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Volumn Part F129447, Issue , 1996, Pages 498-507

Multiplicative equations over commuting matrices

Author keywords

[No Author keywords available]

Indexed keywords

GERMANIUM; POLYNOMIAL APPROXIMATION; POLYNOMIALS;

EID: 84906731094     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (83)

References (40)
  • 2
    • 84942491445 scopus 로고
    • Logarithmic forms and group varieties
    • A. Baker, G. Wüstholz: Logarithmic forms and group varieties, J. reine angew. Math. 442 (1993), 19-62.
    • (1993) J. Reine Angew. Math. , vol.442 , pp. 19-62
    • Baker, A.1    Wüstholz, G.2
  • 3
    • 0027873264 scopus 로고
    • Las vegas algorithms for matrix groups
    • R. Beals, L. Babai: Las Vegas algorithms for matrix groups, Proc. 34th IEEE FOCS (1993), 427-436.
    • (1993) Proc. 34th IEEE FOCS , pp. 427-436
    • Beals, R.1    Babai, L.2
  • 4
    • 85031620045 scopus 로고    scopus 로고
    • Deciding finiteness of matrix groups in deterministic polynomial time
    • to appear
    • L. Babai, R. Beals, D. Rockmore: Deciding finiteness of matrix groups in deterministic polynomial time, Israel J. Math., to appear.
    • Israel J. Math.
    • Babai, L.1    Beals, R.2    Rockmore, D.3
  • 5
    • 0029510685 scopus 로고
    • Algorithms for matrix groups and the tits alternative
    • R. Beals: Algorithms for matrix groups and the Tits alternative, Proc. 36th IEEE FOCS (1995), pp. 593-602.
    • (1995) Proc. 36th IEEE FOCS , pp. 593-602
    • Beals, R.1
  • 6
    • 0342800688 scopus 로고
    • Membership testing in commutative transformation semigroups
    • M. Beaudry: Membership testing in commutative transformation semigroups, Information and Computation 79 (1988), 84-93.
    • (1988) Information and Computation , vol.79 , pp. 84-93
    • Beaudry, M.1
  • 7
    • 85031689877 scopus 로고    scopus 로고
    • Computing Jordan normal forms exactly for commuting matrices in polynomial time
    • J. Cai: Computing Jordan Normal Forms exactly for commuting matrices in polynomial time, SUNY Buffalo CS Tech Report 94-16.
    • SUNY Buffalo CS Tech Report 94-16
    • Cai, J.1
  • 8
    • 84936760286 scopus 로고
    • The complexity of the membership problem for 2-generated commutative semigroups of rational matrices
    • J-y. Cai, R. J. Lipton, Y. Zalcstein: The complexity of the membership problem for 2-generated commutative semigroups of rational matrices, Proc 35th IEEE FOCS (1994), 135-142.
    • (1994) Proc 35th IEEE FOCS , pp. 135-142
    • Cai, J.-Y.1    Lipton, R.J.2    Zalcstein, Y.3
  • 10
    • 84945709818 scopus 로고
    • Subresultants and reduced polynomial remainder sequences
    • G. E. Collins: Subresultants and reduced polynomial remainder sequences, J. ACM (1967), 128-142.
    • (1967) J. ACM , pp. 128-142
    • Collins, G.E.1
  • 11
    • 0010949451 scopus 로고
    • Decomposition of algebras over finite fields and number fields
    • W. M. Eberly: Decomposition of algebras over finite fields and number fields, Computational Complexity 1 (1991), 179-206.
    • (1991) Computational Complexity , vol.1 , pp. 179-206
    • Eberly, W.M.1
  • 12
    • 0021973388 scopus 로고
    • Polynomial time solutions of some problems in abstract algebra
    • K. Friedl, L. Rónyai: Polynomial time solutions of some problems in abstract algebra, Proc 17th ACM STOC (1985), 153-162.
    • (1985) Proc 17th ACM STOC , pp. 153-162
    • Friedl, K.1    Rónyai, L.2
  • 15
    • 0027886529 scopus 로고
    • Testing equalities of multiplicative representations in polynomial time
    • G. Ge: Testing equalities of multiplicative representations in polynomial time, Proc 34th IEEE FOCS (1993), 422-426.
    • (1993) Proc 34th IEEE FOCS , pp. 422-426
    • Ge, G.1
  • 16
    • 84968512995 scopus 로고    scopus 로고
    • Recognizing units in number fields
    • G. Ge: Recognizing units in number fields, Math. Comp. 63, No. 207, 377-387.
    • Math. Comp. , vol.63 , Issue.207 , pp. 377-387
    • Ge, G.1
  • 19
    • 84968456476 scopus 로고
    • Fast decomposition of polynomials into irreducible ones and the solution of systems of algebraic equations
    • D.Yu. Grigoryev, A.L. Chistov: Fast decomposition of polynomials into irreducible ones and the solution of systems of algebraic equations, Soviet Math. Dokl. 29 (1984), 380-383.
    • (1984) Soviet Math. Dokl. , vol.29 , pp. 380-383
    • Grigoryev, D.Yu.1    Chistov, A.L.2
  • 20
    • 0343979741 scopus 로고
    • Polynomial time algorithms for finding integer relations among real numbers
    • J. Håstad, B. Helfrich, J. Lagarias, C. P. Schnorr: Polynomial time algorithms for finding integer relations among real numbers, Proc 3rd STACS (1986), 105-118.
    • (1986) Proc 3rd STACS , pp. 105-118
    • Håstad, J.1    Helfrich, B.2    Lagarias, J.3    Schnorr, C.P.4
  • 23
    • 0022793656 scopus 로고
    • Polynomial-time algorithms for the orbit problem
    • R. Kannan, R. Lipton: Polynomial-time algorithms for the orbit problem, J. ACM 33, No. 4 (1986), 808-821.
    • (1986) J. ACM , vol.33 , Issue.4 , pp. 808-821
    • Kannan, R.1    Lipton, R.2
  • 24
    • 0343670970 scopus 로고
    • Solvability of the problem of occurrence in finitely generated soluble groups over the field of algebraic numbers
    • translated from Algebra i Logika 7 (1968), 53-63
    • V. M. Kopytov: Solvability of the problem of occurrence in finitely generated soluble groups over the field of algebraic numbers, Algebra and Logic 7 (1968), 388-393, translated from Algebra i Logika 7 (1968), 53-63.
    • (1968) Algebra and Logic , vol.7 , pp. 388-393
    • Kopytov, V.M.1
  • 25
    • 0022014061 scopus 로고
    • Factoring polynomials over algebraic number fields
    • S. Landau: Factoring polynomials over algebraic number fields, SIAM J. Comput. 14 (1985), 184-195
    • (1985) SIAM J. Comput. , vol.14 , pp. 184-195
    • Landau, S.1
  • 26
    • 85031665385 scopus 로고
    • Erratum
    • Erratum in SLAM J. Comput. 20 (1991).
    • (1991) SLAM J. Comput. , vol.20
  • 27
    • 85031899865 scopus 로고
    • Factoring polynomials over algebraic number fields
    • Springer L.N.C.S.
    • A. K. Lenstra: Factoring polynomials over algebraic number fields, Proc. EUROCAL'83, Springer L.N.C.S. Vol. 162, 1983, pp. 245-254.
    • (1983) Proc. EUROCAL'83 , vol.162 , pp. 245-254
    • Lenstra, A.K.1
  • 28
    • 0020845921 scopus 로고
    • Integer programming with a fixed number of variables
    • H. W. Lenstra: Integer programming with a fixed number of variables, Mathematics of Operations Research 8 (1983), 538-548.
    • (1983) Mathematics of Operations Research , vol.8 , pp. 538-548
    • Lenstra, H.W.1
  • 29
    • 34250244723 scopus 로고
    • Factoring polynomials with rational coefficients
    • A. K. Lenstra, H. W. Lenstra, L. Lovasz: Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534.
    • (1982) Math. Ann. , vol.261 , pp. 515-534
    • Lenstra, A.K.1    Lenstra, H.W.2    Lovasz, L.3
  • 30
    • 85065731689 scopus 로고
    • Computing in solvable matrix groups
    • E. M. Luks: Computing in solvable matrix groups, Proc. 33rd IEEE FOCS (1992), 111-120.
    • (1992) Proc. 33rd IEEE FOCS , pp. 111-120
    • Luks, E.M.1
  • 31
    • 0043026726 scopus 로고
    • Linear relations on algebraic groups
    • A. Baker, ed, Cambridge University Press
    • D. W. Masser: Linear relations on algebraic groups, in New Advances in Transcendence Theory, A. Baker, ed, Cambridge University Press, 1988, 248-262.
    • (1988) New Advances in Transcendence Theory , pp. 248-262
    • Masser, D.W.1
  • 32
    • 0009374607 scopus 로고
    • The occurrence problem for a direct product of groups (in Russian)
    • K. A. Mihaïlova: The occurrence problem for a direct product of groups (in Russian), Dokl. Akad. Nauk 119 (1958), 1103-1105.
    • (1958) Dokl. Akad. Nauk , vol.119 , pp. 1103-1105
    • Mihaïlova, K.A.1
  • 33
    • 85031693882 scopus 로고    scopus 로고
    • G. Ostheimer: private communication. [Pa]
    • G. Ostheimer: private communication. [Pa]
  • 34
    • 0014751960 scopus 로고
    • Undecidability in 3 by 3 matrices
    • M. S. Paterson: Undecidability in 3 by 3 matrices, J. of Math. and Physics 49 (1970), 105-107.
    • (1970) J. of Math. and Physics , vol.49 , pp. 105-107
    • Paterson, M.S.1
  • 35
    • 0000492177 scopus 로고
    • Computing the structure of finite algebras
    • L. Rónyai: Computing the structure of finite algebras, Journal of Symbolic Computation 9, (1990), 355-373.
    • (1990) Journal of Symbolic Computation , vol.9 , pp. 355-373
    • Rónyai, L.1
  • 37
    • 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
  • 38
    • 0000644892 scopus 로고
    • Free subgroups in linear groups
    • J. Tits: Free subgroups in linear groups, J. Algebra 20 (1972), 250-270.
    • (1972) J. Algebra , vol.20 , pp. 250-270
    • Tits, J.1
  • 40
    • 84925463455 scopus 로고
    • Probabilistic algorithms for sparse polynomials
    • L.N.C.S. Springer-Verlag
    • R. E. Zippel: Probabilistic algorithms for sparse polynomials, Proc. EUROSAM 79, L.N.C.S. 72 (1979), Springer-Verlag, pp. 216-226.
    • (1979) Proc. EUROSAM 79 , vol.72 , pp. 216-226
    • Zippel, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.