-
1
-
-
0027575150
-
Factoring rational polynomials over the complex numbers
-
MR 94a:12001
-
C. BAJAJ, J. CANNY, T. GARRITY AND J. WARREN, "Factoring rational polynomials over the complex numbers", SIAM J. Comput. 22 (1993), 318-331. MR 94a:12001
-
(1993)
SIAM J. Comput.
, vol.22
, pp. 318-331
-
-
Bajaj, C.1
Canny, J.2
Garrity, T.3
Warren, J.4
-
2
-
-
84944812247
-
Factoring polynomials over finite fields
-
MR 36:2314
-
E. R. BERLEKAMP, "Factoring polynomials over finite fields", Bell System Tech. J., 46 (1967), 1853-1859. MR 36:2314
-
(1967)
Bell System Tech. J.
, vol.46
, pp. 1853-1859
-
-
Berlekamp, E.R.1
-
3
-
-
84968518238
-
Factoring polynomials over large finite fields
-
MR 43:1948
-
E. R. BERLEKAMP, "Factoring polynomials over large finite fields", Math. Comp., 24 (1970), 713-735. MR 43:1948
-
(1970)
Math. Comp.
, vol.24
, pp. 713-735
-
-
Berlekamp, E.R.1
-
4
-
-
0003615227
-
-
Springer-Verlag, New York, Berlin. MR 99a:68070
-
L. BLUM, F. CUCKER, M. SHUB AND S. SMALE, Complexity and Real Computation, Springer-Verlag, New York, Berlin, 1998. MR 99a:68070
-
(1998)
Complexity and Real Computation
-
-
Blum, L.1
Cucker, F.2
Shub, M.3
Smale, S.4
-
5
-
-
0015143623
-
On Euclid's algorithm and the computation of polynomial greatest common divisors
-
MR 46:6570
-
W. S. BROWN, On Euclid's algorithm and the computation of polynomial greatest common divisors, J. ACM 18 (1971), 478-504. MR 46:6570
-
(1971)
J. ACM
, vol.18
, pp. 478-504
-
-
Brown, W.S.1
-
6
-
-
34249916280
-
On fast multiplication of polynomials over arbitrary algebras
-
MR 92i:68068
-
D. G. CANTOR AND E. KALTOFEN, "On fast multiplication of polynomials over arbitrary algebras", Acta. Inform. 28 (1991), 693-701. MR 92i:68068
-
(1991)
Acta. Inform.
, vol.28
, pp. 693-701
-
-
Cantor, D.G.1
Kaltofen, E.2
-
7
-
-
84966220369
-
A new algorithm for factoring polynomials over finite fields
-
MR 82e:12020
-
D. G. CANTOR AND H. ZASSENHAUS "A new algorithm for factoring polynomials over finite fields", Math. Comp. 36 (1981), no. 154, 587-592. MR 82e:12020
-
(1981)
Math. Comp.
, vol.36
, Issue.154
, pp. 587-592
-
-
Cantor, D.G.1
Zassenhaus, H.2
-
8
-
-
0001103577
-
An algorithm of polynomial complexity for factoring polynomials, and determination of the components of a variety in a subexponential time
-
(Russian) Theory of the complexity of computations, II., [English translation: J. Sov. Math. 34 (1986).] MR 86g:11077
-
A. L. CHISTOV, "An algorithm of polynomial complexity for factoring polynomials, and determination of the components of a variety in a subexponential time" (Russian), Theory of the complexity of computations, II., Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 137 (1984), 124-188. [English translation: J. Sov. Math. 34 (1986).] MR 86g:11077
-
(1984)
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)
, vol.137
, pp. 124-188
-
-
Chistov, A.L.1
-
9
-
-
0012408783
-
Efficient factorization of polynomials over local fields
-
(Russian) [English translation: Soviet Math. Dokl. 35 (1987), no. 2, 434-438.] MR 88d:11118
-
A. L. CHISTOV, "Efficient factorization of polynomials over local fields" (Russian), Dokl. Akad. Nauk SSSR 293 (1987), no. 5, 1073-1077. [English translation: Soviet Math. Dokl. 35 (1987), no. 2, 434-438.] MR 88d:11118
-
(1987)
Dokl. Akad. Nauk SSSR
, vol.293
, Issue.5
, pp. 1073-1077
-
-
Chistov, A.L.1
-
10
-
-
0003386755
-
Efficient factoring polynomials over local fields and its applications
-
Kyoto, Math. Soc. Japan, Tokyo, 1991. MR 93e:11152
-
A. L. CHISTOV, "Efficient factoring polynomials over local fields and its applications", Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 1509-1519, Math. Soc. Japan, Tokyo, 1991. MR 93e:11152
-
(1990)
Proceedings of the International Congress of Mathematicians
, vol.1-2
, pp. 1509-1519
-
-
Chistov, A.L.1
-
11
-
-
21144460202
-
Solving linear equations over GF(2): Block Lanczos algorithm
-
MR 94i:65044
-
D. COPPERSMITH, "Solving linear equations over GF(2): block Lanczos algorithm", Linear Algebra and Its Applications, 192 (1993), 33-60. MR 94i:65044
-
(1993)
Linear Algebra and Its Applications
, vol.192
, pp. 33-60
-
-
Coppersmith, D.1
-
12
-
-
84968521645
-
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
-
MR 94c:11124
-
D. COPPERSMITH, "Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm", Math. Comp. 62 (1994), no. 205, 333-350. MR 94c:11124
-
(1994)
Math. Comp.
, vol.62
, Issue.205
, pp. 333-350
-
-
Coppersmith, D.1
-
13
-
-
0003352688
-
Using algebraic geometry
-
Springer-Verlag, New York. MR 99h:13033
-
D. COX, J. LITTLE AND D. O'SHEA, Using algebraic geometry. Graduate Texts in Mathematics, 185. Springer-Verlag, New York, 1998. MR 99h:13033
-
(1998)
Graduate Texts in Mathematics
, vol.185
-
-
Cox, D.1
Little, J.2
O'Shea, D.3
-
14
-
-
0026107119
-
Absolute factorization of polynomials: A geometric approach
-
MR 92d:12018
-
D. DUVAL, "Absolute factorization of polynomials: a geometric approach", SIAM J. Comput. 20 (1991), 1-21. MR 92d:12018
-
(1991)
SIAM J. Comput.
, vol.20
, pp. 1-21
-
-
Duval, D.1
-
15
-
-
0035869860
-
Absolute irreducibility of polynomials via Newton polytopes
-
CMP 2001:09
-
S. GAO (Gao's papers are available at http://www.math.clemson.edu/faculty/Gao), "Absolute irreducibility of polynomials via Newton polytopes", J. of Algebra 237 (2001), 501-520. CMP 2001:09
-
(2001)
J. of Algebra
, vol.237
, pp. 501-520
-
-
Gao, S.1
-
16
-
-
0035638243
-
Decomposition of polytopes and polynomials
-
CMP 1 832-732
-
S. GAO AND A. G. B. LAUDER, "Decomposition of polytopes and polynomials", Discrete and Computational Geometry 26 (2001), 89-104. CMP 1 832-732
-
(2001)
Discrete and Computational Geometry
, vol.26
, pp. 89-104
-
-
Gao, S.1
Lauder, A.G.B.2
-
19
-
-
0012370505
-
Hensel lifting and bivariate polynomial factorisation over finite fields
-
S. GAO AND A. G. B. LAUDER, "Hensel lifting and bivariate polynomial factorisation over finite fields," to appear in Mathematics of Computation. (17 pages)
-
Mathematics of Computation.
, pp. 17
-
-
Gao, S.1
Lauder, A.G.B.2
-
20
-
-
0000338611
-
Berlekamp's and Niederreiter's polynomial factorization algorithms
-
Proc. 2nd International Conference on Finite Fields: Theory, Applications, and Algorithms, Las Vegas. MR 95f:11106
-
S. GAO AND J. VON ZUR GATHEN, "Berlekamp's and Niederreiter's polynomial factorization algorithms", Proc. 2nd International Conference on Finite Fields: Theory, Applications, and Algorithms, Las Vegas, 1993. Contemporary Mathematics, vol. 168, 1994, 101-116. MR 95f:11106
-
(1994)
Contemporary Mathematics
, vol.168
, pp. 101-116
-
-
Gao, S.1
Von zur Gathen, J.2
-
21
-
-
0020828328
-
Irreducibility of multivariate polynomials
-
MR 87f:12002a
-
J. VON ZUR GATHEN, "Irreducibility of multivariate polynomials", J. Comput. System Sci. 31 (1985), no. 2, 225-264. MR 87f:12002a
-
(1985)
J. Comput. System Sci.
, vol.31
, Issue.2
, pp. 225-264
-
-
Von zur Gathen, J.1
-
23
-
-
84966248331
-
Factorization of multivariate polynomials over finite fields
-
MR 87a:12005
-
J. VON ZUR GATHEN AND E. KALTOFEN, "Factorization of multivariate polynomials over finite fields", Math. Comp. 45 (1985), no. 171, 251-261. MR 87a:12005
-
(1985)
Math. Comp.
, vol.45
, Issue.171
, pp. 251-261
-
-
Von zur Gathen, J.1
Kaltofen, E.2
-
24
-
-
0020828408
-
Factoring sparse multivariate polynomials
-
MR 87f:12002b
-
J. VON ZUR GATHEN AND E. KALTOFEN, "Factoring sparse multivariate polynomials", J. of Comput. System Sci. 31 (1985), 265-287. MR 87f:12002b
-
(1985)
J. of Comput. System Sci.
, vol.31
, pp. 265-287
-
-
Von zur Gathen, J.1
Kaltofen, E.2
-
25
-
-
0001605828
-
Computing Frobenius maps and factoring polynomials
-
MR 94d:12011
-
J. VON ZUR GATHEN AND V. SHOUP, "Computing Frobenius maps and factoring polynomials", Computational Complexity 2 (1992), 187-224. MR 94d:12011
-
(1992)
Computational Complexity
, vol.2
, pp. 187-224
-
-
Von zur Gathen, J.1
Shoup, V.2
-
26
-
-
0004056503
-
-
Kluwer, Boston/Dordrecht/London, MR 96a:68049
-
K. O. GEDDES, S. R. CZAPOR AND G. LABAHN, Algorithms for Computer Algebra, Kluwer, Boston/Dordrecht/London, 1992. MR 96a:68049
-
(1992)
Algorithms for Computer Algebra
-
-
Geddes, K.O.1
Czapor, S.R.2
Labahn, G.3
-
27
-
-
0003057792
-
Factoring polynomials over a finite field and solution of systems of algebraic equations
-
(Russian), Theory of the complexity of computations, II., [English translation: J. Sov. Math. 34 (1986)]. MR 86g:11077
-
D. YU GRIGORYEV, "Factoring polynomials over a finite field and solution of systems of algebraic equations" (Russian), Theory of the complexity of computations, II., Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 137 (1984), 124-188 [English translation: J. Sov. Math. 34 (1986)]. MR 86g:11077
-
(1984)
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)
, vol.137
, pp. 124-188
-
-
Yu Grigoryev, D.1
-
28
-
-
0012449803
-
Fast factorization of polynomials into irreducible ones and the solution of systems of algebraic equations
-
(Russian) [English translation: Soviet Math. Dokl. 29 (1984), no. 2, 380-383.] MR 86d:11101
-
D. YU GRIGORYEV AND A. L. CHISTOV, "Fast factorization of polynomials into irreducible ones and the solution of systems of algebraic equations" (Russian), Dokl. Akad. Nauk SSSR 275 (1984), no. 6, 1302-1306. [English translation: Soviet Math. Dokl. 29 (1984), no. 2, 380-383.] MR 86d:11101
-
(1984)
Dokl. Akad. Nauk SSSR
, vol.275
, Issue.6
, pp. 1302-1306
-
-
Yu Grigoryev, D.1
Chistov, A.L.2
-
29
-
-
0003897060
-
-
Springer-Verlag, Berlin, New York. MR 57:3116
-
R. HARTSHORNE, Algebraic Geometry, Springer-Verlag, Berlin, New York, 1977. MR 57:3116
-
(1977)
Algebraic Geometry
-
-
Hartshorne, R.1
-
30
-
-
0022060323
-
Polynomial-time reductions from multivariate to bi- and univariate integral polynomial factorization
-
MR 86j:12001
-
E. KALTOFEN, "Polynomial-time reductions from multivariate to bi- and univariate integral polynomial factorization", SIAM J. Comput. 14 (1985), no. 2, 469-489. MR 86j:12001
-
(1985)
SIAM J. Comput.
, vol.14
, Issue.2
, pp. 469-489
-
-
Kaltofen, E.1
-
31
-
-
0012371788
-
Computing the irreducible real factors and components of an algebraic curve
-
MR 96a:14063
-
E. KALTOFEN, "Computing the irreducible real factors and components of an algebraic curve", Appl. Algebra Engrg. Comm. Comput. 1 (1990), 135-148. MR 96a:14063
-
(1990)
Appl. Algebra Engrg. Comm. Comput.
, vol.1
, pp. 135-148
-
-
Kaltofen, E.1
-
32
-
-
0029291305
-
Effective Noether irreducibility forms and applications
-
Symposium on the Theory of Computing (New Orleans, LA, 1991). MR 96g:68053
-
E. KALTOFEN, "Effective Noether irreducibility forms and applications", Symposium on the Theory of Computing (New Orleans, LA, 1991). J. Comput. System Sci. 50 (1995), no. 2, 274-295. MR 96g:68053
-
(1995)
J. Comput. System Sci.
, vol.50
, Issue.2
, pp. 274-295
-
-
Kaltofen, E.1
-
33
-
-
84968495217
-
On Wiedemann's method of solving sparse linear systems
-
Springer-Verlag. MR 94b:68003
-
E. KALTOFEN AND B. D. SAUNDERS, "On Wiedemann's method of solving sparse linear systems", in Proc. AAECC-9, LNCS 539, Springer-Verlag, 1991, 29-38. MR 94b:68003
-
(1991)
Proc. AAECC-9, LNCS
, vol.539
, pp. 29-38
-
-
Kaltofen, E.1
Saunders, B.D.2
-
34
-
-
0032365366
-
Subquadratic-time factoring of polynomials over finite fields
-
MR 99m:68097
-
E. KALTOFEN AND V. SHOUP, "Subquadratic-time factoring of polynomials over finite fields", Math. Comp. 67 (1998), no. 223, 1179-1197. MR 99m:68097
-
(1998)
Math. Comp.
, vol.67
, Issue.223
, pp. 1179-1197
-
-
Kaltofen, E.1
Shoup, V.2
-
35
-
-
84992074342
-
Computing with polynomials given by black boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators
-
MR 91k:68100
-
E. KALTOFEN AND B. TRAGER, "Computing with polynomials given by black boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators", J. Symbolic Comput. 9 (1990), 301-320. MR 91k:68100
-
(1990)
J. Symbolic Comput.
, vol.9
, pp. 301-320
-
-
Kaltofen, E.1
Trager, B.2
-
36
-
-
84988216913
-
Solving large sparse systems over finite fields
-
Advances in Cryptology, CRYPTO '90 (A.J. Menezes and S.A. Vanstone, eds.) Springer-Verlag. MR 94b:94002
-
B. A. LAMACCHIA AND A. M. ODLYZKO, "Solving large sparse systems over finite fields", Advances in Cryptology, CRYPTO '90 (A.J. Menezes and S.A. Vanstone, eds.), LNCS 537, Springer-Verlag, 109-133. MR 94b:94002
-
LNCS
, vol.537
, pp. 109-133
-
-
Lamacchia, B.A.1
Odlyzko, A.M.2
-
37
-
-
0001427288
-
Integration of rational functions: Rational computation of the logarithmic part
-
MR 91h:68091
-
D. LAZARD AND R. RIOBOO, "Integration of rational functions: rational computation of the logarithmic part", J. Symbolic Comput. 9 (1990), no. 2, 113-115. MR 91h:68091
-
(1990)
J. Symbolic Comput.
, vol.9
, Issue.2
, pp. 113-115
-
-
Lazard, D.1
Rioboo, R.2
-
38
-
-
0020847988
-
Factoring multivariate integral polynomials
-
MR 86g:12001a
-
A. K. LENSTRA, "Factoring multivariate integral polynomials", Theoret. Comput. Sci. 34 (1984), no. 1-2, 207-213. MR 86g:12001a
-
(1984)
Theoret. Comput. Sci.
, vol.34
, Issue.1-2
, pp. 207-213
-
-
Lenstra, A.K.1
-
39
-
-
0020733320
-
Factoring multivariate polynomials over finite fields
-
MR 87a:11124
-
A. K. LENSTRA, "Factoring multivariate polynomials over finite fields", J. Comput. System Sci. 30 (1985), no. 2, 235-248. MR 87a:11124
-
(1985)
J. Comput. System Sci.
, vol.30
, Issue.2
, pp. 235-248
-
-
Lenstra, A.K.1
-
40
-
-
0023366347
-
Factoring multivariate polynomials over algebraic number fields
-
MR 88j:12001
-
A. K. LENSTRA, "Factoring multivariate polynomials over algebraic number fields", SIAM J. Comput. 16 (1987), no. 3, 591-598, MR 88j:12001
-
(1987)
SIAM J. Comput.
, vol.16
, Issue.3
, pp. 591-598
-
-
Lenstra, A.K.1
-
41
-
-
34250244723
-
Factoring polynomials with rational coefficients
-
MR 84a:12002
-
A. K. LENSTRA, H. W. LENSTRA, JR. AND L. LOVÁSZ, "Factoring polynomials with rational coefficients", Mathematische Annalen, 161 (1982), 515-534. MR 84a:12002
-
(1982)
Mathematische Annalen
, vol.161
, pp. 515-534
-
-
Lenstra, A.K.1
Lenstra H.W., Jr.2
Lovász, L.3
-
42
-
-
84957682846
-
A block Lanczos Algorithm for finding dependencies over GF(2)
-
Advances in cryptology-EUROCRYPT '95 (Saint-Malo, 1995) Springer, Berlin. MR 97c:11115
-
P. L. MONTGOMERY, "A block Lanczos Algorithm for finding dependencies over GF(2)", Advances in cryptology-EUROCRYPT '95 (Saint-Malo, 1995), LNCS 921, Springer, Berlin, 1995, 106-120. MR 97c:11115
-
(1995)
LNCS
, vol.921
, pp. 106-120
-
-
Montgomery, P.L.1
-
44
-
-
0016495356
-
Multivariate polynomial factorization
-
MR 53:335a
-
D. R. MUSSER, "Multivariate polynomial factorization", J. ACM 22 (1975), 291-308. MR 53:335a
-
(1975)
J. ACM
, vol.22
, pp. 291-308
-
-
Musser, D.R.1
-
45
-
-
0012438766
-
A new efficient factorization algorithm for polynomials over small finite fields
-
MR 94h:11112
-
H. NIEDERREITER, "A new efficient factorization algorithm for polynomials over small finite fields", Appl. Alg. Eng. Comm. Comp. 4 (1993), 81-87. MR 94h:11112
-
(1993)
Appl. Alg. Eng. Comm. Comp.
, vol.4
, pp. 81-87
-
-
Niederreiter, H.1
-
46
-
-
0031169815
-
Solving a polynomial equation: Some history and recent progress
-
MR 99b:65066
-
V. Y. PAN, "Solving a polynomial equation: some history and recent progress", SIAM Rev. 39 (1997), 187-220. MR 99b:65066
-
(1997)
SIAM Rev.
, vol.39
, pp. 187-220
-
-
Pan, V.Y.1
-
47
-
-
0012411219
-
A new modular interpolation algorithm for factoring multivariate polynomials
-
(extended abstract) Proc. 1994 Algorithmic Number Theory Symposium (L. M. Adleman and M.-D. Huang, eds.) pringer-Verlag. MR 96d:12013
-
R. RUBINFELD AND R. ZIPPEL "A new modular interpolation algorithm for factoring multivariate polynomials (extended abstract)", in Proc. 1994 Algorithmic Number Theory Symposium (L. M. Adleman and M.-D. Huang, eds.), LNCS 877, Springer-Verlag, 1994, 93-107. MR 96d:12013
-
(1994)
LNCS
, vol.877
, pp. 93-107
-
-
Rubinfeld, R.1
Zippel, R.2
-
48
-
-
0001662951
-
Reduzibilität ebener kurven
-
MR 88J:14010
-
W. RUPPERT, "Reduzibilität ebener Kurven", J. reine angew. Math. 369 (1986), 167-191. MR 88J:14010
-
(1986)
J. Reine Angew. Math.
, vol.369
, pp. 167-191
-
-
Ruppert, W.1
-
49
-
-
0000611856
-
Reducibility of polynomials f(x,y) modulo p
-
MR 2000d:11128
-
W. M. RUPPERT, "Reducibility of polynomials f(x,y) modulo p", J. Number Theory 77 (1999), 62-70. MR 2000d:11128
-
(1999)
J. Number Theory
, vol.77
, pp. 62-70
-
-
Ruppert, W.M.1
-
50
-
-
34250459760
-
Schnelle multiplikation großer zahlen
-
MR 45:1431
-
[50] A. SCHÖNHAGE AND V. STRASSEN, "Schnelle Multiplikation großer Zahlen", Computing 7 (1971), 281-292. MR 45:1431
-
(1971)
Computing
, vol.7
, pp. 281-292
-
-
Schönhage, A.1
Strassen, V.2
-
51
-
-
84976779342
-
Fast probabilistic algorithms for verification of polynomial identities
-
MR 82m:68078
-
J.T. SCHWARTZ, "Fast probabilistic algorithms for verification of polynomial identities," J. ACM 27 (1980), 710-717. MR 82m:68078
-
(1980)
J. ACM
, vol.27
, pp. 710-717
-
-
Schwartz, J.T.1
-
52
-
-
0000210144
-
An improved multivariate polynomial factorization algorithm
-
MR 58:27887
-
P. S. WANG, "An improved multivariate polynomial factorization algorithm", Math. Comp. 32 (1978), 1215-1231. MR 58:27887
-
(1978)
Math. Comp.
, vol.32
, pp. 1215-1231
-
-
Wang, P.S.1
-
53
-
-
0022583143
-
Solving sparse linear equations over finite fields
-
MR 87g:11166
-
D. H. WIEDEMANN, "Solving sparse linear equations over finite fields", IEEE Trans. Inform. Theory 32 (1986), 54-62. MR 87g:11166
-
(1986)
IEEE Trans. Inform. Theory
, vol.32
, pp. 54-62
-
-
Wiedemann, D.H.1
-
54
-
-
84925463455
-
Probabilistic algorithms for sparse polynomials
-
Symbolic and algebraic computation (EUROSAM '79, Internat. Sympos., Marseille, 1979), Springer, Berlin-New York. MR 81g:68061
-
R. ZIPPEL, "Probabilistic algorithms for sparse polynomials", Symbolic and algebraic computation (EUROSAM '79, Internat. Sympos., Marseille, 1979), pp. 216-226, Lecture Notes in Comput. Sci., 72, Springer, Berlin-New York, 1979. MR 81g:68061
-
(1979)
Lecture Notes in Comput. Sci.
, vol.72
, pp. 216-226
-
-
Zippel, R.1
|