynomial sequences
    • G.E. Collins, Subresultants and related polynomial sequences, J. Assoc. Comput. Mach. 14 (1967) 128-142.
    • (1967) J. Assoc. Comput. Mach. , vol.14 , pp. 128-142
    • Collins, G.E.1
  • 8
    • 0000415960 scopus 로고
    • Sur la complexitédu théorème des zéros
    • M. Florenzano, J. Guddat, M. Jimenez, H. Th. Jongen, G. Lopez Lagomasino, F. Marcellan (Eds.), Approximation and Optimization in the Caribbean II, Peter Lange Verlag, Frankfurt am Main
    • N. Fitchas, M. Giusti, F. Smietanski, Sur la complexitédu théorème des zéros, in: M. Florenzano, J. Guddat, M. Jimenez, H. Th. Jongen, G. Lopez Lagomasino, F. Marcellan (Eds.), Approximation and Optimization in the Caribbean II, Proceedings 2nd Int. Conf. on Non-Linear Optimization and Approximation, Approximation and Optimization, vol. 8, Peter Lange Verlag, Frankfurt am Main, 1995, pp. 247-329.
    • (1995) Proceedings 2nd Int. Conf. on Non-Linear Optimization and Approximation, Approximation and Optimization , vol.8 , pp. 247-329
    • Fitchas, N.1    Giusti, M.2    Smietanski, F.3
  • 13
    • 0000936391 scopus 로고
    • La détermination des points isolés et de la dimension d'une variétéalgébrique peut se faire en temps polynomial
    • D. Eisenbud, L. Robbiano (Eds.), Cambridge University Press, Cambridge
    • M. Giusti, J. Heintz, La détermination des points isolés et de la dimension d'une variétéalgébrique peut se faire en temps polynomial, in: D. Eisenbud, L. Robbiano (Eds.), Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica, vol. 34, Cambridge University Press, Cambridge, 1993, pp. 216-256.
    • (1993) Computational Algebraic Geometry and Commutative Algebra, Symposia Matematica , vol.34 , pp. 216-256
    • Giusti, M.1    Heintz, J.2
  • 23
    • 0002694831 scopus 로고
    • Absolute primality of polynomials is decidable in random polynomial-time in the number of variables
    • LNCS, Springer, Berlin
    • J. Heintz, M. Sieveking, Absolute primality of polynomials is decidable in random polynomial-time in the number of variables, Proceedings ICALP 81, LNCS, vol. 115, Springer, Berlin, 1981, pp. 16-28.
    • (1981) Proceedings ICALP 81 , vol.115 , pp. 16-28
    • Heintz, J.1    Sieveking, M.2
  • 24
    • 84976819141 scopus 로고
    • Probabilistic algorithms for deciding equivalence of straight-line programs
    • O.H. Ibarra, S. Moran, Probabilistic algorithms for deciding equivalence of straight-line programs, J. ACM 30 (1983) 217-228.
    • (1983) J. ACM , vol.30 , pp. 217-228
    • Ibarra, O.H.1    Moran, S.2
  • 25
    • 0019625689 scopus 로고
    • Probabilistic algorithms and straight-line programs for some rank decision problems
    • O.H. Ibarra, S. Moran, L.E. Rosier, Probabilistic algorithms and straight-line programs for some rank decision problems, Information Processing Letters 12(5) (1981) 227-232.
    • (1981) Information Processing Letters , vol.12 , Issue.5 , pp. 227-232
    • Ibarra, O.H.1    Moran, S.2    Rosier, L.E.3
  • 26
    • 0021939156 scopus 로고
    • Computing with polynomials given by straight-line programs I: Greatest common divisors
    • ACM, New York
    • E. Kaltofen, Computing with polynomials given by straight-line programs I: greatest common divisors, Proceedings of the 17th Ann. ACM Symposium on Theory of Computing, ACM, New York, 1985, pp. 131-142.
    • (1985) Proceedings of the 17th Ann. ACM Symposium on Theory of Computing , pp. 131-142
    • Kaltofen, E.1
  • 27
    • 0023826531 scopus 로고
    • Greatest common divisors of polynomials given by straight-line programs
    • E. Kaltofen, Greatest common divisors of polynomials given by straight-line programs, J. ACM 35(1) (1988) 231-264.
    • (1988) J. ACM , vol.35 , Issue.1 , pp. 231-264
    • Kaltofen, E.1
  • 28
    • 0010017974 scopus 로고
    • Factorization of polynomials given by straight-line programs
    • S. Micali (Ed.), JAI Press Inc.
    • E. Kaltofen, Factorization of polynomials given by straight-line programs, in: S. Micali (Ed.), Randomness in Computation, Advances in Computing Research, vol. 5, JAI Press Inc., 1989, pp. 375-412
    • (1989) Randomness in Computation, Advances in Computing Research , vol.5 , pp. 375-412
    • Kaltofen, E.1
  • 29
    • 0001379976 scopus 로고
    • Une approche informatique pour l' approximation diophantienne
    • T. Krick, L.M. Pardo, Une approche informatique pour l' approximation diophantienne, C.R. Acad. Sci. Paris Série I 318 (1994) 407-412.
    • (1994) C.R. Acad. Sci. Paris Série I , vol.318 , pp. 407-412
    • Krick, T.1    Pardo, L.M.2
  • 30
    • 0000697864 scopus 로고    scopus 로고
    • A computational method for diophantine approximation
    • L. González-Vega, T. Recio (Eds.), Algorithms in Algebraic Geometry and Applications, Proceedings of MEGA'94, Birkhauser, Basel
    • T. Krick, L.M. Pardo, A computational method for diophantine approximation, in: L. González-Vega, T. Recio (Eds.), Algorithms in Algebraic Geometry and Applications, Proceedings of MEGA'94, Progress in Mathematics, vol. 143, Birkhauser, Basel, 1996, pp. 193-254.
    • (1996) Progress in Mathematics , vol.143 , pp. 193-254
    • Krick, T.1    Pardo, L.M.2
  • 32
    • 0347464370 scopus 로고
    • An algorithm for computing multivariate polynomial resultants
    • J. Llovet, R. Sendra, J.A. Jaén, R. Martínez, An algorithm for computing multivariate polynomial resultants, Computer Science, 1992, pp. 159-165.
    • (1992) Computer Science , pp. 159-165
    • Llovet, J.1    Sendra, R.2    Jaén, J.A.3    Martínez, R.4
  • 35
    • 0000006297 scopus 로고
    • A probabilistic remark on algebraic program testing
    • R.A. De Millo, R.J. Lipton, A probabilistic remark on algebraic program testing, Inf. Proc. Letters 7(4) (1978) 193-195.
    • (1978) Inf. Proc. Letters , vol.7 , Issue.4 , pp. 193-195
    • De Millo, R.A.1    Lipton, R.J.2
  • 36
    • 0032479656 scopus 로고    scopus 로고
    • An effective algorithm for quantifier elimination over algebraically closed fields using straight-line programs
    • S. Puddu, J. Sabia, An effective algorithm for quantifier elimination over algebraically closed fields using straight-line programs, J. Pure Appl. Algebra 129 (1998) 173-200.
    • (1998) J. Pure Appl. Algebra , vol.129 , pp. 173-200
    • Puddu, S.1    Sabia, J.2
  • 39
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • J.T. Schwartz, Fast probabilistic algorithms for verification of polynomial identities, J. ACM 27 (1980) 701-717.
    • (1980) J. ACM , vol.27 , pp. 701-717
    • Schwartz, J.T.1
  • 40
    • 44049120140 scopus 로고
    • An extended polynomial gcd algorithm using Hankel matrices
    • R. Sendra, J. Llovet, An extended polynomial gcd algorithm using Hankel matrices, Journal of Symbolic Computation 13 (1992) 25-39.
    • (1992) Journal of Symbolic Computation , vol.13 , pp. 25-39
    • Sendra, R.1    Llovet, J.2
  • 42
    • 0003285494 scopus 로고
    • Parallel linear algebra
    • J.H. Reif (Ed.), Morgan Kaufmann, Los Altos, CA
    • J. von zur Gathen, Parallel linear algebra, in: J.H. Reif (Ed.), Synthesis of Parallel Algorithms, Morgan Kaufmann, Los Altos, CA, 1993, pp. 573-617.
    • (1993) Synthesis of Parallel Algorithms , pp. 573-617
    • Von Zur Gathen, J.1
  • 43
    • 84925463455 scopus 로고
    • Probabilistic algorithms for sparse polynomials
    • LNCS
    • R. Zippel, Probabilistic algorithms for sparse polynomials, Proceedings EUROSAM' 79, LNCS, vol. 72, 1979, pp. 216-226.
    • (1979) Proceedings EUROSAM' 79 , vol.72 , pp. 216-226
    • Zippel, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.