1% REDUCE BIBLIOGRAPHY 2 3% Part 1: A-F 4 5% Copyright (c) 1990 The RAND Corporation. All Rights Reserved. 6 7% Additions and corrections are solicited. Please send them, in the 8% same format as these entries if possible, to reduce at rand.org. 9 10 11@Article{Abbott:85, 12 author = "J. A. Abbott and R. J. Bradford and J. H. Davenport", 13 title = "A Remark on Factorisation", 14 journal = "{SIGSAM} Bulletin", 15 year = "1985", 16 volume = "19", 17 number = "2", 18 pages = "31--33", 19 month = may, 20} 21 22@InProceedings{Abbott:86, 23 author = "J. A. Abbott and R. J. Bradford and J. H. Davenport", 24 title = "The {Bath} Algebraic Number Package", 25 booktitle = "Proc. of {SYMSAC} '86", 26 year = "1986", 27 pages = "250--253", 28} 29 30@InProceedings{Abbott:87, 31 author = "J. A. Abbott and J. H. Davenport", 32 title = "Polynomial Factorization: An Exploration of 33 {Lenstra's} Algorithm", 34 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 35 Science", 36 year = "1987", 37 volume = "378", 38 pages = "391--402", 39 publisher = "Springer-Verlag", 40} 41 42@InProceedings{Abbott:87a, 43 author = "J. A. Abbott", 44 title = "Integration: Solving the {Risch} Differential 45 Equation", 46 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 47 Science", 48 year = "1987", 49 volume = "378", 50 pages = "465--467", 51 publisher = "Springer-Verlag", 52} 53 54@PhdThesis{Abbott:88, 55 author = "J. A. Abbott", 56 title = "Factorisation of Polynomials over Algebraic Number 57 Fields", 58 school = "Univ. of Bath, England", 59 year = "1988", 60} 61 62@Article{Abbott:88a, 63 author = "J. A. Abbott and J. H. Davenport", 64 title = "A Remark on a Paper by {Wang}: Another Surprising 65 Property of 42", 66 journal = "Math. Comp.", 67 year = "1988", 68 volume = "51", 69 pages = "837--839", 70} 71 72@InProceedings{Abbott:89, 73 author = "J. A. Abbott", 74 title = "Recovery of Algebraic Numbers from their p-Adic 75 Approximations", 76 booktitle = "Proc. of {ISSAC} '89", 77 publisher = "{ACM} Press, New York", 78 year = "1989", 79 pages = "112--120", 80} 81 82@TechReport{Abbott:89a, 83 author = "J. A. Abbott and R. J. Bradford and J. H. Davenport", 84 title = "A Remark on the Multiplication of Sparse Polynomials", 85 number = "TR 89-21", 86 year = "1989", 87 institution = "School of Mathematical Sciences, University of Bath", 88} 89 90@InProceedings{Abdali:88, 91 author = "S. K. Abdali and D. S. Wise", 92 title = "Experiments with Quadtree Representation of Matrices", 93 booktitle = "Proc. of {ISSAC} '88", 94 publisher = "Springer-Verlag", 95 year = "1988", 96 volume = "358", 97 pages = "96--108", 98} 99 100@Article{Abiezzi:83, 101 author = "Salim S. {Abi-Ezzi}", 102 title = "Clarification to the Symbolic Mode in {REDUCE}", 103 journal = "{SIGSAM} Bulletin", 104 year = "1983", 105 volume = "17", 106 number = "3 and 4", 107 pages = "43--47", 108 month = aug # " and " # nov, 109} 110 111@Article{Adams:83, 112 author = "K. J. Adams", 113 title = "Analytic Estimates for the Dynamic Aperture of 114 Nonlinear Lattices", 115 journal = "IEEE Trans. Nucl. Sci.", 116 year = "1983", 117 volume = "NS-30", 118 pages = "2436--2438", 119} 120 121%"For an accelerator lattice..." REDUCE was used to obtain low order 122%coefficients in the calculation of the amplitude. 123 124@Article{Adkins:83, 125 author = "G. S. Adkins", 126 title = "Analytic Evaluation of an {O}($\alpha$) Vertex 127 Correction to the Rate of Orthopositronium", 128 journal = "Phys. Rev. A", 129 year = "1983", 130 volume = "27", 131 pages = "530--532", 132 abstract = "The order-$\alpha$ correction to the lowest order 133 orthopositronium decay rate due to the two outer-vertex 134 graphs obtained in analytic form.", 135} 136 137@Article{Adkins:83a, 138 author = "G. S. Adkins and F. R. Brown", 139 title = "Rate for Positronium Decay to Five Photons", 140 journal = "Phys. Rev. A", 141 year = "1983", 142 volume = "28", 143 pages = "1164--1165", 144 abstract = "{REDUCE} used to calculate trace of $\gamma$ matrices. 145 Large calculation.", 146} 147 148@Article{Adkins:85, 149 author = "G. S. Adkins", 150 title = "Inner-Vertex Contributions to the Decay Rate of 151 Orthopositronium", 152 journal = "Phys. Rev. A", 153 year = "1985", 154 volume = "31", 155 pages = "1250--1252", 156 abstract = "{REDUCE} trace calculations. {"}In this paper the 157 order-$\alpha$ contribution to the inner-vertex graphs 158 to the decay rate of orthopositronium is obtained in 159 analytic form.{"}", 160} 161 162@Article{Aguilera-Navarro:87, 163 author = "V. C. Aguilera-Navarro and R. Guardiola and C. Keller 164 and M. de Llano and M. Popovic and M. Fortes", 165 title = "Van der {Waals} Perturbation Theory for Fermion and 166 Boson Ground-State Matter", 167 journal = "Phys. Rev. A", 168 year = "1987", 169 volume = "35", 170 pages = "563--584", 171} 172 173%Uses computer algebra to rearrange ideal-gas-based low-density 174%expansions; to them REDUCE or MACSYMA provide just the expertise they 175%require to substitute forms into equations, and so makes their 176%formulation possible. 177 178@Article{Aldins:69, 179 author = "J. Aldins and S. J. Brodsky and A. J. Dufner and T. 180 Kinoshita", 181 title = "Photon-Photon Scattering Contribution to the Sixth 182 Order Magnetic Moments of the Muon and Electron", 183 journal = "Phys. Rev. Lett.", 184 year = "1969", 185 volume = "23", 186 pages = "441--443", 187} 188 189@TechReport{Alekseev:86, 190 author = "A. I. Alekseev and V. F. Edneral", 191 title = "Tensor Structure of Axial Gauge Polarization Operator 192 in the Infrared Region", 193 institution = "IHEP", 194 year = "1986", 195 type = "Preprint", 196 number = "86-46", 197} 198 199@Article{Alekseev:87, 200 author = "A. I. Alekseev and V. F. Edneral", 201 title = "Tensor Structure of Gluon Polarization Operator in the 202 Axial Gauge for Infra-Red Region", 203 journal = "Journal of Nuclear Physics", 204 year = "1987", 205 pages = "1105--1114", 206} 207 208@TechReport{Alekseev:87a, 209 author = "A. I. Alekseev and V. F. Edneral", 210 title = "On Evaluation of {Feynman} Integrals in Axial Gauge", 211 institution = "IHEP", 212 year = "1987", 213 type = "Preprint", 214 number = "87-118", 215} 216 217%The recurrent algorithm for axial gauge calculations of 218%one-loop massless {Feynman} integrals in the n-dimensional 219%momentum space is described. The algorithm we suggest is 220%realized on the basis of REDUCE system and presented as 221%a procedure. It is rather effective for cumbersome 222%combinations of those integrals. 223 224@Article{Alfeld:82, 225 author = "P. Alfeld", 226 title = "Fixed Point Iteration with Inexact Function Values", 227 journal = "Math. Comp.", 228 year = "1982", 229 volume = "38", 230 pages = "87--98", 231} 232 233%Numerical analysis generating an improved iterative scheme. "The 234%technical manipulations in this paper were carried out using the 235%symbol manipulation language REDUCE." 236 237@TechReport{Amirkhanov:87, 238 author = "I. V. Amirkhanov and E. P. Zhydkov and I. E. 239 Zhydkova", 240 title = "The Conditions of Bounding of the Oscillation 241 Amplitudes of Charge Particle within the Resonance 242 Vicinity Investigations", 243 institution = "J.I.N.R., Dubna", 244 year = "1987", 245 number = "P11-87-452", 246} 247 248@Article{Antweiler:89, 249 author = "Werner Antweiler and Andreas Strotmann and Volker 250 Winkelmann", 251 title = "A {{\TeX-{REDUCE}-Interface}}", 252 journal = "SIGSAM Bulletin", 253 year = "1989", 254 volume = "23", 255 month = feb, 256 pages = "26--33", 257} 258 259@Article{Appelquist:70, 260 author = "T. W. Appelquist and S. J. Brodsky", 261 title = "The Order $\alpha^{2}$ Electrodynamic Corrections to 262 the {Lamb} Shift", 263 journal = "Phys. Rev. Letters", 264 year = "1970", 265 volume = "24", 266 pages = "562--565", 267} 268 269@TechReport{Arbuzov:86, 270 author = "B. A. Arbuzov and E. E. Boos and A. I. Davydychev", 271 title = "Infrared Asymptotics of Gluonic {Green} Functions in 272 Covariant Gauge", 273 institution = "IHEP", 274 year = "1986", 275 type = "Preprint", 276 number = "86-123", 277} 278 279@Article{Aso:81, 280 author = "T. Aso and T. Nonoyama and S. Kato", 281 title = "Numerical Simulation of Semidiurnal Atmospheric 282 Tides", 283 journal = "J. Geophysical R.", 284 year = "1981", 285 volume = "86", 286 number = "11", 287 pages = "388--400", 288} 289 290%"Numerical modeling of the solar and lunar semidiurnal atmospheric 291%tides has been performed by invoking a comprehensive approach that 292%includes both algebraic manipluation and numerical solution of the 293%primitive equation system." Used REDUCE to overcome difficulties of 294%complication and error. 295 296@Article{Atherton:73, 297 author = "R. W. Atherton and G. M. Homsey", 298 title = "Use of Symbolic Computation to Generate Evolution 299 Equations and Asymptotic Solutions to Elliptic 300 Equations", 301 journal = "Journ. Comp. Phys.", 302 year = "1973", 303 volume = "1", 304 pages = "45--59", 305} 306 307@Article{Aurenche:84, 308 author = "P. Aurenche and A. Douir and R. Baier and M. Fontannaz 309 and D. Schiff", 310 title = "Photoproduction of Hadrons at Large Transverse 311 Momentum in Second Order {QCD}", 312 journal = "Phys. Lett.", 313 year = "1984", 314 volume = "135B", 315 pages = "164--168", 316} 317 318% Uses REDUCE and SCHOONSCHIP in the extension of calculations to a 319%higher order to keep pace with experimental results. 320 321@Article{Aurenche:84a, 322 author = "P. Aurenche and A. Douir and R. Baier and M. Fontannaz 323 and D. Schiff", 324 title = "Prompt Photon Production at Large $p_{\tau}$ in {GCD} 325 Beyond the Leading Order", 326 journal = "Phys. Lett.", 327 year = "1984", 328 volume = "140B", 329 pages = "87--92", 330} 331 332%Uses REDUCE and SCHOONSCHIP. 333 334@Article{Autin:89, 335 author = "B. Autin and J. Bengtsson", 336 title = "Symbolic Evaluation of Integrals Occurring in 337 Accelerator Orbit Theory", 338 journal = "J. Symbolic Computation", 339 year = "1989", 340 volume = "7", 341 number = "2", 342 pages = "183--187", 343 month = feb, 344} 345 346@Article{Baekler:84, 347 author = "P. Baekler and F. W. Hehl", 348 title = "A Charged {Taub-NUT} Metric with Torsion: A New 349 Axially Symmetric Solution of the {Poincar\'{e}} Gauge 350 Field Theory", 351 journal = "Phys. Lett.", 352 year = "1984", 353 volume = "100A", 354 pages = "277--316", 355} 356 357@TechReport{Baekler:84a, 358 author = "Peter Baekler and Friedrich W. Hehl", 359 title = "On the Dynamics of the Torsion of Spacetime: Exact 360 Solutions in a Gauge Theoretical Model of Gravity", 361 institution = "Department of Physics, University of California, Los 362 Angeles", 363 year = "1984", 364 number = "UCLA/84/TEP/19", 365 page = "18", 366 month = dec, 367} 368 369@InProceedings{Baekler:86, 370 author = "P. Baekler and F. W. Hehl and E. W. Mielke", 371 title = "Nonmetricity and Torsion: Facts and Fancies in Gauge 372 Approaches to Gravity", 373 editor = "R. Ruffini", 374 booktitle = "Proc. 4th Marcel Grossmann Meeting on General 375 Relativity, ed.", 376 publisher = "North-Holland, Amsterdam", 377 year = "1986", 378 pages = "277--316", 379} 380 381@Article{Baekler:87, 382 author = "P. Baekler and R. Hecht and F. W. Hehl and T. 383 Shirafuji", 384 title = "Mass and Spin of Exact Solutions of the {Poincar\'{e}} 385 Gauge Theory", 386 journal = "Prog. Theor. Phys.", 387 year = "1987", 388 volume = "78", 389 pages = "16--21", 390} 391 392@Article{Baekler:87a, 393 author = "P. Baekler and M. Guerses", 394 title = "Exact Solutions of the {Poincar\'{e}} Gauge Theory 395 from Its Linearized Field Equations", 396 journal = "Lett. Math. Phys.", 397 year = "1987", 398 volume = "14", 399 pages = "185--191", 400} 401 402@Article{Baekler:87b, 403 author = "P. Baekler and E. W. Mielke and F. W. Hehl", 404 title = "Kinky Torsion in a {Poincar\'{e}} Gauge Model of 405 Gravity Coupled to a Massless Scalar Field", 406 journal = "Nuclear Phys.", 407 year = "1987", 408 volume = "B288", 409 pages = "800--812", 410} 411 412@Article{Baekler:88, 413 author = "P. Baekler and M. Seitz and V. Winkelmann", 414 title = "Cyclindrically Symmetric Solutions of 415 Self-Consistently Coupled {Dirac} Fields in Gauge 416 Theories of Gravity", 417 journal = "Class. Quantum Grav.", 418 year = "1988", 419 volume = "5", 420 pages = "479--490", 421} 422 423@Article{Baekler:88a, 424 author = "P. Baekler and M. Guerses and F. W. Hehl and J. D. 425 McCrea", 426 title = "The Exterior Gravitational Field of a Charged Spinning 427 Source in the {Poincar\'{e}} Gauge Theory: A 428 {Kerr-Newman} Metric with Dynamic Torsion", 429 journal = "Phys. Lett.", 430 year = "1988", 431 volume = "A128", 432 pages = "245--250", 433} 434 435@Article{Baekler:88b, 436 author = "P. Baekler and M. Guerses and F. W. Hehl", 437 title = "A New Method to Solve the Field Equations of 438 {Poincar\'{e}} Gauge Theories", 439 journal = "Class. Quantum Grav.", 440 year = "1988", 441} 442 443@TechReport{Bajla:78, 444 author = "I. Bajla and G. A. Ososkov and A. C. Hearn", 445 title = "The Orthogonalization Program of Polynomials in Two 446 Variables in {REDUCE}-2 Language", 447 institution = "J.I.N.R., Dubna", 448 year = "1978", 449 type = "Report", 450 number = "P10-11944", 451} 452 453%The analytical algorithm for constructing orthogonal 454%polynomials in two variables, based on the Gram-Schmidt 455%orthogonalization method, is proposed. 456 457@InProceedings{Balian:78, 458 author = "R. Balian and G. Parisi and A. Voros", 459 title = "Quartic Oscillator", 460 year = "1978", 461 month = may, 462 booktitle = "Proc. of the Colloq. on Mathematical Problems in 463 {Feynman} Path Integrals, Marseille", 464} 465 466%On the example of the semi-classical expansion for the levels 467%of the quartic oscillator -(d**2/dq**2)+q**4, we show how the 468%complex WKB method provides information about the 469%singularities of the Borel transform of the semi-classical 470%series. 471 472@Article{Baker:81, 473 author = "G. A. Baker and L. P. Benofy and M. Fortes and M. de 474 Llano and S. M. Peltier and A. Plastino", 475 title = "Hard-Core Square-Well Fermion", 476 journal = "Phys. Rev. A", 477 year = "1982", 478 volume = "26", 479 pages = "3575--3588", 480} 481 482%The mixed use of FORTRAN and REDUCE, various derivative were calculated 483%algebraically, but the double series was evaluated numerically. 484 485@Article{Bark:78, 486 author = "Fritz H. Bark and Herman Tinoco", 487 title = "Stability of Plane {Poiseuille} Flow of a Dilute 488 Suspension of Slender Fibres", 489 journal = "J. Fluid Mech.", 490 year = "1978", 491 volume = "87", 492 pages = "321--333", 493} 494 495%The linear hydrodynamic stability problem for plane Poiseuille 496%flow of a dilute suspension of rigid fibers is solved 497%numerically. The constitutive equation given by Batchelor 498%is used to model the rheological properties of the suspension. 499%The resulting eigenvalue problem is shown to be singular. 500 501@Article{Barthes-Biesel:73, 502 author = "D. Barthes-Biesel and A. Acrivos", 503 title = "On Computer Generated Analytic Solutions to the 504 Equations of Fluid Mechanics, The Case of Creeping 505 Flows", 506 journal = "Journ. Comp. Phys.", 507 year = "1973", 508 volume = "3", 509 pages = "403--411", 510} 511 512@Article{Barton:72, 513 author = "David Barton and Anthony C. Hearn", 514 title = "Comment on Problem \#2 - The {Y(2n)} Functions", 515 journal = "SIGSAM Bulletin", 516 year = "1972", 517 volume = "15", 518} 519 520%A compact program for the solution of SIGSAM Problem \#2 521%is presented. 522 523@Article{Bateman:86, 524 author = "G. Bateman and R. G. Storer", 525 title = "Direct Determination of Axisymmetric 526 Magnetohydrodynamic Equilibrium in {Hamada} 527 Coordinates", 528 journal = "Journ. Comp. Phys.", 529 year = "1986", 530 volume = "64", 531 pages = "161--176", 532} 533 534%Plasma. "REDUCE was used to analyse the general set of equations 535%for large numbers of Fourier harmonics ...." 536 537@TechReport{Bennett, 538 author = "J. P. Bennett and J. H. Davenport and H. M. Sauro", 539 title = "Solution of Some Equations in Biochemistry", 540 institution = "School of Mathematical Sciences, University of Bath, 541 England", 542 number = "88-12", 543} 544 545@Article{Berends:81, 546 author = "A. Berends and R. Kleiss and P. de Causmaecher and T. 547 T. Wu", 548 title = "Single Bremsstrahlung Process in Gauge Theories", 549 journal = "Phys. Lett.", 550 year = "1981", 551 volume = "103B", 552 pages = "124--128", 553} 554 555%Used REDUCE to calculate 25 {Feynman} diagrams to produce theoretical 556%results which could be checked against experiment. 557 558@TechReport{Berkovich:89, 559 author = "L. M. Berkovich and V. P. Gerdt and Z. T. Kostova and 560 M. L. Nechaevsky", 561 title = "Second Order Reducible Linear Differential Equations", 562 institution = "J.I.N.R., Dubna", 563 year = "1989", 564 type = "Preprint", 565 number = "E5-89-141", 566} 567 568@Article{Berman:63, 569 author = "S. M. Berman and Y. S. Tsai", 570 title = "Intermediate Boson Pair Production as a Means for 571 Determining its Magnetic Moment", 572 journal = "Phys. Rev. Lett.", 573 year = "1963", 574 volume = "11", 575 pages = "483--487", 576} 577 578@Article{Bessis:85, 579 author = "N. Bessis and G. Bessis and D. Roux", 580 title = "Closed-Form Expressions for the {Dirac-Coulomb} Radial 581 $r^{t}$ Integrals", 582 journal = "Phys. Rev. A", 583 year = "1985", 584 volume = "32", 585 pages = "2044--2050", 586} 587 588%No direct algebraic manipluation, but the formula is stated to be 589%well suited to evaluation by REDUCE or MACSYMA, and this is an 590%advantage of their formula. 591 592@TechReport{Billoire:78, 593 author = "A. Billoire and R. Lacaze and A. Morel and H. 594 Navelet", 595 title = "The {OZI} Rule Violating Radiative Decays of the Heavy 596 Pseudoscalars", 597 institution = "{CEN}-Saclay", 598 year = "1978", 599 type = "Report", 600 number = "DpH-T 43/78", 601} 602 603%Submitted to Phys. Letters B. 604%In lowest order QCD the rates for radiative transitions violating the OZI 605%rule of heavy pseudoscalars are found to be extremely small. 606 607@Article{Biro:86, 608 author = "T. S. Biro and J. Zimanyi and M. Zimanyi", 609 title = "Hadrochemistry in Relativistic Mean Fields", 610 journal = "Physics Letters", 611 year = "1986", 612 volume = "167B", 613 number = "3", 614 pages = "271--276", 615 month = feb, 616} 617 618@Article{Biro:87, 619 author = "T. S. Biro and K. Niita and A. L. de Paoli and W. 620 Bauer and W. Cassing and U. Mosel", 621 title = "Microscopic Theory of Photon Production in 622 Proton-Nucleus and Nucleus-Nucleus Collisions", 623 journal = "Nuclear Physics", 624 year = "1987", 625 volume = "475A", 626 pages = "579--597", 627 month = dec, 628} 629 630MONTH = "December"} 631 632@TechReport{Birrell:77, 633 author = "N. D. Birrell", 634 title = "The Application of Adiabatic Regularization to 635 Calculations of Cosmological Interest", 636 institution = "Dept. Math, King's College, London", 637 year = "1977", 638} 639 640@Article{Biswas:75, 641 author = "S. N. Biswas and S. R. Chaudhuri and K. S. Taank and 642 J. A. Campbell", 643 title = "Neutrino Production in Stellar Matter by Photons in a 644 Renormalizable Scalar-Boson-Exchange Model of Weak 645 Interactions", 646 journal = "Phys. Rev. D", 647 year = "1975", 648 volume = "8", 649 pages = "2523--2525", 650} 651 652@TechReport{Bittencourt:90, 653 author = "Guilherme Bittencourt and Jacques Calmet", 654 title = "Integrating Computer Algebra and Knowledge 655 Representation", 656 institution = "{Universit\"{a}t} Karlsruhe Institut {f\"{u}r} 657 Algorithmen und Kognitive Systeme", 658 year = "1990", 659 type = "Preprint", 660} 661 662@Article{Boege:86, 663 author = "W. Boege and R. Gebauer and H. Kredel", 664 title = "Some Examples for Solving Systems of Algebraic 665 Equations by Calculating {Groebner} Bases", 666 journal = "J. Symbolic Computation", 667 year = "1986", 668 volume = "2", 669 number = "1", 670 pages = "83--98", 671 month = mar, 672} 673 674@Article{Bogdanova:88, 675 author = "N. Bogdanova and H. Hogreve", 676 title = "A {REDUCE} Package for Exact {Coulomb} Interaction 677 Matrix Elements", 678 journal = "Comp. Phys. Commun.", 679 year = "1988", 680 volume = "48", 681 number = "2", 682 pages = "319--326", 683 month = feb, 684} 685 686@Article{Bordoni:81, 687 author = "Luciana Bordoni and Attilio Colagrossi", 688 title = "An Application of {REDUCE} to Industrial Mechanics", 689 journal = "{SIGSAM} Bulletin", 690 year = "1981", 691 volume = "15", 692 number = "2", 693 pages = "8--12", 694 month = may, 695} 696 697@InProceedings{Bowyer:87, 698 author = "A. Bowyer and J. H. Davenport and P. S. Milne and J. 699 A. Padget and A. F. Wallis", 700 title = "Applications of Computer Algebra in Solid Modelling", 701 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 702 Science", 703 year = "1987", 704 volume = "378", 705 pages = "244--245", 706 publisher = "Springer-Verlag", 707} 708 709@TechReport{Boyd:78, 710 author = "John P. Boyd", 711 title = "The Effects of Latitudinal Shear on Equatorial Waves, 712 Part {I}: Theory and Methods", 713 institution = "Dept. of Atmos. and Oceanic Science, Univ. of 714 Michigan", 715 year = "1978", 716 type = "Preprint", 717 month = jan, 718} 719 720%To be published in Journal of The Atmospheric Sciences. 721%By using the method of multiple scales in height and a 722%variety of methods in latitude, analytic solutions for 723%equatorial waves in combined vertical and horizontal shear 724%are derived. 725 726@InProceedings{Brackx:87, 727 author = "F. Brackx and H. Serras", 728 title = "Boundary Value Problems for the {Laplacian} in 729 {Euclidean} Space Solved by Symbolic Computation", 730 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 731 Science", 732 year = "1987", 733 volume = "378", 734 pages = "208--215", 735 publisher = "Springer-Verlag", 736} 737 738@Article{Brackx:87a, 739 author = "F. Brackx and D. Constales and R. Delanghe and H. 740 Serras", 741 title = "{Clifford} Algebra with {REDUCE}", 742 journal = "Rend. Circ. Mat. Palermo, Ser. II", 743 year = "1987", 744 volume = "16", 745 pages = "11--19", 746} 747 748@Article{Brackx:89, 749 author = "F. Brackx and D. Constales and A. Ronveaux and H. 750 Serras", 751 title = "On the Harmonic and Monogenic Decomposition of 752 Polynomials", 753 journal = "J. Symbolic Computation", 754 year = "1989", 755 volume = "8", 756 number = "3", 757 pages = "297--304", 758 month = sep, 759} 760 761@InProceedings{Bradford:86, 762 author = "R. J. Bradford and A. C. Hearn and J. A. Padget and E. 763 {Schr\"{u}fer}", 764 title = "Enlarging the {REDUCE} Domain of Computation", 765 booktitle = "Proc. of {SYMSAC} '86", 766 year = "1986", 767 pages = "100--106", 768} 769 770@InProceedings{Bradford:88, 771 author = "R. J. Bradford and J. H. Davenport", 772 title = "Effective Tests for Cyclotomic Polynomials", 773 booktitle = "Proc. of {ISSAC} '88", 774 publisher = "Springer-Verlag", 775 year = "1988", 776 volume = "358", 777 pages = "244--251", 778} 779 780@Article{Broadhurst:85, 781 author = "D. J. Broadhurst", 782 title = "Evaluation of a Class of {Feynman} Diagrams for all 783 Numbers of Loops and Dimensions", 784 journal = "Phys. Lett. B", 785 year = "1985", 786 volume = "164", 787 pages = "356--360", 788} 789 790%Uses REDUCE to calculate explicitely the l-loop member of a class of 791%massless, dimensionally regularized {Feynman} diagrams, in order to verify 792%an explicit formula. 793 794@Article{Brodsky:62, 795 author = "S. J. Brodsky and A. C. Hearn and R. G. Parsons", 796 title = "Determination of the Real Part of the {Compton} 797 Amplitude at a Nucleon Resonance", 798 journal = "Phys. Rev.", 799 year = "1962", 800 volume = "187", 801 pages = "1899--1904", 802} 803 804@Article{Brodsky:67, 805 author = "S. J. Brodsky and J. D. Sullivan", 806 title = "W-Boson Contribution to the Anomalous Magnetic Moment 807 of the Muon", 808 journal = "Phys. Rev.", 809 year = "1967", 810 volume = "156", 811 pages = "1644--1647", 812} 813 814@InProceedings{Brodsky:69, 815 author = "S. J. Brodsky", 816 title = "Status of Quantum Electrodynamics", 817 year = "1969", 818 booktitle = "Proc. International Symposium on Electron and Photon 819 Interactions at High Energies, Liverpool, England", 820} 821 822@TechReport{Brodsky:70, 823 author = "S. J. Brodsky", 824 title = "Quantum Electrodynamic Theory: Its Relation to 825 Precision Low Energy Experiments", 826 institution = "SLAC", 827 year = "1970", 828 type = "Report", 829 number = "SLAC-PUB-795", 830 month = aug, 831} 832 833%Stanford Linear Accelerator Center Report. 834 835@InProceedings{Brodsky:71, 836 author = "S. J. Brodsky", 837 title = "Algebraic Computation Techniques in Quantum 838 Electrodynamics", 839 year = "1971", 840 volume = "II", 841 pages = "IV-1--IV-27", 842 booktitle = "Proc. {2nd} Computing Methods in Theoretical Physics, 843 Marseilles", 844} 845 846@TechReport{Brodsky:72, 847 author = "S. J. Brodsky", 848 title = "Atomic Physics and Quantum Electrodynamics in the 849 Infinite Momentum Frame", 850 institution = "SLAC", 851 year = "1972", 852 type = "Report", 853 number = "SLAC-PUB-1118", 854 month = aug, 855} 856 857%Presented at the Third International Conference on Atomic Physics. 858 859@Article{Brodsky:72a, 860 author = "S. J. Brodsky and J. F. Gunion and R. L. Jaffe", 861 title = "Test for Fractionally Charged Partons from 862 Deep-Inelastic Bremsstrahlung in the Scaling Region", 863 journal = "Phys. Rev. D", 864 year = "1972", 865 volume = "6", 866 pages = "2487--2494", 867} 868 869@Article{Brodsky:72b, 870 author = "S. J. Brodsky and R. Roskies", 871 title = "Quantum Electrodynamics and Renormalization Theory in 872 The Infinite Momentum Frame", 873 journal = "Phys. Lett.", 874 year = "1972", 875 volume = "41B", 876 pages = "517--520", 877} 878 879@Article{Brodsky:73, 880 author = "S. J. Brodsky and R. Roskies and R. Suaya", 881 title = "Quantum Electrodynamics and Renormalization Theory in 882 the Infinite-Momentum Frame", 883 journal = "Phys. Rev. D", 884 year = "1973", 885 volume = "8", 886 pages = "4574--4594", 887} 888 889@Article{Broughan:82, 890 author = "K. A. Broughan", 891 title = "{Grad-Fokker-Planck} Plasma Equations. Part 1. 892 {Collision} Moments", 893 journal = "J. Plasma Phys.", 894 year = "1982", 895 volume = "27", 896 pages = "437--452", 897} 898 899%REDUCE used in collaboration with hand calculation. REDUCE did the 900%substitutions, with hand integrations. "Thirteen moments are taken of the 901%collision term in Boltzmann-Fokker-Planck equation....plasma..." 902 903@Article{Brown:79, 904 author = "W. S. Brown and A. C. Hearn", 905 title = "Applications of Symbolic Algebraic Computation", 906 journal = "Comp. Phys. Comm.", 907 year = "1979", 908 volume = "17", 909 pages = "207--215", 910} 911 912%This paper is a survey of applications of systems for symbolic 913%algebraic computation. 914 915@Article{Bryan-Jones:87, 916 author = "Jane Bryan-Jones", 917 title = "A Tutorial in Computer Algebra for Statisticians", 918 journal = "The Professional Statistician", 919 year = "1987", 920 volume = "6", 921 number = "6", 922 month = dec, 923 pages = "TBD", 924} 925 926@TechReport{Calmet:72, 927 author = "Jacques Calmet", 928 title = "Further Evaluation of the Sixth Order Corrections to 929 the Anomalous Magnetic Moment of the Electron", 930 institution = "Department of Physics, University of Utah", 931 year = "1972", 932} 933 934%We report on the contributions to the $\alpha^{3}$ 935%part of the anomalous magnetic moment of the electron from the 936%seven so-called cross and ladder diagrams. 937 938@Article{Calmet:72a, 939 author = "Jacques Calmet", 940 title = "A {REDUCE} Approach to the Calculation of {Feynman} 941 Diagrams", 942 journal = "Comp. Phys. Comm.", 943 year = "1972", 944 volume = "4", 945 pages = "199--204", 946} 947 948%A brief survey of two existing REDUCE programs (by Campbell-Hearn 949%and by Calmet) dealing with algebraic computation of {Feynman} diagrams is 950%given. Work in progress on a more general approach to this problem 951%is discussed. 952 953@Article{Calmet:74, 954 author = "Jacques Calmet", 955 title = "Computer Recognition of Divergences in {Feynman} 956 Graphs", 957 journal = "SIGSAM Bulletin", 958 year = "1974", 959 volume = "8", 960 number = "3", 961 pages = "74--75", 962 month = aug, 963} 964 965%A description of a program for the recognition of divergences 966%in {Feynman} graphs is given. 967 968@InCollection{Calmet:83, 969 author = "J. Calmet and J. A. van Hulzen", 970 title = "Computer Algebra Applications", 971 editor = "B. Buchberger and G. E. Collins and R. Loos and R. 972 Albrecht", 973 booktitle = "Computer Algebra Symbolic and Algebraic Computation", 974 edition = "2nd", 975 publisher = "Springer-Verlag", 976 year = "1983", 977} 978 979@Article{Campbell:67, 980 author = "J. A. Campbell", 981 title = "Algebraic Computation of Radiative Corrections for 982 Electron-Positron Scattering", 983 journal = "Nucl. Phys.", 984 year = "1967", 985 volume = "B1", 986 pages = "283--300", 987} 988 989@Article{Campbell:68, 990 author = "J. A. Campbell", 991 title = "Astrophysical Consequences of the Existence of Charged 992 Intermediate Vector Bosons", 993 journal = "Aust. Journ. of Phys.", 994 year = "1968", 995 volume = "21", 996 pages = "139--148", 997} 998 999@Article{Campbell:70, 1000 author = "J. A. Campbell and A. C. Hearn", 1001 title = "Symbolic Analysis of {Feynman} Diagrams by Computer", 1002 journal = "Journ. of Comp. Phys.", 1003 year = "1970", 1004 volume = "5", 1005 pages = "280--327", 1006} 1007 1008@Article{Campbell:70a, 1009 author = "J. A. Campbell and R. B. Clark and D. Horn", 1010 title = "Low-T Theorems for Charged-Pion Photoproduction", 1011 journal = "Phys. Rev. D", 1012 year = "1970", 1013 volume = "2", 1014 pages = "217--224", 1015} 1016 1017@Article{Campbell:74, 1018 author = "J. A. Campbell", 1019 title = "Symbolic Computing and Its Relationship to Particle 1020 Physics", 1021 journal = "Acta Physica Austriaca", 1022 year = "1974", 1023 volume = "XIII", 1024 pages = "595--647", 1025} 1026 1027@Article{Campbell:87, 1028 author = "J. A. Campbell and P. O. {Fr\"{o}man} and E. Walles", 1029 title = "Explicit series formulae for the evaluation of 1030 integrals by the method of steepest descents", 1031 journal = "Studies in Applied Mathematics", 1032 year = "1987", 1033 volume = "77", 1034 pages = "151--172", 1035} 1036 1037@TechReport{Caprasse:84, 1038 author = "H. Caprasse", 1039 title = "Description et Utilisation {d'Une} Extension du 1040 Programme {REDUCE}", 1041 institution = "Physique Th\'{e}orique et Math\'{e}matique, 1042 Universit\'{e} de Li\`{e}ge", 1043 year = "1984", 1044 month = oct, 1045} 1046 1047@Article{Caprasse:85, 1048 author = "H. Caprasse and M. Hans", 1049 title = "A New Use of Operators in the Algebraic Mode of 1050 {REDUCE}", 1051 journal = "{SIGSAM} Bulletin", 1052 year = "1985", 1053 volume = "19", 1054 number = "3", 1055 pages = "46--52", 1056 month = aug, 1057} 1058 1059@Article{Caprasse:86, 1060 author = "H. Caprasse", 1061 title = "Description of an Extension of the Matrix Package of 1062 {REDUCE}", 1063 journal = "{SIGSAM} Bulletin", 1064 year = "1986", 1065 volume = "20", 1066 number = "4", 1067 pages = "7--10", 1068 month = dec, 1069} 1070 1071@Article{Caprasse:86a, 1072 author = "H. Caprasse", 1073 title = "A Complete Simplification Package for the Absolute 1074 Value Function in {REDUCE}", 1075 journal = "{SIGSAM} Bulletin", 1076 year = "1986", 1077 volume = "20", 1078 number = "1 and 2", 1079 pages = "18--21", 1080 month = feb # " and " # may, 1081} 1082 1083%Implementation for REDUCE 3.2 of the function "ABS". 1084 1085@InProceedings{Caprasse:88, 1086 author = "H. Caprasse and J. Demaret and E. Schruefer", 1087 title = "Can {EXCALC} be Used to Investigate {High-dimensional} 1088 Cosmological Models with {Non-Linear Lagrangians}", 1089 booktitle = "Proc. of {ISSAC} '88", 1090 publisher = "Springer-Verlag", 1091 year = "1988", 1092 pages = "116--124", 1093} 1094 1095@Article{Caprasse:90, 1096 author = "H. Caprasse", 1097 title = "Renormalization Group, Function Iterations and 1098 Computer Algebra", 1099 journal = "J. Symbolic Computation", 1100 year = "1990", 1101 volume = "9", 1102 number = "1", 1103 pages = "61--72", 1104 month = jan, 1105} 1106 1107%Based on a renormalization group equation met in Quantum Field Theory, 1108%Continuous Iterations of a large class of functions are computed using 1109%REDUCE. 1110 1111@Article{Caprasse:89a, 1112 author = "H. Caprasse", 1113 title = "Les Th\'{e}ories des {Champs} dans le monde de 1114 {REDUCE} (in French)", 1115 journal = "{CALSYF} (to appear)", 1116 year = "1989", 1117} 1118 1119@Article{Carlson:80, 1120 author = "P. Carlson", 1121 title = "Coordinate Free Relativity", 1122 journal = "J. Math. Phys.", 1123 year = "1980", 1124 volume = "21", 1125 pages = "1149--1154", 1126} 1127 1128%REDUCE programs for tetrad formulation of GR. 1129 1130@PhdThesis{Carroll:73, 1131 author = "R. Carroll", 1132 title = "The Anomalous Magnetic Moment of the Electron in the 1133 Mass Operator Formalism", 1134 school = "University of Michigan", 1135 year = "1973", 1136} 1137 1138@Article{Carroll:75, 1139 author = "R. Carroll", 1140 title = "Mass-Operator Calculation of the Electron g-Factor", 1141 journal = "Phys. Rev. D", 1142 year = "1975", 1143 volume = "8", 1144 pages = "2344--2354", 1145} 1146 1147@TechReport{Cejchan, 1148 author = "A. Cejchan and J. Nadrchal", 1149 title = "Application of {REDUCE}-2 and Analytic Integration 1150 Program in the Theoretical Solid State Physics", 1151 institution = "Institute of Physics, CSAV, Prague", 1152} 1153 1154@InProceedings{Chaffy:88, 1155 author = "C. Chaffy-Camus", 1156 title = "An Application of {REDUCE} to the Approximation of 1157 {f(x,y)}", 1158 booktitle = "Proc. of {ISSAC} '88", 1159 publisher = "Springer-Verlag", 1160 year = "1988", 1161 volume = "358", 1162 pages = "73--84", 1163} 1164 1165@Article{Chinnick:86, 1166 author = "K. Chinnick and C. Gibson and J. F. Griffiths and W. 1167 Kordylewski", 1168 title = "Isothermal Interpretations of Oscillatory Ignition 1169 During Hydrogen Oxidation in an Open System. {I}. 1170 {Analytical} Predictions and Experimental Measurements 1171 of Periodicity", 1172 journal = "Proc. Royal Soc. Lond.", 1173 year = "1986", 1174 volume = "A405", 1175 pages = "117--128", 1176} 1177 1178%Used REDUCE to solve Jacobian, but answer too complicated to be of any use. 1179 1180@Article{Cline:90, 1181 author = "Terry Cline and Harold Abelson and Warren Harris", 1182 title = "Symbolic Computing in Engineering Design", 1183 journal = "AI EDAM", 1184 year = "1990", 1185 month = feb, 1186} 1187 1188@TechReport{Cohen:76, 1189 author = "H. I. Cohen and O. Leringe and Y. Sundblad", 1190 title = "The Use of Algebraic Computing in General Relativity", 1191 institution = "The Royal Institute of Technology Department of 1192 Mechanics", 1193 year = "1976", 1194 number = "TRITA-MEK-76-02", 1195} 1196 1197@TechReport{Cohen:76a, 1198 author = "I. Cohen and F. Bark", 1199 title = "Perturbation Calculations for the Spin Up Problem 1200 Using {REDUCE}", 1201 institution = "The Royal Institute of Technology, Department of 1202 Mechanics", 1203 year = "1976", 1204 number = "TRITA-MEK-76-03", 1205} 1206 1207@TechReport{Cohen:77, 1208 author = "I. Cohen and S. Yu. Slavyanov", 1209 title = "Smooth Perturbations of the {Schr\"{o}dinger} Equation 1210 with a Linear Potential Related to the Charmonium 1211 Models", 1212 institution = "University of Stockholm Institute of Physics", 1213 year = "1977", 1214 type = "USIP Report", 1215 number = "77-17", 1216} 1217 1218@Article{Cohen:79, 1219 author = "J. P. Fitch and H. I. Cohen", 1220 title = "Using {CAMAL} for Algebraic Calculations in General 1221 Relativity", 1222 journal = "General Relativity and Gravitation", 1223 volume = "11", 1224 year = "1979", 1225 pages = "411--418", 1226} 1227 1228@Article{Cohen:84, 1229 author = "H. I. Cohen and I. B. Frick and J. E. {\AA}man", 1230 title = "Algebraic Computing in General Relativity", 1231 journal = "General Relativity and Gravitation, ed.", 1232 year = "1984", 1233 pages = "139--162", 1234} 1235 1236%General relativity review. 1237 1238@InProceedings{Cohen:89, 1239 author = "Joel S. Cohen", 1240 title = "The Effective Use of Computer Algebra Systems", 1241 year = "1989", 1242 pages = "677--698", 1243 booktitle = "Transactions of the Sixth Army Conference on Applied 1244 Mathematics and Computing", 1245} 1246 1247% Review of author's experience with four computer algebra systems. 1248 1249@Article{Connor:84, 1250 author = "J. N. L. Connor and P. R. Curtis and D. Farrelly", 1251 title = "The Uniform Asymptotic Swallowtail Approximation: 1252 Practical Methods for Oscillating Integrals with Four 1253 Coalescing Saddle Points", 1254 journal = "J. Phys. A", 1255 year = "1984", 1256 volume = "17", 1257 pages = "283--310", 1258} 1259 1260%Used REDUCE and SCHOONSCHIP for some algebraic manipulations, and then 1261%checked the results with MACSYMA; this is the most distrustful 1262%reference we have found. 1263 1264@Article{Connor:84a, 1265 author = "J. N. L. Connor and P. R. Curtis and C. J. Edge and A. 1266 Lagan`{a}", 1267 title = "The Uniform Asymptotic Swallowtail Approximation: 1268 Application to the Collinear {$H+F_{2}$}", 1269 journal = "J. Chem. Phys.", 1270 year = "1984", 1271 volume = "80", 1272 number = "3", 1273 pages = "1362--1363", 1274 month = feb, 1275} 1276 1277@Article{Conwell:84, 1278 author = "P. R. Conwell and P. W. Barber and C. K. Rushworth", 1279 title = "Resonant Spectra of Dielectric Sphere", 1280 journal = "J. Opt. Soc. Am. A", 1281 year = "1984", 1282 volume = "1", 1283 pages = "62--67", 1284} 1285 1286%REDUCE used to confirm independently convergence and accuracy of 1287%Numerical Bessel function routine, expanding series by REDUCE and 1288%using bigfloats. Described as slow but worthwhile. 1289 1290@InProceedings{Cowan:79, 1291 author = "Richard M. Cowan and Martin L. Griss", 1292 title = "Hashing -- The Key to Rapid Pattern Matching", 1293 booktitle = "Proc. {EUROSAM} 1979, Lecture Notes in Computer 1294 Science", 1295 year = "1979", 1296 volume = "72", 1297 pages = "266--278", 1298 publisher = "Springer-Verlag", 1299} 1300 1301@Article{Cung:75, 1302 author = "V. K. Cung", 1303 title = "Differential Cross Section of e+ + e- to e+ + mu- + 1304 nubar(mu) + nubar(e)", 1305 journal = "Phys. Lett.", 1306 year = "1975", 1307 volume = "55B", 1308 pages = "67--70", 1309} 1310 1311@TechReport{Darbaidze:86, 1312 author = "Ya. Z. Darbaidze", 1313 title = "A Gluon Bremsstrahlung in Supersymmetry {QCD}", 1314 institution = "JINR", 1315 year = "1986", 1316 type = "Preprint", 1317 number = "P2-86-825", 1318} 1319 1320@Article{Darbaidze:86a, 1321 author = "J. Z. Darbaidze and V. A. Matveev and Z. V. 1322 Merebashvili and L. A. Slepchenko", 1323 title = "Gluon Bremsstrahlung in Supersymmetric {QCD}", 1324 journal = "Phys. Lett.", 1325 year = "1986", 1326 volume = "B177", 1327 page = "188", 1328} 1329 1330@TechReport{Darbaidze:88, 1331 author = "Ya. Z. Darbaidze and Z. V. Merebashvili and V. A. 1332 Rostovtsev", 1333 title = "Some Computer Realizations of the {REDUCE-3} 1334 Calculations for Exclusive Processes", 1335 institution = "JINR", 1336 year = "1988", 1337 type = "Preprint", 1338 number = "P2-88-769", 1339} 1340 1341@TechReport{Darbaidze:89, 1342 author = "Ya. Z. Darbaidze and V. A. Rostovtsev", 1343 title = "Analysis of the Differential Equations for the 1344 Exclusive Processes and Explanation for the {"Mystery"} 1345 of the {Gamma-Distribution}", 1346 institution = "JINR", 1347 year = "1989", 1348 type = "Preprint", 1349 number = "E2-89-286", 1350} 1351 1352@InProceedings{Dautcourt:79, 1353 author = "G. Dautcourt", 1354 title = "Application of {REDUCE} to Algebraic Computations in 1355 General Relativity and Astrophysics", 1356 year = "1979", 1357 month = sep, 1358 booktitle = "Proc. of the Workshop in Symbolic Computation, Dubna, 1359 {U.S.S.R.}", 1360} 1361 1362%Reports the use of the system REDUCE 2 for general relativistic 1363%calculations. 1364 1365@TechReport{Dautcourt:80, 1366 author = "G. Dautcourt and K. P. Jann", 1367 title = "A Program Package in {REDUCE} 2 for Algebraic 1368 Computations in General Relativity", 1369 year = "1980", 1370 institution = "Zentralinstitut fuer Astrophysik der Akademie der 1371 Wissenschaften", 1372} 1373 1374@Article{Dautcourt:81, 1375 author = "G. Dautcourt and K. P. Jann and E. Riemer and M. 1376 Riemer", 1377 title = "User's Guide to {REDUCE} Subroutines For Algebraic 1378 Computations in General Relativity", 1379 journal = "Astron. Nachr.", 1380 year = "1981", 1381 volume = "302", 1382 pages = "1--13", 1383} 1384 1385@Article{Dautcourt:83, 1386 author = "G. Dautcourt", 1387 title = "The Cosmological Problem as an Initial Value Problem 1388 on the Observer's Past Light Cone: Geometry", 1389 journal = "J. Phys. A", 1390 year = "1983", 1391 volume = "16", 1392 pages = "3507--3528", 1393} 1394 1395%Checked calculations with REDUCE, mainly Riemann tensor in null 1396%coordinates. 1397 1398@Article{Davenport:81, 1399 author = "James Harold Davenport", 1400 title = "On the Integration of Algebraic Functions", 1401 journal = "Lecture Notes in Computer Science", 1402 year = "1981", 1403 volume = "102", 1404 pages = "1--197", 1405} 1406 1407@Article{Davenport:82, 1408 author = "James H. Davenport", 1409 title = "Fast {REDUCE:} The {trade-off} between efficiency and 1410 generality", 1411 journal = "{SIGSAM} Bulletin", 1412 year = "1982", 1413 volume = "16", 1414 number = "1", 1415 pages = "8--11", 1416 month = feb, 1417} 1418 1419@Article{Davenport:82a, 1420 author = "James H. Davenport", 1421 title = "What do we want from a {high-level} language?", 1422 journal = "{SIGSAM} Bulletin", 1423 year = "1982", 1424 volume = "16", 1425 number = "4", 1426 pages = "6--9", 1427 month = nov, 1428} 1429 1430@InProceedings{Davenport:85, 1431 author = "James Davenport and Julian Padget", 1432 title = "{HEUGCD:} How Elementary Upperbounds Generate Cheaper 1433 Data", 1434 booktitle = "Proc. {EUROCAL} 1985, Lecture Notes in Computer 1435 Science", 1436 year = "1985", 1437 volume = "204", 1438 pages = "18--28", 1439 publisher = "Springer-Verlag", 1440} 1441 1442@Article{Davenport:88, 1443 author = "J. H. Davenport", 1444 title = "The World of Computer Algebra", 1445 journal = "New Scientist", 1446 year = "1988", 1447 month = sep, 1448 volume = "1629", 1449 pages = "71--72", 1450} 1451 1452@Book{Davenport:88a, 1453 author = "J. H. Davenport and Y. Siret and E. Tournier", 1454 title = "Computer Algebra, Systems and Algorithms for Algebraic 1455 Computation", 1456 publisher = "Academic Press", 1457 year = "1988", 1458} 1459 1460@TechReport{Della-Dora:81, 1461 author = "J. Della Dora and E. Tournier", 1462 title = "Solutions Formelles {D'Equations} Differentielles au 1463 Voisinage de Points Singuliers Reguliers", 1464 institution = "Centre National de la Recherche Scientifique", 1465 year = "1981", 1466 type = "Report", 1467 number = "239", 1468} 1469 1470@InProceedings{Della-Dora:84, 1471 author = "J. Della Dora and E. Tournier", 1472 title = "Homogeneous Linear Difference Equation 1473 {(Frobenius-Boole Method)}", 1474 booktitle = "Proc. {EUROSAM} 1984, Lecture Notes in Computer 1475 Science", 1476 year = "1984", 1477 volume = "174", 1478 pages = "2--12", 1479 publisher = "Springer-Verlag", 1480} 1481 1482@TechReport{Della-Dora:85, 1483 author = "Jean Della-Dora and Claire Dicrescenzo and Dominique 1484 Duval", 1485 title = "About a New Method for Computing in Algebraic Number 1486 Fields", 1487 institution = "Universit\'{e} de Grenoble, Institut Fourier, France", 1488 year = "1985", 1489 month = nov, 1490} 1491 1492@Article{Demaret:89, 1493 author = "J. Demaret and H. Caprasse and A. Moussiaux and Ph. 1494 Tombal and D. Papadopoulos", 1495 title = "{Ten-dimensional Lovelock-type Space-Times}", 1496 journal = "{To appear} Phys. Rev. D", 1497 year = "1989", 1498 month = jul, 1499} 1500 1501@Article{DeMenna:87, 1502 author = "L. De Menna and G. Miano and G. Rubinacci", 1503 title = "Volterra's Series Solutions of Free Boundary Plasma 1504 Equilibria", 1505 journal = "Phys. Fluids", 1506 year = "1987", 1507 volume = "30", 1508 pages = "409--416", 1509} 1510 1511%Magnetohydrodynamics. "We have carried out the computations up to 1512%the fourth order, (the fourth order has been obtained by means of the 1513%symbolic program REDUCE". 1514 1515@Article{Demichev:85, 1516 author = "A. P. Demichev and A. Ya. Rodionov", 1517 title = "A {REDUCE} Program for the Calculation of Geometrical 1518 Characteristics of Compactified Multidimensional 1519 {Riemannian} Space", 1520 journal = "Comp. Phys. Comm.", 1521 year = "1985", 1522 volume = "38", 1523 pages = "441--448", 1524} 1525 1526%Covariant theories in N dimensional ($N \geq 4$) space-time. 1527%REDUCE programs to calculate Ricci, Einstein and Yang-Mills curvature 1528%and energy-momentum tensor. 1529 1530@TechReport{Demichev:86, 1531 author = "A. P. Demichev and A. Ya. Rodionov", 1532 title = "Freund-{Rubin} Type Solutions for Different 1533 Compactifications of the Eleven-Dimensional Space", 1534 institution = "Institute for High Energy Physics", 1535 year = "1986", 1536 type = "Preprint", 1537 number = "86-85", 1538} 1539 1540%The results of calculating geometrical characteristics of 1541%seven-dimensional quotient spaces are represented. These 1542%quantities are necessary for the construction of compactifying 1543%solutions of the eleven-dimensional supergravity. 1544 1545@Article{deRop:88, 1546 author = "Y. de Rop and J. Demaret", 1547 title = "Using {EXCALC} to Study Nondiagonal Multidimensional 1548 Spatially Homogeneous Cosmologies", 1549 journal = "Gen. Rel. Grav.", 1550 year = "1988", 1551 volume = "20", 1552 pages = "1127--1139", 1553} 1554 1555@TechReport{DeVos:89, 1556 author = "Alexis De Vos", 1557 title = "The use of {Reduce} in solar energy conversion 1558 theory", 1559 institution = "State University of Gent, {CAGe} Computer Algebra 1560 Group", 1561 year = "1989", 1562 type = "Reports of the {CAGe} Project", 1563 number = "4", 1564 month = aug, 1565} 1566 1567@InProceedings{Dewar:89, 1568 author = "M. C. Dewar", 1569 title = "{IRENA --} An Integrated Symbolic and Numerical 1570 Computation Environment", 1571 booktitle = "Proc. of {ISSAC} '89", 1572 publisher = "{ACM} Press, New York", 1573 year = "1989", 1574 pages = "171--179", 1575} 1576 1577@Article{Dhar:85, 1578 author = "D. Dhar and J-M. Maillard", 1579 title = "Susceptibility of the Checkerboard {Ising} Model", 1580 journal = "J. Phys. A", 1581 year = "1985", 1582 volume = "18", 1583 pages = "L383--L388", 1584} 1585 1586%Used REDUCE for tedious algebra, and got a simple answer. Statistical 1587%mechanics(?). "At the disorder variety, the n-point correlation 1588%functions of the checkerboard Potts model has a simple causal 1589%structure. An exact expression for the susceptibility in the Ising 1590%case is obtained." 1591 1592@TechReport{Dicrescenzo:85, 1593 author = "Claire Dicrescenzo", 1594 title = "Algebraic Computation on Algebraic Numbers", 1595 institution = "Institut Fourier, Laboratoire de Math\'{e}matiques, 1596 France", 1597 year = "1985", 1598 month = dec, 1599} 1600 1601%Examples are given of a new method, implemented on REDUCE, 1602%for computing algebraically on algebraic numbers. 1603 1604@TechReport{Diver, 1605 author = "D. A. Diver and E. Q. Laing and C. C. Sellar", 1606 title = "Waves in a Cold Plasma with a Spatially Rotating 1607 Magnetic Field", 1608 institution = "Department of Physics and Astronomy, University of 1609 Glasgow, Plasma Physics Group", 1610 type = "Report", 1611 number = "GU TPA 88/12-1", 1612} 1613 1614%"...The algebraic manipulation system REDUCE was used in constructing the 1615%following tensor definitions which allows us to make fewer 1616%approximations than other authors." 1617 1618@InProceedings{Diver:86, 1619 author = "D. A. Diver and E. W. Laing", 1620 title = "Proc. 8th {Europhysics} Conference on Computational 1621 Physics", 1622 year = "1986", 1623 booktitle = "Computing in Plasma Physics", 1624} 1625 1626@InProceedings{Diver:88, 1627 author = "D. A. Diver and E. W. Laing", 1628 title = "Proc. {XV} {European} Conference on Controlled Fusion 1629 and Plasma Heating", 1630 year = "1988", 1631} 1632 1633@TechReport{Diver:88a, 1634 author = "D. A. Diver and E. W. Laing", 1635 title = "Alfven Resonance Absorption in a Magnetofluid", 1636 year = "1988", 1637 type = "Internal Report", 1638 number = "GUTPA 88/04-01", 1639 month = jul, 1640} 1641 1642%Presented at 15th UK Plasma Physics Conference, UMIST. 1643 1644@TechReport{Dorfi:85, 1645 author = "E. A. Dorfi and L. O'C. Drury", 1646 title = "Simple Adaptive Grids for {1D} Initial Value 1647 Problems", 1648 institution = "Max-Plack-Institut fuer Kernphysik, Heidelberg, West 1649 Germany", 1650 year = "1985", 1651 number = "MPI H-1985-V21", 1652} 1653 1654@Article{Dorizzi:86, 1655 author = "B. Dorizzi and B. Grammaticos and J. Hietarinta and A. 1656 Ramani and F. Schwarz", 1657 title = "New integrable three dimensional quartic potentials", 1658 journal = "Phys. Lett.", 1659 year = "1986", 1660 volume = "116A", 1661 pages = "432--436", 1662} 1663 1664%REDUCE is used to construct and verify constants of motion. 1665 1666@TechReport{dosSantos:85, 1667 author = "R. P. dos Santos and P. P. Srivastava", 1668 title = "Two-loop Effective Potential for Wess-Zumino Model 1669 using Superfields", 1670 institution = "International Centre for Theoretical Physics", 1671 year = "1985", 1672 number = "IC/85/205", 1673 month = oct, 1674} 1675 1676%"For the case of several interacting chiral superfields the propagators 1677%for the unconstrained superfield potentials in the 'shifted' theory, 1678%where the supersymmetry is explicity broken, are derived in a compact 1679%form. They are used to compute one-loop effective potential in the 1680%general case, while a superfield calculation of renormalized effective 1681%potential to two loops for the Wess-Zumino model is performed." 1682 1683@Article{dosSantos:87, 1684 author = "Renato P. dos Santos", 1685 title = "Using {REDUCE} in Supersymmetry", 1686 journal = "J. Symb. Comp.", 1687 year = "1989", 1688 volume = "7", 1689 pages = "523--525", 1690} 1691 1692@PhdThesis{dosSantos:87a, 1693 author = "R. P. dos Santos", 1694 title = "{O} M\'{e}todo de Supercampos para o C\'{a}lculo de 1695 Potencial Efetivo em Modelos com Supercampos Quirais: 1696 Os Modelos de Wess e Zumino e de {O'Raifeartaigh}", 1697 school = "Centro Brasileiro de Pesquisas F\'{i}sicas", 1698 year = "1987", 1699} 1700 1701%(In Portuguese) Using the method of Superfields, the effective 1702%potential for supersymmetric models of Wess-Zumino and of 1703%O'Raifeartaigh is evaluated up to two-loop order. The spontaneous 1704%supersymmetry breaking is discussed. REDUCE plays very important 1705%role in evaluation of the Feynman superdiagrams and in 1706%renormalization. 1707 1708@TechReport{dosSantos:88a, 1709 author = "Renato P. dos Santos", 1710 title = "Introdu\c{c}\~{a}o ao Sistema {REDUCE} de C\'{a}lculo 1711 Alg\'{e}brico", 1712 institution = "CBPF, Rio de Janeiro, Brazil", 1713 year = "1988", 1714 number = "CBPF-NT-001/88", 1715} 1716 1717%(In Portuguese) Lecture notes of a course on REDUCE. 1718 1719@Article{Dubowsky:75, 1720 author = "S. Dubowsky and J. L. Grant", 1721 title = "Application of Symbolic Manipulation to Time Domain 1722 Analysis of Nonlinear Dynamic Systems", 1723 journal = "Journ. of Dynamic Systems, Measurement, and Control", 1724 year = "1975", 1725 number = "75-Aut-J", 1726} 1727 1728@Article{Dudley:89, 1729 author = "M. L. Dudley and R. W. James", 1730 title = "{Computer-aided} Derivation of Spherical Harmonic 1731 Spectral Equations in Astrogeophyics", 1732 journal = "J. Symbolic Computation", 1733 year = "1989", 1734 volume = "8", 1735 number = "4", 1736 pages = "423--427", 1737 month = oct, 1738} 1739 1740@Article{Dufner:69, 1741 author = "A. M. Dufner and Y. S. Tsai", 1742 title = "Phenomenological Analysis of the $\gamma${NN*} Form 1743 Factors", 1744 journal = "Phys. Rev.", 1745 year = "1969", 1746 volume = "168", 1747 pages = "1801--1809", 1748} 1749 1750@InProceedings{Dulyan:87, 1751 author = "L. S. Dulyan", 1752 title = "The Calculation of {QCD} Triangular {Feynman} Graphs 1753 in the External Gluonic Field Using {REDUCE}-2 System", 1754 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 1755 Science", 1756 year = "1987", 1757 volume = "378", 1758 pages = "172--173", 1759 publisher = "Springer-Verlag", 1760} 1761 1762@Article{Duncan:86, 1763 author = "Anthony Duncan and Ralph Roskies", 1764 title = "Representations of Unusual Mathematical Structures in 1765 Scientific Applications of Symbolic Computation", 1766 journal = "J. Symbolic Computation", 1767 year = "1986", 1768 volume = "2", 1769 number = "2", 1770 pages = "201--206", 1771 month = jun, 1772} 1773 1774%We present examples of techniques we have used to apply REDUCE to problems 1775%in particle physics which have mathematical structures unknown to REDUCE. 1776 1777@PhdThesis{Duval:87, 1778 author = "Dominique Duval", 1779 title = "Diverses questions relatives au Calcul Formel Avec des 1780 Nombres Alg\'{e}briques", 1781 school = "L'Universit\'{e} Scientifique, Technologique et 1782 M\'{e}dicale de Grenoble", 1783 year = "1987", 1784} 1785 1786@Article{Earles:70, 1787 author = "D. Earles", 1788 title = "A Measurement of the Electron-Production of Muon 1789 Pairs", 1790 journal = "Phys. Rev. Lett.", 1791 year = "1970", 1792 volume = "25", 1793 pages = "129--133", 1794} 1795 1796@Article{Eastwood:87, 1797 author = "James W. Eastwood", 1798 title = "Orthovec: A {REDUCE} Program for {3-D} Vector Analysis 1799 in Orthogonal Curvilinear Coordinates", 1800 journal = "Comp. Phys. Commun.", 1801 year = "1987", 1802 volume = "47", 1803 number = "1", 1804 pages = "139--147", 1805 month = oct, 1806} 1807 1808@TechReport{Edelen:81, 1809 author = "Dominic G. B. Edelen", 1810 title = "Programs for Calculation of Isovector Fields in the 1811 {REDUCE}-2 Environment", 1812 institution = "Center for the Application of Mathematics, Lehigh 1813 University", 1814 year = "1981", 1815 number = "TBD", 1816 month = aug, 1817} 1818 1819@Article{Edelen:82, 1820 author = "D. G. B. Edelen", 1821 title = "Isovector Fields for Problems in the Mechanics of 1822 Solids and Fluids", 1823 journal = "Int. Journ. Eng. Sci.", 1824 year = "1982", 1825 volume = "20", 1826 pages = "803--815", 1827} 1828 1829%Prolongation methods as a REDUCE package for this, available from 1830%Center for Applications of Mathematics, Lehigh Univ., Bethlehem, PA 1831%18015. Applications to mechanics of solids and fluids. 1832 1833@Book{Edneral:89, 1834 author = "Viktor F. Edneral and Aleksandr P. Kryukov and 1835 Anatolii Ia. Rodionov", 1836 title = "The language of the analytic computer program 1837 {REDUCE}", 1838 publisher = "Moscow, {Izd-vo}, Moskovskogo {un-ta}", 1839 year = "1989", 1840} 1841 1842%This monograph -- first in The Soviet Union with a systematic treatment 1843%of the analytical computer (program) REDUCE. 1844 1845@Article{Eisenberger:90, 1846 author = "Moshe Eisenberger", 1847 title = "Application of Symbolic Algebra to the Analysis of 1848 Plates on Variable Elastic Foundation", 1849 journal = "J. Symbolic Computation", 1850 year = "1990", 1851 volume = "9", 1852 number = "2", 1853 pages = "207--213", 1854 month = feb, 1855} 1856 1857@TechReport{Eissfeller:86, 1858 author = "Bernd {Ei{\ss}feller} and {G\"{u}nter} W. Hein", 1859 title = "A Contribution to {3D-Operational} Geodesy", 1860 institution = "{Universit\"{a}rer} Studiengang Vermessungswesen and 1861 {Universit\"{a}t} der Bundeswehr {M\"{u}nchen}", 1862 year = "1986", 1863 number = "Heft 17", 1864 month = dec, 1865} 1866 1867@PhdThesis{Eitelbach:73, 1868 author = "D. L. Eitelbach", 1869 title = "Automatic Analysis of Problems in Elementary 1870 Mechanics", 1871 school = "University of Illinois", 1872 year = "1973", 1873} 1874 1875@Article{Eleuterio:82, 1876 author = "S. M. Eleut\'{e}rio and R. V. Mendes", 1877 title = "Note on Equivalence and Singularities: An Application 1878 of Computer Algebra", 1879 journal = "Journ. Comp. Phys.", 1880 year = "1982", 1881 volume = "48", 1882 pages = "150--156", 1883} 1884 1885%GR equivalence, commenting on \AAman & Karlhede. 1886 1887@Article{Eliseev:85, 1888 author = "V. P. Eliseev and R. N. Fedorova and V. V. Kornyak", 1889 title = "A {REDUCE} Program for Determining Point and Contact 1890 {Lie} Symmetries of Differential Equations", 1891 journal = "Comp. Phys. Comm.", 1892 year = "1985", 1893 volume = "36", 1894 pages = "383--389", 1895} 1896 1897%"A universal REDUCE program for obtaining the systems of 1898%determining equations of the Lie algebra of point and contact 1899%symmetries is proposed". 1900 1901@Article{Elishakoff:87, 1902 author = "Isaac Elishakoff and Joseph Hollkamp", 1903 title = "Computerized Symbolic Solution for a Nonconservative 1904 System in Which Instability Occurs by Flutter in One 1905 Range of a Parameter and by Divergence in Another", 1906 journal = "Comp. Methods in Applied Mechanics and Engineering", 1907 year = "1987", 1908 volume = "62", 1909 pages = "27--46", 1910} 1911 1912%"...the problem is solved by the Galerkin method in conjunction with 1913%computerized symbolic algebra". The system used is REDUCE. "It 1914%carries out algebraic operations irrespective of their complexity". 1915%Includes snatches of code and algebraic answers. Mainly 1916%differentiation and substitution, plus a little integration. The 1917%coefficients get rather large (18 digits or so). 1918 1919@Article{Elishakoff:87a, 1920 author = "Isaac Elishakoff and Brian Couch", 1921 title = "Application of Symbolic Algebra to the Instability of 1922 a Nonconservative System", 1923 journal = "J. Symbolic Computation", 1924 year = "1987", 1925 volume = "4", 1926 number = "3", 1927 pages = "391--396", 1928 month = dec, 1929} 1930 1931@Article{Esteban:90, 1932 author = "E. P. Esteban and E. Ramos", 1933 title = "Algebraic computing and the {Newman-Penrose} 1934 formalism", 1935 journal = "Computers in Physics", 1936 year = "1990", 1937 pages = "285--290", 1938 month = may # "/" # jun, 1939} 1940 1941@Article{Falck:89, 1942 author = "N. K. Falck and D. Graudenz and G. Kramer", 1943 title = "Cross section for {five-parton} production in $e^{+} 1944 e^{-}$ annihilation", 1945 journal = "Comp. Phys. Comm.", 1946 year = "1989", 1947 volume = "56", 1948 pages = "181--198", 1949 number = "2", 1950 month = dec, 1951} 1952 1953@Article{Fazio:84, 1954 author = "P. M. Fazio and G. E. Copeland", 1955 title = "Cooper-Type Minima in Multipole Cross Sections of 1956 Atomic Hydrogen", 1957 journal = "Phys. Rev. Lett.", 1958 year = "1984", 1959 volume = "53", 1960 number = "2", 1961 month = jul, 1962} 1963 1964@InProceedings{Fedorova:87, 1965 author = "R. N. Fedorova and V. P. Gerdt and N. N. Govorun and 1966 V. P. Shirikov", 1967 title = "Computer Algebra in Physical Research of {Joint 1968 Institute} for {Nuclear Research}", 1969 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 1970 Science", 1971 year = "1987", 1972 volume = "378", 1973 pages = "1--10", 1974 publisher = "Springer-Verlag", 1975} 1976 1977@InProceedings{Fedorova:87a, 1978 author = "R. N. Fedorova and V. V. Kornyak", 1979 title = "Computer Algebra Application for Determining Local 1980 Symmetries of Differential Equations", 1981 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 1982 Science", 1983 year = "1987", 1984 volume = "378", 1985 pages = "174--175", 1986 publisher = "Springer-Verlag", 1987} 1988 1989@Article{Feldmar:86, 1990 author = "E. Feldmar and K. S. {K\"{o}lbig}", 1991 title = "{REDUCE} Procedures for the Manipulation of 1992 Generalized Power Series", 1993 journal = "Comp. Phys. Comm.", 1994 year = "1986", 1995 volume = "39", 1996 pages = "267--284", 1997} 1998 1999@Article{Feuillebois:84, 2000 author = "F. Feuillebois", 2001 title = "Sedimentation in a Dispersion with Vertical 2002 Inhomogenieties", 2003 journal = "Journ. Fluid Mech.", 2004 year = "1984", 2005 volume = "139", 2006 pages = "145--171", 2007} 2008 2009%Uses REDUCE and INT to evaluate some integrals in the expansion of 2010%1/s, a small quantity. 2011 2012@Article{Fitch:73, 2013 author = "John Fitch", 2014 title = "Problems \#3 and \#4 in {REDUCE} and {MACSYMA}", 2015 journal = "SIGSAM Bulletin", 2016 year = "1973", 2017 pages = "10--11", 2018} 2019 2020%The algebra systems REDUCE and MACSYMA are used to solve SIGSAM 2021%Problem \#3, the Reversion of a Double Series, and SIGSAM Problem \#4, 2022%the Lie Transform Solution of the Harmonic Oscillator. 2023 2024@InProceedings{Fitch:81, 2025 author = "J. P. Fitch", 2026 title = "User-based Integration Software", 2027 booktitle = "Proc. 1981 {ACM} Symposium on Symbolic and Algebraic 2028 Computation", 2029 year = "1981", 2030 pages = "245--248", 2031} 2032 2033@InProceedings{Fitch:83, 2034 author = "J. P. Fitch", 2035 title = "Implementing {REDUCE} on a Microprocessor", 2036 booktitle = "Proc. {EUROCAL} 1983, Lecture Notes in Computer 2037 Science", 2038 year = "1983", 2039 volume = "162", 2040 pages = "128--136", 2041 publisher = "Springer-Verlag", 2042} 2043 2044@Article{Fitch:85, 2045 author = "J. P. Fitch", 2046 title = "Solving Algebraic Problems with {REDUCE}", 2047 journal = "J. of Symbolic Computation", 2048 year = "1985", 2049 volume = "1", 2050 number = "2", 2051 pages = "211--227", 2052 month = jun, 2053} 2054 2055@InProceedings{Fitch:85a, 2056 author = "J. P. Fitch", 2057 title = "Applying Computer Algebra", 2058 booktitle = "International Conference on Computer Algebra and its 2059 Application in Theory", 2060 year = "1985", 2061 pages = "262--275", 2062} 2063 2064@InProceedings{Fitch:87, 2065 author = "J. P. Fitch", 2066 title = "Utilisation du Calcul Formel", 2067 booktitle = "Calcul Formel et Automatique", 2068 editor = "P. Chenin", 2069 publisher = "Editions du {CNRS}", 2070 year = "1987", 2071 pages = "119--136", 2072} 2073 2074@InProceedings{Fitch:87a, 2075 author = "J. P. Fitch and R. G. Hall", 2076 title = "Symbolic Computation and the Finite Element Method", 2077 booktitle = "Proc. {EUROCAL} '87, Lecture Notes in Computer 2078 Science", 2079 year = "1987", 2080 volume = "378", 2081 pages = "95--96", 2082 publisher = "Springer-Verlag", 2083} 2084 2085@InProceedings{Fitch:89, 2086 author = "J. P. Fitch", 2087 title = "Can {REDUCE} be run in parallel?", 2088 booktitle = "Proc. of {ISSAC} '89", 2089 publisher = "{ACM} Press, New York", 2090 year = "1989", 2091 pages = "155--162", 2092} 2093 2094@Article{Fitch:89a, 2095 author = "J. Fitch", 2096 title = "Compiling for Parallelism", 2097 journal = "Computer Algebra and Parallelism", 2098 editor = "J. Della Dora and J. Fitch", 2099 year = "1989", 2100 pages = "19--31", 2101 publisher = "Academic Press, London", 2102} 2103 2104@TechReport{Flatau:86, 2105 author = "Piotr J. Flatau and John P. Boyd and William R. 2106 Cotton", 2107 title = "Symbolic Algebra in Applied Mathematics and 2108 Geophysical Fluid Dynamics - {REDUCE} Examples", 2109 institution = "Dept. of Atmospheric and Oceanic Science, University 2110 of Michigan, and Dept. of Atmospheric Science, Colorado 2111 State University", 2112 year = "1986", 2113} 2114 2115@TechReport{Flath:86, 2116 author = "Dan Flath", 2117 title = "Remarks on Tensor Operators", 2118 institution = "National University of Singapore, Department of 2119 Mathematics", 2120 type = "Research Report", 2121 year = "1986", 2122 number = "266", 2123 month = jul, 2124} 2125 2126@Article{Fleischer:71, 2127 author = "J. Fleischer", 2128 title = "Partial Wave Analysis of Nucleon-Nucleon 2129 {Bethe}-{Salpeter} Equation on the Computer", 2130 journal = "Journ. of Comp. Phys.", 2131 year = "1971", 2132 volume = "12", 2133 pages = "112--123", 2134} 2135 2136@Article{Fleischer:73, 2137 author = "J. Fleischer and J. L. Gammel and M. T. Menzel", 2138 title = "Matrix {Pad\'{e}} Approximants for the {1SO}- and 2139 {3PO}- Partial Waves in Nucleon-Nucleon Scattering", 2140 journal = "Phys. Rev. D", 2141 year = "1973", 2142 volume = "8", 2143 pages = "1545--1552", 2144} 2145 2146@Article{Fleischer:75, 2147 author = "J. Fleischer and J. A. Tjon", 2148 title = "Bethe-{Salpeter} Equation for {J}=0 Nucleon-Nucleon 2149 Scattering with One-Boson Exchange", 2150 journal = "Nuclear Physics", 2151 year = "1975", 2152 volume = "B84", 2153 pages = "375--396", 2154} 2155 2156@Article{Fogelholm:82, 2157 author = "Rabbe Fogelholm and Inge B. Frick", 2158 title = "Standard {LISP} for the {VAX:} A Provisional 2159 Implementation", 2160 journal = "{SIGSAM} Bulletin", 2161 year = "1982", 2162 volume = "16", 2163 number = "4", 2164 pages = "10--12", 2165 month = nov, 2166} 2167 2168@Article{Foster:89, 2169 author = "Kenneth R. Foster and Haim H. Bau", 2170 title = "Symbolic Manipulation Programs for the Personal 2171 Computer", 2172 journal = "Science", 2173 year = "1989", 2174 volume = "243", 2175 pages = "679--243", 2176 month = feb, 2177} 2178 2179%Reviews several algebra programs that run on small machines. Doesn't 2180%rate the PC version of REDUCE very highly because of the small workspace. 2181 2182@Article{Fox:71, 2183 author = "J. A. Fox", 2184 title = "Recalculation of the Crossed Graph Contribution to the 2185 4th Order {Lamb} Shift", 2186 journal = "Phys. Rev. D", 2187 year = "1971", 2188 volume = "3", 2189 pages = "3228--3230", 2190} 2191 2192@Article{Fox:74, 2193 author = "John A. Fox and Anthony C. Hearn", 2194 title = "Analytic Computation of Some Integrals in Fourth Order 2195 Quantum Electrodynamics", 2196 journal = "Journ. Comp. Phys.", 2197 year = "1974", 2198 volume = "14", 2199 pages = "301--317", 2200} 2201 2202%A program for the analytic evaluation of some parametric integrals 2203%which occur in fourth order QED calculations is described. 2204 2205@Article{Franceschetti:85, 2206 author = "G. Franceschetti and I. Pinto", 2207 title = "Nonlinear Propagation and Scattering: Analytical 2208 Solution and Symbolic Code Implementation", 2209 journal = "J. Opt. Soc. Am. A", 2210 year = "1985", 2211 volume = "2", 2212 pages = "997--1006", 2213} 2214 2215%Volterra series using REDUCE. Perturbation expansions. 2216 2217@InProceedings{Freire:88, 2218 author = "E. Freire and E. Gamero and E. Ponce and L. G. 2219 Franquelo", 2220 title = "An Algorithm for Symbolic Computation of Center 2221 Manifolds", 2222 booktitle = "Proc. of {ISSAC} '88", 2223 publisher = "Springer-Verlag", 2224 year = "1988", 2225 volume = "358", 2226 pages = "218--230", 2227} 2228 2229@InProceedings{Freire:89, 2230 author = "E. Freire and E. Gamero and E. Ponce", 2231 title = "An Algorithm for Symbolic Computation of {Hopf} 2232 Bifurcation", 2233 booktitle = "Proc. Computers and Mathematics '89", 2234 editor = "E. Kaltofen and S. M. Watt", 2235 year = "1989", 2236 pages = "109--118", 2237 publisher = "Springer-Verlag, New York", 2238} 2239 2240@TechReport{Frick:82, 2241 author = "I. G. Frick and R. Fogelholm", 2242 title = "An Implementation of {Standard} {Lisp} Built on Top of 2243 {Franz Lisp}", 2244 institution = "University of Stockholm, Institute of Physics", 2245 year = "1982", 2246 type = "Report", 2247 month = apr, 2248} 2249 2250%A Standard LISP system has been built for the VAX-11 2251%large-address-space computer by embedding the required 2252%function definitions in the available Franz Lisp system 2253%for VAX/UNIX. 2254 2255@Article{Fujimoto:84, 2256 author = "Y. Fujimoto and T. Garavaglia", 2257 title = "Phase Diagrams in {Scalar QED}", 2258 journal = "Physics Letters", 2259 year = "1984", 2260 volume = "148B", 2261 number = "1,2,3", 2262 pages = "220--224", 2263 month = nov, 2264} 2265 2266@Article{Fuzio:85, 2267 author = "P. M. Fuzio and G. E. Copeland", 2268 title = "Partial Radiative-Recombination Cross Sections for 2269 Excited States of Hydrogen", 2270 journal = "Phys. Rev. A", 2271 year = "1985", 2272 volume = "31", 2273 number = "1", 2274 pages = "187--195", 2275} 2276 2277%"The squares of the dipole and quadrupole matrix elements for the 2278%free-to-bond transitions of hydrogen uptp high bound states are 2279%derived in closed analytic form using a method suitable for computer 2280%algebra". 2281 2282