Contents - Student subdomain for University of Bath

More documents

Recommendations

Info

252 BIBLIOGRAPHY [Har16] G.H. Hardy. The Integration of Functions of a Single Variable (2nd. ed.). Cambridge Tract 2, C.U.P., 1916. Jbuch. 46, 1916. [Har11] [Has53] [HD03] [Hea05] [Her72] [Hor69] [Hor71] [Hou59] [HP07] [Hur12] [HW79] [IEE85] [IL80] [IPS10] [IPS11] M.C. Harrison. Explicit Solution By Radicals of Algebraic Curves of Genus 5 or 6. http://arxiv.org/abs/1103.4946, 2011. C.B. Haselgrove. Implementations of the Todd-Coxeter Algorithm on EDSAC-1. Unpublished, 1953. A.J. Holt and J.H. Davenport. Resolving Large Prime(s) Variants for Discrete Logarithm Computation. In P.G. Farrell, editor, Proceedings 9th IMA Conf. Coding and Cryptography, pages 207–222, 2003. A.C. Hearn. REDUCE: The First Forty Years. In Proceedings A3L, pages 19–24, 2005. E. Hermite. Sur l’intégration des fractions rationelles. Nouvelles Annales de Mathématiques, 11:145–148, 1872. E. Horowitz. Algorithm for Symbolic Integration of Rational Functions. PhD thesis, Univ. of Wisconsin, 1969. E. Horowitz. Algorithms for Partial Fraction Decomposition and Rational Function Integration. In Proceedings Second Symposium on Symbolic and Algebraic Manipulation, pages 441–457, 1971. A.S. Householder. Dandelin, Lobačevskiĭor Graeffe? Amer. Math. Monthly, 66:464–466, 1959. H. Hong and J. Perry. Are Buchberger’s criteria necessary for the chain condition? J. Symbolic Comp., 42:717–732, 2007. A. Hurwitz. Über den Satz von Budan-Fourier. Math. Annalen, 71:584–591, 1912. G.H. Hardy and E.M. Wright. An Introduction to the Theory of Numbers (5th. ed.). Clarendon Press, 1979. IEEE. IEEE Standard 754 for Binary Floating-Point Arithmetic. IEEE, 1985. O.H. Ibarra and B.S. Leininger. The Complexity of the Equivalence Problem for Straight-line Programs. In Proceedings ACM STOC 1980, pages 273–280, 1980. I. Idrees, G. Pfister, and S. Steidel. Parallelization of Modular Algorithms. http://arxiv.org/abs/1005.5663v1, 2010. I. Idrees, G. Pfister, and S. Steidel. Parallelization of Modular Algorithms. J. Symbolic Comp., 46:672–684, 2011.
BIBLIOGRAPHY 253 [Isa85] I.M. Isaacs. Solution of polynomials by real radicals. Amer. Math. Monthly, 92:571–575, 1985. [Jen79] Jenks.R.D. MODLISP. In Proceedings EUROSAM 79, pages 466– 480, 1979. [JHM11] R. Jones, A. Hosking, and E. Moss. The garbage collection handbook: The Art of Automatic Memory Management (1st ed.). Chapman & Hall/CRC, 2011. [Joh71] S.C. Johnson. On the Problem of Recognizing Zero. J. ACM, 18:559–565, 1971. [Joh74] [JR10] [JS92] [Kah53] [Kal88] [Kal89] S.C. Johnson. Sparse Polynomial Arithmetic. In Proceedings EU- ROSAM 74, pages 63–71, 1974. D.J. Jeffrey and A.D. Rich. Reducing Expression Size Using Rule- Based Integration. In S. Autexier et al., editor, Proceedings CICM 2010, pages 234–246, 2010. R.D. Jenks and R.S. Sutor. AXIOM: The Scientific Computation System. Springer-Verlag, 1992. H.G. Kahrimanian. Analytic differentiation by a digital computer. Master’s thesis, M.A. Thesis, 1953. E. Kaltofen. Greatest Common Divisors of Polynomials given by Straight-line Programs. J. ACM, 35:231–264, 1988. M. Kalkbrener. Solving systems of algebraic equations by using Gröbner bases. In Proceedings EUROCAL 87, pages 282–292, 1989. [Kar81] M. Karr. Summation in Finite Terms. J. ACM, 28:305–350, 1981. [KMS83] E. Kaltofen, D.R. Musser, and B.D. Saunders. A Generalized Class of Polynomials That are Hard to Factor. SIAM J. Comp., 12:473–483, 1983. [Knu74] [Knu98] [KO63] [KRW90] D.E. Knuth. Big Omicron and big Omega and big Theta. ACM SIGACT News 2, 8:18–24, 1974. D.E. Knuth. The Art of Computer Programming, Vol. II, Seminumerical Algorithms. Third Edition, 1998. A. Karatsuba and J. Ofman. Multiplication of multidigit numbers on automata. Sov. Phys. Dokl., 7:595–596, 1963. A. Kandri-Rody and V. Weispfenning. Non-commutative Gröbner bases in algebras of solvable type. J. Symbolic Comp., 9:1–26, 1990.
Page 1 and 2:
Contents 1 Introduction 13 1.1 Hist
Page 3 and 4:
CONTENTS 3 4 Modular Methods 113 4.
Page 5 and 6:
CONTENTS 5 A Algebraic Background 2
Page 7 and 8:
List of Figures 2.1 A polynomial SL
Page 9 and 10:
LIST OF FIGURES 9 List of Open Prob
Page 11 and 12:
Preface This text is under active d
Page 13 and 14:
Chapter 1 Introduction Computer alg
Page 15 and 16:
1.1. HISTORY AND SYSTEMS 15 1.1 His
Page 17 and 18:
1.2. EXPANSION AND SIMPLIFICATION 1
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
1.3. ALGEBRAIC DEFINITIONS 23 which
Page 25 and 26:
1.3. ALGEBRAIC DEFINITIONS 25 Propo
Page 27 and 28:
1.5. SOME MAPLE 27 Definition 18 (F
Page 29 and 30:
Chapter 2 Polynomials Polynomials a
Page 31 and 32:
2.1. WHAT ARE POLYNOMIALS? 31 2.1.1
Page 33 and 34:
2.1. WHAT ARE POLYNOMIALS? 33 MULTI
Page 35 and 36:
2.1. WHAT ARE POLYNOMIALS? 35 not n
Page 37 and 38:
2.1. WHAT ARE POLYNOMIALS? 37 While
Page 39 and 40:
2.1. WHAT ARE POLYNOMIALS? 39 p:=x+
Page 41 and 42:
2.2. RATIONAL FUNCTIONS 41 Proposit
Page 43 and 44:
2.3. GREATEST COMMON DIVISORS 43 2.
Page 45 and 46:
2.3. GREATEST COMMON DIVISORS 45 Le
Page 47 and 48:
2.3. GREATEST COMMON DIVISORS 47 93
Page 49 and 50:
2.3. GREATEST COMMON DIVISORS 49 a
Page 51 and 52:
2.3. GREATEST COMMON DIVISORS 51 #
Page 53 and 54:
2.4. NON-COMMUTATIVE POLYNOMIALS 53
Page 55 and 56:
Chapter 3 Polynomial Equations In t
Page 57 and 58:
3.1. EQUATIONS IN ONE VARIABLE 57 S
Page 59 and 60:
3.1. EQUATIONS IN ONE VARIABLE 59 I
Page 61 and 62:
3.1. EQUATIONS IN ONE VARIABLE 61 T
Page 63 and 64:
3.1. EQUATIONS IN ONE VARIABLE 63 S
Page 65 and 66:
3.2. LINEAR EQUATIONS IN SEVERAL VA
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
3.3. NONLINEAR MULTIVARIATE EQUATIO
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
3.5. EQUATIONS AND INEQUALITIES 101
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
3.6. CONCLUSIONS 111 Partial Proof.
Page 113 and 114:
Chapter 4 Modular Methods In chapte
Page 115 and 116:
4.1. GCD IN ONE VARIABLE 115 The co
Page 117 and 118:
4.1. GCD IN ONE VARIABLE 117 This l
Page 119 and 120:
4.1. GCD IN ONE VARIABLE 119 be mad
Page 121 and 122:
4.1. GCD IN ONE VARIABLE 121 Figure
Page 123 and 124:
4.1. GCD IN ONE VARIABLE 123 Figure
Page 125 and 126:
4.2. POLYNOMIALS IN TWO VARIABLES 1
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
4.3. POLYNOMIALS IN SEVERAL VARIABL
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
4.4. FURTHER APPLICATIONS 139 2 7 3
Page 141 and 142:
4.4. FURTHER APPLICATIONS 141 i.e.
Page 143 and 144:
4.5. GRÖBNER BASES 143 Observation
Page 145 and 146:
4.5. GRÖBNER BASES 145 Table 4.2:
Page 147 and 148:
4.5. GRÖBNER BASES 147 Figure 4.17
Page 149 and 150:
Chapter 5 p-adic Methods In this ch
Page 151 and 152:
5.2. MODULAR METHODS 151 nomials, b
Page 153 and 154:
5.4. FROM Z P TO Z? 153 Figure 5.3:
Page 155 and 156:
5.5. HENSEL LIFTING 155 polynomials
Page 157 and 158:
5.5. HENSEL LIFTING 157 Figure 5.4:
Page 159 and 160:
5.5. HENSEL LIFTING 159 Figure 5.7:
Page 161 and 162:
5.7. UNIVARIATE FACTORING SOLVED 16
Page 163 and 164:
5.8. MULTIVARIATE FACTORING 163 Ope
Page 165 and 166:
Chapter 6 Algebraic Numbers and fun
Page 167 and 168:
6.1. THE D5 APPROACH TO ALGEBRAIC N
Page 169 and 170:
Chapter 7 Calculus Throughout this
Page 171 and 172:
7.2. INTEGRATION OF RATIONAL EXPRES
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
7.3. THEORY: LIOUVILLE’S THEOREM
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
7.4. INTEGRATION OF LOGARITHMIC EXP
Page 185 and 186:
7.5. INTEGRATION OF EXPONENTIAL EXP
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
7.7. THE RISCH DIFFERENTIAL EQUATIO
Page 193 and 194:
7.8. THE PARALLEL APPROACH 193 i.e.
Page 195 and 196:
7.10. OTHER CALCULUS PROBLEMS 195 7
Page 197 and 198:
Chapter 8 Algebra versus Analysis W
Page 199 and 200:
8.2. BRANCH CUTS 199 8.2 Branch Cut
Page 201 and 202: 8.2. BRANCH CUTS 201 Note that the
Page 203 and 204: 8.5. INTEGRATING ‘REAL’ FUNCTIO
Page 205 and 206: Appendix A Algebraic Background A.1
Page 207 and 208: A.1. THE RESULTANT 207 Proposition
Page 209 and 210: A.2. USEFUL ESTIMATES 209 Corollary
Page 211 and 212: A.2. USEFUL ESTIMATES 211 Propositi
Page 213 and 214: A.2. USEFUL ESTIMATES 213 centring
Page 215 and 216: A.3. CHINESE REMAINDER THEOREM 215
Page 217 and 218: A.5. VANDERMONDE SYSTEMS 217 Clearl
Page 219 and 220: A.5. VANDERMONDE SYSTEMS 219 wherea
Page 221 and 222: Appendix B Excursus This appendix i
Page 223 and 224: B.2. EQUALITY OF FACTORED POLYNOMIA
Page 225 and 226: B.3. KARATSUBA’S METHOD 225 addit
Page 227 and 228: B.4. STRASSEN’S METHOD 227 answer
Page 229 and 230: B.4. STRASSEN’S METHOD 229 If the
Page 231 and 232: Appendix C Systems This appendix di
Page 233 and 234: C.2. MACSYMA 233 (1) -> a:=1 Figure
Page 235 and 236: C.3. MAPLE 235 > (x^2-1)^10/(x+1)^1
Page 237 and 238: C.3. MAPLE 237 Table C.2: Another s
Page 239 and 240: C.5. REDUCE 239 1: (x^2-1)^10/(x+1)
Page 241 and 242: Appendix D Index of Notation Notati
Page 243 and 244: Bibliography [Abb02] J.A. Abbott. S
Page 245 and 246: BIBLIOGRAPHY 245 [BCM94] [BCR98] [B
Page 247 and 248: BIBLIOGRAPHY 247 [Buc79] [Buc84] [B
Page 249 and 250: BIBLIOGRAPHY 249 [CW90] D. Coppersm
Page 251: BIBLIOGRAPHY 251 [FGT01] E. Fortuna
Page 255 and 256: BIBLIOGRAPHY 255 [Loo82] R. Loos. G
Page 257 and 258: BIBLIOGRAPHY 257 [Per09] [PQR09] [P
Page 259 and 260: BIBLIOGRAPHY 259 [SS11] J. Schicho
Page 261 and 262: BIBLIOGRAPHY 261 [Zip79b] R.E. Zipp
Page 263 and 264: INDEX 263 Budan-Fourier theorem, 63
Page 265 and 266: INDEX 265 Polynomial, 186 Least com
Page 267 and 268: INDEX 267 Toeplitz Matrix, 65 Trage
show all

Contents - Student subdomain for University of Bath

Create successful ePaper yourself

Delete template?

Save as template?