@string{j:acm_comm_comp_algebra        = {ACM Communications in Computer Algebra}}
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@string{pro:issac:89    = {{ISSAC~'89}: {P}roceedings of the 1989 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:90    = {{ISSAC~'90}: {P}roceedings of the 1990 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:91    = {{ISSAC~'91}: {P}roceedings of the 1991 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:92    = {{ISSAC~'92}: {P}roceedings of the 1992 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:93    = {{ISSAC~'93}: {P}roceedings of the 1993 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:94    = {{ISSAC~'94}: {P}roceedings of the 1994 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:95    = {{ISSAC~'95}: {P}roceedings of the 1995 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:96    = {{ISSAC~'96}: {P}roceedings of the 1996 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:97    = {{ISSAC~'97}: {P}roceedings of the 1997 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:98    = {{ISSAC~'98}: {P}roceedings of the 1998 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:99    = {{ISSAC~'99}: {P}roceedings of the 1999 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:00    = {{ISSAC~'00}: {P}roceedings of the 2000 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:01    = {{ISSAC~'01}: {P}roceedings of the 2001 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:02    = {{ISSAC~'02}: {P}roceedings of the 2002 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:03    = {{ISSAC~'03}: {P}roceedings of the 2003 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:04    = {{ISSAC~'04}: {P}roceedings of the 2004 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:05    = {{ISSAC~'05}: {P}roceedings of the 2005 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:06    = {{ISSAC~'06}: {P}roceedings of the 2006 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:07    = {{ISSAC~'07}: {P}roceedings of the 2007 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:08    = {{ISSAC~'08}: {P}roceedings of the 2008 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:issac:09    = {{ISSAC~'09}: {P}roceedings of the 2009 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}

@string{pro:symsac:71   = {{SYMSAC~'71}: {P}roceedings of the second {ACM} {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:symsac:76   = {{SYMSAC~'76}: {P}roceedings of the third {ACM} {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:symsac:81   = {{SYMSAC~'81}: {P}roceedings of the fourth {ACM} {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}
@string{pro:symsac:86   = {{SYMSAC~'86}: {P}roceedings of the fifth {ACM} {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}}

@string{pro:stoc:92     = {{STOC~'92}: {P}roceedings of the twenty--fourth annual {ACM} {S}ymposium on {T}heory of {C}omputing}}
@string{pro:stoc:93     = {{STOC~'93}: {P}roceedings of the twenty--fifth annual {ACM} {S}ymposium on {T}heory of {C}omputing}}
@string{pro:stoc:94     = {{STOC~'94}: {P}roceedings of the twenty--sixth annual {ACM} {S}ymposium on {T}heory of {C}omputing}}
@string{pro:stoc:95     = {{STOC~'95}: {P}roceedings of the twenty--seventh annual {ACM} {S}ymposium on {T}heory of {C}omputing}}

@string{pro:imacs:93    = {{IMACS~'93}: {P}roceedings of the 1993 {IMACS} {S}ymposium}}

@article{Harvey2009multipoint,
    author        = {David Harvey},
    title         = {Faster polynomial multiplication via multipoint {K}ronecker substitution},
    journal       = j:symb_comp,
    volume        = {44},
    number        = {10},
    year          = {2009},
    issn          = {0747-7171},
    pages         = {1502--1510},
    doi           = {10.1016/j.jsc.2009.05.004},
    publisher     = pub:academic,
    address       = adr:new_york,
    keywords      = {},
}

@book{Daly2003horizon,
    editor        = {Timothy Daly},
    title         = {{A}xiom: {T}he 30 year horizon},
    pages         = {1100+},
    year          = {2003},
    publisher     = {\url{www.axiom-developer.org}},
    url           = {http://portal.axiom-developer.org/public/book2.pdf},
    keywords      = {},
}

@book{Knuth1985seminumerical,
    author        = {Donald E. Knuth},
    title         = {{T}he {A}rt of {C}omputer {P}rogramming: {S}eminumerical {A}lgorithms},
    edition       = edt:second,
    year          = {1985},
    publisher     = pub:addison,
    address       = adr:reading,
    isbn          = {0-201-03822-6},
    keywords      = {},
}

@book{Knuth1998sorting,
    author        = {Donald E. Knuth},
    title         = {{T}he {A}rt of {C}omputer {P}rogramming: {S}orting and {S}earching},
    edition       = edt:second,
    year          = {1998},
    publisher     = pub:addison,
    address       = adr:reading,
    isbn          = {0-201-89685-0},
    keywords      = {},
}

@article{vanHoeij2002knapsack,
    author        = {Mark van Hoeij},
    title         = {{F}actoring {P}olynomials and the {K}napsack {P}roblem},
    journal       = j:number_theory,
    volume        = {95},
    number        = {2},
    pages         = {167--189},
    year          = {2002},
    issn          = {0022-314X},
    doi           = {10.1006/jnth.2001.2763},
    url           = {www.math.fsu.edu/~hoeij/knapsack/paper/knapsack.ps},
    keywords      = {univariate, polynomial, factorization, LLL},
}

@article{Belabas2004relative,
    author        = {Karim Belabas},
    title         = {{A} relative van {H}oeij algorithm over number fields},
    journal       = j:symb_comp,
    volume        = {37},
    number        = {5},
    pages         = {641--668},
    year          = {2004},
    publisher     = pub:academic,
    address       = adr:new_york,
    url           = {http://www.ufr-mi.u-bordeaux.fr/~belabas/research/vanhoeij.pdf},
    keywords      = {},
}

@book{Nijenhuis1978combinatorial,
    author        = {Albert Nijenhuis and Herbert S. Wilf},
    title         = {{C}ombinatorial {A}lgorithms: {F}or {C}omputers and {C}alculators},
    edition       = edt:second,
    year          = {1978},
    publisher     = pub:academic,
    address       = adr:new_york,
    keywords      = {},
}

@article{Joyner2008axiom,
    author        = {David Joyner},
    title         = {{O}pen source computer algebra systems: {A}xiom},
    journal       = j:acm_comm_comp_algebra,
    volume        = {42},
    number        = {1-2},
    pages         = {39--47},
    year          = {2008},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {1932-2240},
    doi           = {10.1145/1394042.1394046},
    keywords      = {},
}

@article{Joyner2006maxima,
    author        = {David Joyner},
    title         = {{O}pen source computer algebra systems: {M}axima},
    journal       = j:acm_comm_comp_algebra,
    volume        = {40},
    number        = {3-4},
    pages         = {108--111},
    year          = {2006},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {1932-2240},
    doi           = {10.1145/1279721.1279726},
    keywords      = {},
}

@article{Wilf1978bisection,
    author        = {Herbert S. Wilf},
    title         = {{A} {G}lobal {B}isection {A}lgorithm for {C}omputing the {Z}eros of {P}olynomials in the {C}omplex {P}lane},
    journal       = j:acm,
    volume        = {25},
    number        = {3},
    pages         = {415--420},
    year          = {1978},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0004-5411},
    doi           = {10.1145/322077.322084},
    keywords      = {},
}

@inproceedings{Gathen1997taylor,
    author        = {Joachim von zur Gathen and J\"{u}rgen Gerhard},
    title         = {{F}ast algorithms for {T}aylor shifts and certain difference equations},
    booktitle     = pro:issac:97,
    pages         = {40--47},
    year          = {1997},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-875-4},
    doi           = {10.1145/258726.258745},
    location      = adr:kihei,
    keywords      = {},
}

@article{Pinkert1976complex,
    author        = {James R. Pinkert},
    title         = {{A}n {E}xact {M}ethod for {F}inding the {R}oots of a {C}omplex {P}olynomial},
    journal       = j:acm_tran_math_soft,
    volume        = {2},
    number        = {4},
    pages         = {351--363},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0098-3500},
    doi           = {10.1145/355705.355710},
    keywords      = {},
}

@inproceedings{Sharma2007complexity,
    author        = {Vikram Sharma},
    title         = {{C}omplexity of real root isolation using continued fractions},
    booktitle     = pro:issac:07,
    pages         = {339--346},
    year          = {2007},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {978-1-59593-743-8},
    doi           = {10.1145/1277548.1277594},
    location      = adr:waterloo,
    keywords      = {},
}

@inproceedings{Collins1976descarte,
    author        = {George E. Collins and Alkiviadis G. Akritas},
    title         = {{P}olynomial real root isolation using {D}escarte's rule of signs},
    booktitle     = pro:symsac:76,
    pages         = {272--275},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800205.806346},
    location      = adr:yorktown,
    keywords      = {},
}

@inproceedings{Johnson1997isolation,
    author        = {Jeremy. R. Johnson and Werner Krandick},
    title         = {{P}olynomial real root isolation using approximate arithmetic},
    booktitle     = pro:issac:97,
    pages         = {225--232},
    year          = {1997},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-875-4},
    doi           = {10.1145/258726.258790},
    location      = adr:kihei,
    keywords      = {},
}

@inproceedings{Johnson2005taylor,
    author        = {Jeremy R. Johnson and Werner Krandick and Anatole D. Ruslanov},
    title         = {{A}rchitecture--aware classical {T}aylor shift by 1},
    booktitle     = pro:issac:05,
    pages         = {200--207},
    year          = {2005},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-59593-095-7},
    doi           = {10.1145/1073884.1073913},
    location      = adr:beijing,
    keywords      = {},
}

@inproceedings{Johnson1992interval,
    author        = {Jeremy. R. Johnson},
    title         = {{R}eal algebraic number computation using interval arithmetic},
    booktitle     = pro:issac:92,
    pages         = {195--205},
    year          = {1992},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-489-9},
    doi           = {10.1145/143242.143311},
    location      = adr:berkeley,
    keywords      = {},
}

@inproceedings{Collins1992infallible,
    author        = {George E. Collins and Werner Krandick},
    title         = {{A}n efficient algorithm for infallible polynomial complex root isolation},
    booktitle     = pro:issac:92,
    pages         = {189--194},
    year          = {1992},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-489-9},
    doi           = {10.1145/143242.143308},
    location      = adr:berkeley,
    keywords      = {},
}

@inproceedings{Collins1996complex,
    author        = {George E. Collins and Werner Krandick},
    title         = {{A} tangent--secant method for polynomial complex root calculation},
    booktitle     = pro:issac:96,
    pages         = {137--141},
    year          = {1996},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-796-0},
    doi           = {10.1145/236869.236921},
    location      = adr:zurich,
    keywords      = {},
}

@inproceedings{Hulzen1982notorious,
    author        = {J. A. van Hulzen},
    title         = {{C}omputer {A}lgebra {S}ystems {V}iewed by a {N}otorious {U}ser},
    booktitle     = {EUROCAM '82: Proceedings of the European Computer Algebra Conference on Computer Algebra},
    publisher     = pub:springer,
    address       = adr:london,
    pages         = {166--180},
    year          = {1982},
    isbn          = {3-540-11607-9},
    keywords      = {},
}

@booklet{Loos1983algebraic,
    author        = {Rudiger Loos},
    title         = {{C}omputing in {A}lgebraic {E}xtensions},
    editor        = {Bruno Buchberger and George E. Collins and Rudiger Loos and Rudolf Albrecht},
    series        = {{C}omputer {A}lgebra: {S}ymbolic and {A}lgebraic {C}omputation},
    publisher     = pub:springer,
    address       = adr:new_york,
    edition       = edt:second,
    pages         = {173--187},
    year          = {1983},
    isbn          = {0-387-81776-K},
    keywords      = {},
}

@booklet{Kaltofen1983factor,
    author        = {Erich Kaltofen},
    title         = {{P}olynomial {F}actorization},
    editor        = {Bruno Buchberger and George E. Collins and Rudiger Loos and Rudolf Albrecht},
    series        = {{C}omputer {A}lgebra: {S}ymbolic and {A}lgebraic {C}omputation},
    publisher     = pub:springer,
    address       = adr:new_york,
    edition       = edt:second,
    pages         = {93--111},
    year          = {1983},
    isbn          = {0-387-81776-K},
    keywords      = {polynomial, factorization},
}

@inproceedings{Liao1995heuristic,
    author        = {Hsin--Chao Liao and Richard J. Fateman},
    title         = {{E}valuation of the heuristic polynomial {GCD}},
    booktitle     = pro:issac:95,
    pages         = {240--247},
    year          = {1995},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-699-9},
    doi           = {10.1145/220346.220376},
    location      = adr:montreal,
    keywords      = {multivariate, polynomial, GCD, heuristic, HEUGCD},
}

@inproceedings{Trager1976algebraic,
    author        = {Barry M. Trager},
    title         = {{A}lgebraic factoring and rational function integration},
    booktitle     = pro:symsac:76,
    pages         = {219--226},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800205.806338},
    location      = adr:yorktown,
    keywords      = {polynomial, factorization, algebraic, number, fields},
}

@misc{Lewis1999comparison,
    author        = {Robert H. Lewis and Michael J. Wester},
    title         = {{C}omparison of {P}olynomial--{O}riented {C}omputer {A}lgebra {S}ystems},
    year          = {1999},
    url           = {http://www.bway.net/~lewis/cacomp.ps},
    keywords      = {},
}

@book{Wester1999guide,
    author        = {Michael J. Wester},
    title         = {{C}omputer {A}lgebra {S}ystems: {A} {P}ractical {G}uide},
    pages         = {452},
    year          = {1999},
    publisher     = pub:wiley,
    address       = adr:hoboken,
    isbn          = {0-471-98353-5},
    keywords      = {},
}

@misc{Wester1999critique,
    author        = {Michael J. Wester},
    title         = {{A} {C}ritique of the {M}athematical {A}bilities of {C}{A} {S}ystems},
    year          = {1999},
    url           = {http://www.math.unm.edu/~wester/cas/book/Wester.pdf},
    keywords      = {},
}

@misc{Wester1999algebra,
    author        = {Michael J. Wester},
    title         = {{C}omputer {A}lgebra {S}ynonyms},
    year          = {1999},
    url           = {http://www.math.unm.edu/~wester/cas/synonyms.pdf},
    keywords      = {},
}

@inproceedings{Moenck1976practical,
    author        = {Robert T. Moenck},
    title         = {{P}ractical fast polynomial multiplication},
    booktitle     = pro:symsac:76,
    pages         = {136--148},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800205.806332},
    location      = adr:yorktown,
    keywords      = {},
}

@book{Bronstein2005integration,
    author        = {Manuel Bronstein},
    title         = {{S}ymbolic {I}ntegration {I}: {T}ranscendental {F}unctions},
    year          = {2005},
    publisher     = pub:springer,
    address       = adr:new_york,
    isbn          = {3-540-21493-3},
    keywords      = {symbolic, integration, transcendental},
}

@book{Geddes1992algorithms,
    author        = {Keith O. Geddes and Stephen R. Czapor and George Labahn},
    title         = {{A}lgorithms for {C}omputer {A}lgebra},
    year          = {1992},
    publisher     = pub:kluwer,
    address       = adr:norwell,
    isbn          = {0-7923-9259-0},
    keywords      = {computer, algebra, algorithms},
}

@book{Gathen1999modern,
    author        = {Joachim von zur Gathen and J\"{u}rgen Gerhard},
    title         = {{M}odern {C}omputer {A}lgebra},
    year          = {1999},
    publisher     = pub:cambridge,
    address       = adr:new_york,
    isbn          = {0-521-64176-4},
    keywords      = {computer, algebra, algorithms},
}

@book{Davenport1988systems,
    author        = {J. H. Davenport and Y. Siret and E. Tournier},
    title         = {{C}omputer algebra: systems and algorithms for algebraic computation},
    year          = {1988},
    publisher     = pub:academic,
    address       = adr:new_york,
    isbn          = {0-12-204230-1},
    keywords      = {computer, algebra, algorithms},
}


@inproceedings{Giovini1991sugar,
    author        = {Alessandro Giovini and Teo Mora and Gianfranco Niesi and Lorenzo Robbiano and Carlo Traverso},
    title         = {``{O}ne sugar cube, please'' or selection strategies in the {B}uchberger algorithm},
    booktitle     = pro:issac:91,
    pages         = {49--54},
    year          = {1991},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-437-6},
    doi           = {10.1145/120694.120701},
    location      = adr:bonn,
    keywords      = {},
}

@article{Davenport2002equality,
    author        = {James H. Davenport},
    title         = {{E}quality in {C}omputer {A}lgebra and {B}eyond},
    journal       = j:symb_comp,
    volume        = {34},
    number        = {4},
    pages         = {259--270},
    year          = {2002},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.2002.0551},
    url           = {http://www.calculemus.net/meetings/siena01/Papers/Davenport.pdf},
    keywords      = {},
}

@article{Collins1996improved,
    author        = {George E. Collins and Mark J. Encarnaci\'{o}n},
    title         = {{I}mproved {T}echniques for {F}actoring {U}nivariate {P}olynomials},
    journal       = j:symb_comp,
    volume        = {21},
    number        = {3},
    pages         = {313--327},
    year          = {1996},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1996.0014},
    keywords      = {univariate, polynomial, factorization, zassenhaus},
}

@misc{Fateman2005encoding,
    author        = {Richard J. Fateman},
    title         = {{C}an you save time in multiplying polynomials by encoding them as integers?},
    url           = {http://www.cs.berkeley.edu/~fateman/papers/polysbyGMP.pdf},
    keywords      = {},
}

@inproceedings{Monagan1993inplace,
    author        = {Michael B. Monagan},
    title         = {{I}n--place {A}rithmetic for {P}olinominals over \({Z}_n\)},
    booktitle     = {DISCO '92: Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems},
    year          = {1993},
    pages         = {22--34},
    publisher     = pub:springer,
    address       = adr:london,
    isbn          = {3-540-57272-4},
    keywords      = {},
}

@inproceedings{Monagan2009parallel,
    author        = {Michael B. Monagan and Roman Pearce},
    title         = {{P}arallel {S}parse {P}olynomial {M}ultiplication {U}sing {H}eaps},
    booktitle     = pro:issac:09,
    pages         = {263--270},
    year          = {2009},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {978-1-60558-609-0},
    doi           = {10.1145/1576702.1576739},
    location      = adr:seoul,
    keywords      = {},
}

@inproceedings{Monagan2007heaps,
    author        = {Michael B. Monagan and Roman Pearce},
    title         = {{P}olynomial {D}ivision {U}sing {D}ynamic {A}rrays, {H}eaps, and {P}acked {E}xponent {V}ectors},
    booktitle     = {CASC '07: Proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing},
    pages         = {295--315},
    year          = {2007},
    publisher     = pub:springer,
    address       = adr:london,
    keywords      = {},
}

@inproceedings{Monagan2006modulo,
    author        = {Michael B. Monagan and Roman Pearce},
    title         = {{R}ational {S}implification {M}odulo a {P}olynomial {I}deal},
    booktitle     = pro:issac:06,
    pages         = {239--245},
    year          = {2006},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-59593-276-3},
    location      = adr:genoa,
    doi           = {10.1145/1145768.1145809},
    keywords      = {},
}

@mastersthesis{Pearce2001relations,
    author        = {Roman Pearce},
    title         = {{R}ational {E}xpression {S}implification with {P}olynomial {S}ide {R}elations},
    school        = {Simon Fraser University},
    year          = {2001},
    url           = {www.cecm.sfu.ca/~rpearcea/rpearce_msc_thesis.pdf},
    keywords      = {},
}

@inproceedings{Li2006levels,
    author        = {Xin Li and Marc Moreno Maza},
    title         = {{E}fficient {I}mplementation of {P}olynomial {A}rithmetic in a {M}ultiple--{L}evel {P}rogramming {E}nvironment},
    booktitle     = {ICMS '06: Proceedings of the Second International Congress on Mathematical Software},
    pages         = {12--23},
    year          = {2006},
    publisher     = pub:springer,
    address       = adr:london,
    isbn          = {3-540-38084-1},
    location      = adr:castro_urdiales,
    keywords      = {},
}

@article{Lenstra1982factor,
    author        = {A. K. Lenstra and H. W. Lenstra and L. Lov\'{a}sz},
    title         = {{F}actoring {P}olynomials with {R}ational coefficients},
    journal       = j:math_annalen,
    volume        = {261},
    number        = {4},
    pages         = {515--534},
    year          = {1982},
    doi           = {10.1007/BF01457454},
    url           = {https://openaccess.leidenuniv.nl/dspace/bitstream/1887/3810/1/346_050.pdf},
    keywords      = {univariate, polynomial, factorization, LLL, polynomial time},
}

@article{Zhi1997optimal,
    author        = {Lihong Zhi},
    title         = {{A}n {O}ptimal {M}ethod for {A}lgebraic {F}actoring},
    journal       = j:comp_sci_and_tech,
    pages         = {1--8},
    year          = {1997},
    url           = {www.mmrc.iss.ac.cn/~lzhi/Publications/zopfac.pdf},
    keywords      = {polynomial, factorization, algebraic, number, fields},
}

@manual{Bronstein2004algebra,
    author        = {Manuel Bronstein and Marc Moreno Maza},
    title         = {\texttt{{A}lgebra} {U}ser {G}uide and {R}eference {M}anual},
    edition       = {1.0.2},
    month         = {April},
    year          = {2004},
    url           = {ftp://ftp-sop.inria.fr/cafe/software/algebra/algebra.dvi.gz},
    keywords      = {},
}

@manual{Aldor2000guide,
    organization  = {Aldor.org},
    title         = {\texttt{{A}ldor} {U}ser {G}uide},
    year          = {2000},
    url           = {www.aldor.org/aldorug.pdf},
    keywords      = {},
}

@article{Faugere1999f4,
    author        = {Jean Charles Faug\`{e}re},
    title         = {{A} {N}ew {E}fficient {A}lgorithm for {C}omputing {G}r\"{o}bner {B}ases ({F4})},
    journal       = j:pure_and_applied_algebra,
    volume        = {139},
    number        = {1-3},
    month         = {June},
    year          = {1999},
    pages         = {61--88},
    url           = {http://www-calfor.lip6.fr/~jcf/Papers/F99a.pdf},
    keywords      = {},
}

@inproceedings{Faugere2002f5,
    author        = {Jean Charles Faug\`{e}re},
    title         = {{A} {N}ew {E}fficient {A}lgorithm for {C}omputing {G}r\"{o}bner {B}ases {W}ithout {R}eduction {T}o {Z}ero ({F5})},
    booktitle     = pro:issac:02,
    pages         = {75--83},
    year          = {2002},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-484-3},
    location      = adr:lille,
    doi           = {10.1145/780506.780516},
    url           = {http://www-calfor.lip6.fr/~jcf/Papers/F02a.pdf},
    keywords      = {},
}

@phdthesis{Saxena1997elimination,
    author        = {Tushar Saxena},
    title         = {{E}fficient {V}ariable {E}limination {U}sing {R}esultants},
    year          = {1997},
    school        = {State University of New York at Albany},
    address       = adr:albany,
    keywords      = {},
}

@inproceedings{Kaltofen1999genericity,
    author        = {Erich Kaltofen and Michael B. Monagan},
    title         = {{O}n the {G}enericity of the {M}odular {P}olynomial {GCD} {A}lgorithm},
    booktitle     = pro:issac:99,
    pages         = {59--66},
    year          = {1999},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-073-2},
    location      = adr:vancouver,
    doi           = {10.1145/309831.309861},
    keywords      = {multivariate, polynomial, GCD, genericity, MODGCD},
}

@article{Richardson1997zero,
    author        = {Daniel Richardson},
    title         = {{H}ow to {R}ecognize {Z}ero},
    journal       = j:symb_comp,
    volume        = {24},
    number        = {6},
    pages         = {627--645},
    year          = {1997},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1997.0157},
    keywords      = {},
}

@inproceedings{Monagan2004algebraic,
    author        = {Michael Monagan and Mark van Hoeij},
    title         = {{A}lgorithms for {P}olynomial {GCD} {C}omputation over {A}lgebraic {F}unction {F}ields},
    booktitle     = pro:issac:04,
    pages         = {297--304},
    year          = {2004},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-827-X},
    location      = adr:santander,
    doi           = {10.1145/1005285.1005328},
    keywords      = {},
}

@article{Gao2003partial,
    author        = {Shuhong Gao},
    title         = {{F}actoring {M}ultivariate {P}olynomials via {P}artial {D}ifferential {E}quations},
    journal       = j:math_comp,
    volume        = {72},
    number        = {242},
    pages         = {801--822},
    year          = {2003},
    publisher     = pub:ams,
    address       = adr:boston,
    issn          = {0025-5718},
    doi           = {10.1090/S0025-5718-02-01428-X},
    keywords      = {multivariate, polynomial, factorization, PDE},
}

@inproceedings{Abbott2000searching,
    author        = {John Abbott and Victor Shoup and Paul Zimmermann},
    title         = {{F}actorization in {Z}[x]: {T}he {S}earching {P}hase},
    booktitle     = pro:issac:00,
    pages         = {1--7},
    year          = {2000},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-218-2},
    doi           = {10.1145/345542.345560},
    location      = adr:st_andrews,
    keywords      = {univariate, polynomial, factorization, zassenhaus, searching phase},
}

@inproceedings{Shoup1993reality,
    author        = {Victor Shoup},
    title         = {{F}actoring {P}olynomials over {F}inite {F}ields: {A}symptotic {C}omplexity vs. {R}eality},
    booktitle     = pro:imacs:93,
    year          = {1993},
    location      = adr:lille,
    keywords      = {polynomial, factorization, finite fields},
}

@inproceedings{Kaltofen1995subquadratic,
    author        = {Erich Kaltofen and Victor Shoup},
    title         = {{S}ubquadratic--{T}ime {F}actoring of {P}olynomials over {F}inite {F}ields},
    booktitle     = pro:stoc:95,
    pages         = {398--406},
    year          = {1995},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-718-9},
    doi           = {10.1145/225058.225166},
    location      = adr:las_vegas,
    keywords      = {polynomial, factorization, finite fields, subquadratic time},
}

@article{Shoup1995factor,
    author        = {Victor Shoup},
    title         = {{A} {N}ew {P}olynomial {F}actorization {A}lgorithm and its {I}mplementation},
    journal       = j:symb_comp,
    volume        = {20},
    number        = {4},
    pages         = {363--397},
    year          = {1995},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1995.1055},
    keywords      = {polynomial, factorization, finite fields},
}

@inproceedings{Gathen1992frobenious,
    author        = {Joachim von zur Gathen and Victor Shoup},
    title         = {{C}omputing {F}robenius {M}aps and {F}actoring {P}olynomials},
    booktitle     = pro:stoc:92,
    pages         = {97--105},
    year          = {1992},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-511-9},
    doi           = {10.1145/129712.129722},
    location      = adr:victoria,
    keywords      = {polynomial, factorization, finite fields, frobenious maps},
}

@article{Gathen1992ComputingFM,
    title         = {Computing Frobenius maps and factoring polynomials},
    author        = {Joachim von zur Gathen and Victor Shoup},
    journal       = {Computational Complexity},
    year          = {1992},
    volume        = {2},
    pages         = {187-224},
    doi           = {10.1007/BF01272074},
    month         = {September},
}

@inproceedings{Gathen1983polytime,
    author        = {Joachim von zur Gathen and Erich Kaltofen},
    title         = {{P}olynomial--{T}ime {F}actorization of {M}ultivariate {P}olynomials over {F}inite {F}ields},
    booktitle     = {Proceedings of the 10th Colloquium on Automata, Languages and Programming},
    pages         = {250--263},
    year          = {1983},
    publisher     = pub:springer,
    address       = adr:london,
    isbn          = {3-540-12317-2},
    keywords      = {multivariate, polynomial, factorization, finite fields, polynomial time},
}

@article{Musser1975factor,
    author        = {David R. Musser},
    title         = {{M}ultivariate {P}olynomial {F}actorization},
    journal       = j:acm,
    volume        = {22},
    number        = {2},
    pages         = {291--308},
    year          = {1975},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0004-5411},
    doi           = {10.1145/321879.321890},
    keywords      = {multivariate, polynomial, factorization, integers},
}

@article{Stoutemyer2007useful,
    author        = {David R. Stoutemyer},
    title         = {{U}seful computations {N}eed {U}seful {N}umbers},
    journal       = j:acm_comm_comp_algebra,
    volume        = {41},
    number        = {3},
    pages         = {75--99},
    year          = {2007},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {1932-2240},
    doi           = {10.1145/1358190.1358192},
    keywords      = {},
}

@inproceedings{Buchberger2001systems,
    author        = {Bruno Buchberger},
    title         = {{G}r\"{o}bner {B}ases: {A} {S}hort {I}ntroduction for {S}ystems {T}heorists},
    booktitle     = {Computer Aided Systems Theory --- EUROCAST 2001--Revised Papers},
    pages         = {1--19},
    year          = {2001},
    publisher     = pub:springer,
    address       = adr:london,
    isbn          = {3-540-42959-X},
    keywords      = {},
}

@article{Gao2004deterministic,
    author        = {Shuhong Gao and Erich Kaltofen and Alan G.B. Lauder},
    title         = {{D}eterministic {D}istinct--{D}egree {F}actorization of {P}olynomials over {F}inite {F}ields},
    journal       = j:symb_comp,
    volume        = {38},
    number        = {6},
    pages         = {1461--1470},
    year          = {2004},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1016/j.jsc.2004.05.004},
    keywords      = {polynomial, factorization, finite fields, deterministic, DDF},
}

@inproceedings{vanHoeij2002modgcd,
    author        = {Mark van Hoeij and Michael Monagan},
    title         = {{A} {M}odular {GCD} {A}lgorithm over {N}umber {F}ields {P}resented with {M}ultiple {E}xtensions},
    booktitle     = pro:issac:02,
    pages         = {109--116},
    year          = {2002},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-484-3},
    doi           = {10.1145/780506.780520},
    location      = adr:lille,
    keywords      = {polynomial, GCD, modular, MODGCD, algebraic, multiple extensions},
}

@article{Gasca2000interpolation,
    author        = {Mariano Gasca and Thomas Sauer},
    title         = {{P}olynomial {I}nterpolation in {S}everal {V}ariables},
    journal       = {Advances in Computational Mathematics},
    volume        = {12},
    number        = {4},
    pages         = {377--410},
    year          = {2000},
    doi           = {10.1023/A:1018981505752},
    keywords      = {},
}

@unpublished{Bernstein2008fast,
    author        = {Daniel J. Bernstein},
    title         = {{F}ast {M}ultiplication and its {A}pplications},
    month         = {May},
    year          = {2008},
    url           = {http://cr.yp.to/lineartime/multapps-20080515.pdf},
    keywords      = {},
}

@article{Ceberio2004greedy,
    author        = {Martine Ceberio and Vladik Kreinovich},
    title         = {{G}reedy {A}lgorithms for {O}ptimizing {M}ultivariate {H}orner {S}chemes},
    journal       = j:sigsam_bulletin,
    volume        = {38},
    number        = {1},
    pages         = {8--15},
    year          = {2004},
    issn          = {0163-5824},
    doi           = {10.1145/980175.980179},
    keywords      = {},
}

@inproceedings{Javadi2007spmod,
    author        = {Seyed Mohammad Mahdi Javadi and Michael Monagan},
    title         = {{A} {S}parse {M}odular {GCD} {A}lgorithm for {P}olynomials over {A}lgebraic {F}unction {F}ields},
    booktitle     = pro:issac:07,
    pages         = {187--194},
    year          = {2007},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {978-1-59593-743-8},
    doi           = {10.1145/1277548.1277575},
    location      = adr:waterloo,
    keywords      = {polynomial, GCD, sparse, modular, SPMOD, algebraic},
}

@mastersthesis{Javadi2006spmod,
    author        = {Seyed Mohammad Mahdi Javadi},
    title         = {{A} {S}parse {M}odular {GCD} {A}lgorithm for {P}olynomials over {A}lgebraic {F}unction {F}ields},
    school        = {Simon Fraser University},
    year          = {2006},
    url           = {http://ir.lib.sfu.ca/retrieve/4165/etd2580.pdf},
    keywords      = {polynomial, GCD, sparse, modular, SPMOD, algebraic},
}

@techreport{Ajwa95groebner,
    author        = {Iyad A. Ajwa and Zhuojun Liu and Paul S. Wang},
    title         = {{G}r\"{o}bner {B}ases {A}lgorithm},
    institution   = {ICM Technical Reports Series},
    number        = {ICM-199502-00},
    year          = {1995},
    keywords      = {},
}

@article{Ulmer1996kovacic,
    author        = {Felix Ulmer and Jacques--Arthur Weil},
    title         = {{N}ote on {K}ovacic's {A}lgorithm},
    journal       = j:symb_comp,
    volume        = {22},
    number        = {2},
    pages         = {179--200},
    year          = {1996},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1996.0047},
    keywords      = {},
}

@inproceedings{Roach1996hyper,
    author        = {Roach, Kelly},
    title         = {{H}ypergeometric {F}unction {R}epresentations},
    booktitle     = pro:issac:96,
    pages         = {301--308},
    isbn          = {0-89791-796-0},
    year          = {1996},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/236869.237088},
    location      = adr:zurich,
    url           = {http://www.planetquantum.com/TheMission/Papers/Issac96.pdf},
    keywords      = {},
}

@inproceedings{Roach1997meijer,
    author        = {Roach, Kelly},
    title         = {{M}eijer--{G} {F}unction {R}epresentations},
    booktitle     = pro:issac:97,
    year          = {1997},
    pages         = {205--211},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-875-4},
    doi           = {10.1145/258726.258784},
    location      = adr:kihei,
    url           = {http://www.planetquantum.com/TheMission/Papers/Issac97.pdf},
    keywords      = {},
}

@inproceedings{Jeffrey2005affine,
    author        = {David J. Jeffrey and Pratibha and Kelly Roach},
    title         = {{A}ffine {T}ransformations of {A}lgebraic {N}umbers},
    booktitle     = pro:issac:05,
    pages         = {193--199},
    year          = {2005},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-59593-095-7},
    doi           = {10.1145/1073884.1073912},
    location      = adr:beijing,
    url           = {http://www.planetquantum.com/TheMission/Papers/ISSAC2005.pdf},
    keywords      = {},
}

@inproceedings{Roach1992integration,
    author        = {Kelly Roach},
    title         = {{I}ndefinite and {D}efinite {I}ntegration},
    booktitle     = {Proceedings of the 1992 Mathematica Developer Conference},
    year          = {1992},
    publisher     = pub:wolfram:research,
    address       = adr:champaign,
    location      = adr:boston,
    url           = {http://library.wolfram.com/infocenter/Conferences/4684/},
    keywords      = {},
}

@inproceedings{Kauers2008heuristic,
    author        = {Manuel Kauers},
    title         = {{I}ntegration of {A}lgebraic {F}unctions: {A} {S}imple {H}euristic for {F}inding the {L}ogarithmic {P}art},
    booktitle     = pro:issac:08,
    pages         = {133--140},
    year          = {2008},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {978-1-59593-904-3},
    doi           = {10.1145/1390768.1390789},
    location      = {Linz/Hagenberg, Austria},
    keywords      = {},
}

@inproceedings{Javadi2007inplace,
    author        = {Seyed Mohammad Mahdi Javadi and Michael Monagan},
    title         = {{I}n--place {A}rithmetic for {U}nivariate {P}olynomials over an {A}lgebraic {N}umber {F}ield},
    booktitle     = {Proceedings of the Second Workshop on Compact Computer Algebra},
    month         = {July},
    year          = {2009},
    location      = adr:grand_bend,
    url           = {http://www.orcca.on.ca/conferences/cca2009/papers/Javadi_Monagan_CCA2009.pdf},
    keywords      = {},
}

@article{Wang1980eezgcd,
    author        = {Paul S. Wang},
    title         = {{T}he {EEZ--GCD} {A}lgorithm},
    journal       = j:sigsam_bulletin,
    volume        = {14},
    number        = {2},
    pages         = {50--60},
    year          = {1980},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0163-5824},
    doi           = {10.1145/1089220.1089228},
    keywords      = {multivariate, polynomial, GCD, EEZGCD},
}

@inproceedings{Monagan1994signature,
    author        = {Michael B. Monagan and Gaston H. Gonnet},
    title         = {{S}ignature {F}unctions for {A}lgebraic {N}umbers},
    booktitle     = pro:issac:94,
    pages         = {291--296},
    year          = {1994},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-638-7},
    doi           = {10.1145/190347.190430},
    location      = adr:oxford,
    keywords      = {},
}

@misc{Gonnet1999heuristic,
    author        = {Gaston H. Gonnet},
    title         = {{H}euristic {A}lgorithms},
    year          = {1999},
    note          = {Notes for the course Computer Algebra II},
    url           = {http://www.inf.ethz.ch/personal/gonnet/CAII/HeuristicAlgorithms.ps},
    keywords      = {},
}

@inproceedings{Abramov1995polynomial,
    author        = {Sergei A. Abramov and Manuel Bronstein and Marko Petkov\v{s}ek},
    title         = {{O}n {P}olynomial {S}olutions of {L}inear {O}perator {E}quations},
    booktitle     = pro:issac:95,
    pages         = {290--296},
    year          = {1995},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-699-9},
    doi           = {10.1145/220346.220384},
    location      = adr:montreal,
    keywords      = {},
}

@inproceedings{Abramov1995rational,
    author        = {Sergei A. Abramov},
    title         = {{R}ational {S}olutions of {L}inear {D}ifference and q--difference {E}quations with {P}olynomial {C}oefficients},
    booktitle     = pro:issac:95,
    pages         = {285--289},
    year          = {1995},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-699-9},
    doi           = {10.1145/220346.220383},
    location      = adr:montreal,
    keywords      = {},
}

@article{Petkovsek1992hyper,
    author        = {Marko Petkov\v{s}ek},
    title         = {{H}ypergeometric {S}olutions of {L}inear {R}ecurrences with {P}olynomial {C}oefficients},
    journal       = j:symb_comp,
    volume        = {14},
    number        = {2-3},
    pages         = {243--264},
    year          = {1992},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1016/0747-7171(92)90038-6},
    keywords      = {},
}

@article{Nemes1997monthly,
    author        = {Istv\'{a}n Nemes and Marko Petkov\v{s}ek and Herbert S. Wilf and Doron Zeilberger},
    title         = {{H}ow to do {M}onthly problems with your computer},
    journal       = {The American Mathematical Monthly},
    volume        = {104},
    number        = {6},
    pages         = {505--519},
    year          = {1997},
    publisher     = pub:maa,
    keywords      = {},
}

@article{Koepf1996identification,
    author        = {Wolfram Koepf},
    title         = {{T}he {I}dentification {P}roblem for {T}ranscendental {F}unctions},
    journal       = {arXiv:math.CA/9603215},
    year          = {1996},
    url           = {http://arxiv.org/abs/math.CA/9603215},
    keywords      = {},
}

@inproceedings{Jeffrey1998piecewise,
    author        = {David J. Jeffrey and A. D. Rich},
    title         = {{R}ecursive integration of piecewise--continuous functions},
    booktitle     = pro:issac:98,
    pages         = {290--294},
    year          = {1998},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-002-3},
    doi           = {10.1145/281508.281649},
    location      = adr:rostock,
    keywords      = {},
}

@inproceedings{Bronstein1998tutorial,
    author        = {Manuel Bronstein},
    title         = {{S}ymbolic {I}ntegration {T}utorial},
    booktitle     = pro:issac:98,
    year          = {1998},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-002-3},
    doi           = {10.1145/281508.281649},
    location      = adr:rostock,
    url           = {http://www-sop.inria.fr/cafe/Manuel.Bronstein/publications/issac98.pdf},
    keywords      = {},
}

@inproceedings{Bronstein1993partial,
    author        = {Manuel Bronstein and Bruno Salvy},
    title         = {{F}ull {P}artial {F}raction {D}ecomposition of {R}ational {F}unctions},
    booktitle     = pro:issac:93,
    pages         = {157--160},
    year          = {1993},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-604-2},
    doi           = {10.1145/164081.164114},
    location      = adr:kiev,
    keywords      = {},
}

@inproceedings{Javadi2009factor,
    author        = {Seyed Mohammad Mahdi Javadi and Michael Monagan},
    title         = {{O}n {F}actorization of {M}ultivariate {P}olynomials over {A}lgebraic {N}umber and {F}unction {F}ields},
    booktitle     = pro:issac:09,
    pages         = {199--206},
    year          = {2009},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {978-1-60558-609-0},
    doi           = {10.1145/1576702.1576731},
    location      = adr:seoul,
    keywords      = {multivariate, polynomial, factorization, algebraic number fields, algebraic function fields},
}

@inproceedings{Zhi2000factor,
    author        = {Lihong Zhi},
    title         = {{A}lgebraic {F}actorization and {GCD} {C}omputation},
    booktitle     = {Mathematics Mechanization and Applications},
    pages         = {325--342},
    year          = {2000},
    publisher     = pub:academic,
    address       = adr:new_york,
    url           = {http://www.mmrc.iss.ac.cn/~lzhi/Publications/mmfac.pdf},
    keywords      = {multivariate, polynomial, factorization},
}

@book{Gerhard2006modular,
    author        = {Juergen Gerhard},
    title         = {{M}odular {A}lgorithms in {S}ymbolic {S}ummation and {S}ymbolic {I}ntegration},
    year          = {2006},
    publisher     = pub:springer,
    address       = adr:heidelberg,
    isbn          = {3-540-24061-6},
    keywords      = {},
}

@article{Frink2001large,
    author        = {Alexander Frink and Christian Bauer and Richard Kreckel},
    title         = {{L}arge {S}cale {S}ymbolic {P}rogramming with {GiNaC}},
    journal       = {Advanced Computing and Analysis Techniques in Physics Research},
    volume        = {583},
    pages         = {185--189},
    year          = {2001},
    publisher     = {American Institute of Physics},
    doi           = {10.1063/1.1405299},
    keywords      = {},
}

@article{Brent1978fps,
    author        = {R. P. Brent and H. T. Kung},
    title         = {{F}ast {A}lgorithms for {M}anipulating {F}ormal {P}ower {S}eries},
    journal       = j:acm,
    volume        = {25},
    number        = {4},
    pages         = {581--595},
    year          = {1978},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0004-5411},
    doi           = {10.1145/322092.322099},
    keywords      = {},
}

@inproceedings{Encarnacion1994modular,
    author        = {Mark J. Encarnaci\'{o}n},
    title         = {{O}n a {M}odular {A}lgorithm for {C}omputing {GCDs} of {P}olynomials over {A}lgebraic {N}umber {F}ields},
    booktitle     = pro:issac:94,
    pages         = {58--65},
    year          = {1994},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-638-7},
    doi           = {10.1145/190347.190365},
    location      = adr:oxford,
    keywords      = {polynomial, GCD, modular, MODGCD, algebraic},
}

@article{Paule1995greatest,
    author        = {Peter Paule},
    title         = {{G}reatest {F}actorial {F}actorization and {S}ymbolic {S}ummation},
    journal       = j:symb_comp,
    volume        = {20},
    number        = {3},
    pages         = {235--268},
    year          = {1995},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1995.1049},
    keywords      = {},
}

@article{Fu2006automated,
    author        = {Hongguang Fu and Xiuqin Zhong and Zhenbing Zeng},
    title         = {{A}utomated and {R}eadable {S}implification of {T}rigonometric {E}xpressions},
    journal       = {Mathematical and Computer Modelling},
    volume        = {55},
    number        = {11-12},
    pages         = {1169-1177},
    year          = {2006},
    publisher     = pub:elsevier,
    address       = adr:oxford,
    issn          = {0895-7177},
    keywords      = {},
}

@book{Jeffrey2001advanced,
    author        = {Alan Jeffrey},
    title         = {{A}dvanced {E}ngineering {M}athematics},
    edition       = edt:first,
    year          = {2001},
    publisher     = pub:academic,
    address       = adr:new_york,
    isbn          = {978-0123825926},
    keywords      = {},
}

@inproceedings{Moses1971simplification,
    author        = {Joel Moses},
    title         = {{A}lgebraic {S}implification: {A} {G}uide for the {P}erplexed},
    booktitle     = pro:symsac:71,
    pages         = {282--304},
    year          = {1971},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800204.806298},
    location      = adr:los_angeles,
    keywords      = {},
}

@article{Wang1976teaching,
    author        = {Paul S. Wang},
    title         = {{I}mplications of {S}ymbolic {C}omputation for the {T}eaching of {M}athematics},
    journal       = j:sigsam_bulletin,
    volume        = {10},
    number        = {3},
    pages         = {15--18},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0163-5824},
    doi           = {10.1145/1088216.1088218},
    keywords      = {},
}

@incollection{Chyzak1998groebner,
    author        = {Fr\'{e}d\'{e}ric Chyzak},
    title         = {{G}r\"{o}bner {B}ases, {S}ymbolic {S}ummation and {S}ymbolic {I}ntegration},
    booktitle     = {Gr\"{o}bner Bases and Applications},
    editor        = {B. Buchberger and F. Winkler},
    volume        = {251},
    pages         = {32--60},
    year          = {1998},
    series        = {London Mathematical Society Lecture Notes Series},
    publisher     = pub:cambridge,
    note          = {Proceedings of the Conference 33 Years of Gröbner Bases},
    isbn          = {0-521-63298-6},
    keywords      = {},
}

@article{Fateman1972simplifying,
    author        = {Richard J. Fateman},
    title         = {{R}ationally {S}implifying {N}on--{R}ational {E}xpressions},
    journal       = j:sigsam_bulletin,
    volume        = {1},
    number        = {23},
    pages         = {8--9},
    year          = {1972},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0163-5824},
    doi           = {10.1145/1093522.1093523},
    keywords      = {},
}

@inproceedings{Carette2004understanding,
    author        = {Jacques Carette},
    title         = {{U}nderstanding {E}xpression {S}implification},
    booktitle     = pro:issac:04,
    pages         = {72--79},
    year          = {2004},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-827-X},
    doi           = {10.1145/1005285.1005298},
    location      = adr:santander,
    keywords      = {},
}

@book{Abramowitz1964handbook,
    author        = {Milton Abramowitz and Irene A. Stegun},
    title         = {{H}andbook of {M}athematical {F}unctions with {F}ormulas, {G}raphs, and {M}athematical {T}ables},
    year          = {1964},
    publisher     = pub:dover,
    address       = adr:new_york,
    edition       = {ninth printing},
    isbn          = {0-486-61272-4},
    url           = {http://www.math.ucla.edu/~cbm/aands/},
    keywords      = {},
}

@inproceedings{Davenport2003difficulties,
    author        = {James H. Davenport},
    title         = {{T}he {D}ifficulties of {D}efinite {I}ntegration},
    booktitle     = {Proceedings of 11th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning},
    year          = {2003},
    location      = adr:rome,
    url           = {http://www.calculemus.net/meetings/rome03/davenport.pdf},
    keywords      = {},
}

@article{Caviness1970canonical,
    author        = {B. F. Caviness},
    title         = {{O}n {C}anonical {F}orms and {S}implification},
    journal       = j:acm,
    volume        = {17},
    number        = {2},
    pages         = {385--396},
    year          = {1970},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0004-5411},
    doi           = {10.1145/321574.321591},
    keywords      = {},
}

@article{Arnon1984basic,
    author        = {Dennis S. Arnon and George E. Collins and Scott McCallum},
    title         = {{C}ylindrical {A}lgebraic {D}ecomposition {I}: {T}he {B}asic {A}lgorithm},
    journal       = {SIAM Journal of Computation},
    volume        = {13},
    number        = {4},
    pages         = {865--877},
    year          = {1984},
    publisher     = {Society for Industrial and Applied Mathematics},
    address       = adr:philadelphia,
    issn          = {0097-5397},
    doi           = {10.1137/0213054},
    keywords      = {},
}

@misc{Bronstein2005pmint,
    author        = {Manuel Bronstein},
    title         = {{P}oor {M}an's {I}ntegrator},
    url           = {http://www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/index.htm},
    keywords      = {},
}

@phdthesis{Gruntz1996limits,
    author        = {Dominik Gruntz},
    title         = {{O}n {C}omputing {L}imits in a {S}ymbolic {M}anipulation {S}ystem},
    year          = {1996},
    school        = {Swiss Federal Institute of Technology},
    address       = adr:zurich,
    keywords      = {},
}

@book{Petkovsek1997AeqB,
    author        = {Marko Petkov\v{s}ek and Herbert S. Wilf and Doron Zeilberger},
    title         = {{A \(=\) B}},
    pages         = {222+},
    year          = {1997},
    publisher     = pub:peters,
    address       = adr:wellesley,
    url           = {http://sites.math.rutgers.edu/~zeilberg/AeqB.pdf},
    keywords      = {},
}

@inproceedings{Mulholland2001trigonometric,
    author        = {Jamie Mulholland and Michael Monagan},
    title         = {{A}lgorithms for {T}rigonometric {P}olynomials},
    booktitle     = pro:issac:01,
    pages         = {245--252},
    year          = {2001},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-58113-417-7},
    doi           = {10.1145/384101.384135},
    location      = adr:london:CA,
    keywords      = {},
}

@article{Akritas2008improving,
    author        = {A. G. Akritas and A. Strzebo\'{n}ski and P. Vigklas},
    title         = {{I}mproving the {P}erformance of the {C}ontinued {F}ractions {M}ethod using new {B}ounds of {P}ositive {R}oots},
    journal       = {Nonlinear Analysis: Modelling and Control},
    volume        = {13},
    number        = {3},
    pages         = {265--279},
    year          = {2008},
    url           = {www.lana.lt/journal/30/Akritas.pdf},
    keywords      = {},
}

@article{Akritas2008study,
    author        = {A. G. Akritas and A. Strzebo\'{n}ski},
    title         = {{A} {C}omparative {S}tudy of {T}wo {R}eal {R}oot {I}solation {M}ethods},
    journal       = {Nonlinear Analysis: Modelling and Control},
    volume        = {10},
    number        = {4},
    pages         = {297--304},
    year          = {2005},
    url           = {www.lana.lt/journal/19/Akritas.pdf},
    keywords      = {},
}

@article{Rump1979root,
    author        = {Siegfried M. Rump},
    title         = {Polynomial Minimum Root Separation},
    journal       = j:math_comp,
    volume        = {33},
    number        = {145},
    pages         = {327--336},
    year          = {1979},
    publisher     = pub:ams,
    address       = adr:boston,
    keywords      = {},
}

@inproceedings{Sagraloff2009certified,
    author        = {Michael Sagraloff and Michael Kerber and Michael Hemmer},
    title         = {Certified Complex Root Isolation via Adaptive Root Separation Bounds},
    booktitle     = {ASCM '09: Proceedings of the 9th Asian Symposium on Computer Mathematics},
    year          = {2009},
    url           = {http://www.mpi-inf.mpg.de/~msagralo/AdaptiveRootBound.pdf},
    keywords      = {},
}

@inproceedings{Zippel1976expansions,
    author        = {Richard E. Zippel},
    title         = {{U}nivariate {P}ower {S}eries {E}xpansions in {A}lgebraic {M}anipulation},
    booktitle     = pro:symsac:76,
    pages         = {198--208},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800205.806335},
    location      = adr:yorktown,
    keywords      = {},
}

@inproceedings{Yun1976squarefree,
    author        = {David Y. Y. Yun},
    title         = {{O}n {S}quare--{F}ree {D}ecomposition {A}lgorithms},
    booktitle     = pro:symsac:76,
    pages         = {26--35},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800205.806320},
    location      = adr:yorktown,
    keywords      = {},
}

@inproceedings{Wang1981partial,
    author        = {Paul S. Wang},
    title         = {{A} p--adic {A}lgorithm for {U}nivariate {P}artial {F}ractions},
    booktitle     = pro:symsac:81,
    pages         = {212--217},
    year          = {1981},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-047-8},
    doi           = {10.1145/800206.806398},
    location      = adr:snowbird,
    keywords      = {},
}


@article{Wang1975integers,
    author        = {Paul S. Wang and Linda Preiss Rothschild},
    title         = {{F}actoring {M}ultivariate {P}olynomials over the {I}ntegers},
    journal       = j:math_comp,
    volume        = {29},
    number        = {131},
    pages         = {935--950},
    year          = {1975},
    publisher     = pub:ams,
    address       = adr:boston,
    keywords      = {},
}

@article{Wang1978improved,
    author        = {Paul S. Wang},
    title         = {{A}n {I}mproved {M}ultivariate {P}olynomial {F}actoring {A}lgorithm},
    journal       = j:math_comp,
    volume        = {32},
    number        = {144},
    pages         = {1215--1231},
    year          = {1978},
    publisher     = pub:ams,
    address       = adr:boston,
    keywords      = {multivariate, polynomial, factorization},
}

@article{Wang1976algebraic,
    author        = {Paul S. Wang},
    title         = {{F}actoring {M}ultivariate {P}olynomials over {A}lgebraic {N}umber {F}ields},
    journal       = j:math_comp,
    volume        = {30},
    number        = {134},
    pages         = {324--336},
    year          = {1976},
    publisher     = pub:ams,
    address       = adr:boston,
    keywords      = {multivariate, polynomial, factorization, algebraic number fields},
}

@inproceedings{Shamir1993hard,
    author        = {Adi Shamir},
    title         = {{O}n the {G}eneration of {M}ultivariate {P}olynomials which are {H}ard to {F}actor},
    booktitle     = pro:stoc:93,
    pages         = {796--804},
    year          = {1993},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-591-7},
    doi           = {10.1145/167088.167291},
    location      = adr:san_diego,
    keywords      = {},
}

@article{Jeffrey1997rectifying,
    author        = {David J. Jeffrey},
    title         = {{R}ectifying {T}ransformations for the {I}ntegration of {R}ational {T}rigonometric {F}unctions},
    journal       = j:symb_comp,
    volume        = {24},
    number        = {5},
    pages         = {563--573},
    year          = {1997},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1997.0152},
    keywords      = {},
}

@inproceedings{Moses1973ezgcd,
    author        = {Joel Moses and David Y. Y. Yun},
    title         = {{T}he {EZ--GCD} {A}lgorithm},
    booktitle     = {ACM '73: Proceedings of the ACM annual conference},
    pages         = {159--166},
    year          = {1973},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800192.805698},
    location      = adr:atlanta,
    keywords      = {multivariate, polynomial, GCD, EZGCD},
}

@article{Jeffrey1994spurious,
    author        = {David J. Jeffrey and A. D. Rich},
    title         = {{T}he {E}valuation of {T}rigonometric {I}ntegrals {A}voiding {S}purious {D}iscontinuities},
    journal       = j:acm_tran_math_soft,
    volume        = {20},
    number        = {1},
    pages         = {124--135},
    year          = {1994},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0098-3500},
    doi           = {10.1145/174603.174409},
    keywords      = {},
}


@book{Cormen2001algorithms,
    author        = {Thomas T. Cormen and Charles E. Leiserson and Ronald L. Rivest},
    title         = {{I}ntroduction to {A}lgorithms},
    edition       = edt:second,
    year          = {2001},
    publisher     = pub:mit,
    address       = adr:cambridge,
    isbn          = {0-262-03141-8},
    keywords      = {},
}

@book{Cohen1996course,
    author        = {Henri Cohen},
    title         = {{A} {C}ourse in {C}omputational {A}lgebraic {N}umber {T}heory},
    edition       = edt:third,
    pages         = {550+},
    year          = {1996},
    publisher     = pub:springer,
    address       = adr:new_york,
    series        = {Graduate Texts in Mathematics},
    volume        = {138},
    isbn          = {3-540-55640-0},
    keywords      = {},
}

@inproceedings{Encarnacion1997norms,
    author        = {Mark J. Encarnaci\'{o}n},
    title         = {{F}actoring {P}olynomials over {A}lgebraic {N}umber {F}ields via {N}orms},
    booktitle     = pro:issac:97,
    pages         = {265--270},
    year          = {1997},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-875-4},
    doi           = {10.1145/258726.258802},
    location      = adr:kihei,
    keywords      = {},
}

@book{Hopcroft2001automata,
    author        = {John E. Hopcroft and Rajeev Motwani and Jeffrey D. Ullman},
    title         = {{I}ntroduction to {A}utomata {T}heory, {L}anguages, and {C}omputation},
    edition       = edt:third,
    year          = {2001},
    publisher     = pub:addison,
    address       = adr:boston,
    isbn          = {0-201-44124-1},
    keywords      = {automata, languages},
}

@phdthesis{Fateman1972essays,
    author        = {R. J. Fateman},
    title         = {{E}ssays in {A}lgebraic {S}implification},
    year          = {1972},
    school        = {Massachusetts Institute of Technology},
    address       = adr:cambridge,
    keywords      = {simplification, rewriting},
}

@inproceedings{Geddes1989risch,
    author        = {K. O. Geddes and L. Y. Stefanus},
    title         = {{O}n the {R}isch--{N}orman {I}ntegration {M}ethod and its {I}mplementation in {MAPLE}},
    booktitle     = pro:issac:89,
    pages         = {212--217},
    year          = {1989},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-325-6},
    doi           = {10.1145/74540.74567},
    location      = adr:portland,
    keywords      = {heuristic, risch, algorithm, maple},
}

@inproceedings{Adamchik1990hyper,
    author        = {V. S. Adamchik and O. I. Marichev},
    title         = {{T}he {A}lgorithm for {C}alculating {I}ntegrals of {H}ypergeometric {T}ype {F}unctions and its {R}ealization in {REDUCE} {S}ystem},
    booktitle     = pro:issac:90,
    pages         = {212--224},
    year          = {1990},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-201-54892-5},
    doi           = {10.1145/96877.96930},
    location      = adr:tokyo,
    keywords      = {symbolic, integration, hypergeometric},
}

@article{Brent1975series,
    author        = {R. P. Brent and H. T. Kung},
    title         = {{\(O((n \cdot \log n)^{3/2})\)} {A}lgorithms for {C}omposition and {R}eversion of {P}ower {S}eries},
    journal       = {Analytic Computational Complexity},
    pages         = {217--225},
    year          = {1975},
    publisher     = pub:academic,
    address       = adr:new_york,
    keywords      = {power series, composition, algorithm},
}

@article{Karr1981summation,
    author        = {Michael Karr},
    title         = {{S}ummation in {F}inite {T}erms},
    journal       = j:acm,
    volume        = {28},
    number        = {2},
    pages         = {305--350},
    year          = {1981},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0004-5411},
    doi           = {10.1145/322248.322255},
    keywords      = {symbolic, summation, algorithm},
}

@article{Weinberger1976factor,
    author        = {P. J. Weinberger and Linda Preiss Rothschild},
    title         = {{F}actoring {P}olynomials {O}ver {A}lgebraic {N}umber {F}ields},
    journal       = j:acm_tran_math_soft,
    volume        = {2},
    number        = {4},
    pages         = {335--350},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0098-3500},
    doi           = {10.1145/355705.355709},
    keywords      = {polynomial, factorization, algebraic number fields},
}

@inproceedings{Karr1985canonical,
    author        = {Michael Karr},
    title         = {{C}anonical {F}orm for {R}ational {E}xponential {E}xpressions},
    booktitle     = {EUROCAL '85: Research Contributions from the European Conference on Computer Algebra-Volume 2},
    pages         = {585--594},
    year          = {1985},
    publisher     = pub:springer,
    address       = adr:london,
    isbn          = {3-540-15984-3},
    keywords      = {canonical forms, simplification},
}

@inproceedings{Horowitz1971modular,
    author        = {E. Horowitz},
    title         = {{M}odular {A}rithmetic and {F}inite {F}ield {T}heory: {A} {T}utorial},
    booktitle     = pro:symsac:71,
    pages         = {188--194},
    year          = {1971},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800204.806287},
    location      = adr:los_angeles,
    keywords      = {tutorial, modular, finite fields},
}

@article{Brown1971subres,
    author        = {W. S. Brown and J. F. Traub},
    title         = {{O}n {E}uclid's {A}lgorithm and the {T}heory of {S}ubresultants},
    journal       = j:acm,
    volume        = {18},
    number        = {4},
    pages         = {505--514},
    year          = {1971},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0004-5411},
    doi           = {10.1145/321662.321665},
    keywords      = {subresultants, algorithm},
}

@inproceedings{Brown1971gcd,
    author        = {W. S. Brown},
    title         = {{O}n {E}uclid's {A}lgorithm and the {C}omputation of {P}olynomial {G}reatest {C}ommon {D}ivisors},
    booktitle     = pro:symsac:71,
    pages         = {195--211},
    year          = {1971},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800204.806288},
    location      = adr:los_angeles,
    keywords      = {polynomial, GCD, dense, modular, MODGCD},
}

@inproceedings{Davenport1981factor,
    author        = {James H. Davenport and Barry M. Trager},
    title         = {{F}actorization over {F}initely {G}enerated {F}ields},
    booktitle     = pro:symsac:81,
    pages         = {200--205},
    year          = {1981},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-047-8},
    doi           = {10.1145/800206.806396},
    location      = adr:snowbird,
    keywords      = {factorization, number fields},
}

@inproceedings{Czapor1991heuristic,
    author        = {S. R. Czapor},
    title         = {{A} {H}euristic {S}election {S}trategy for {L}exicographic {G}r\"{o}ner {B}ases?},
    booktitle     = pro:issac:91,
    pages         = {39--48},
    year          = {1991},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-437-6},
    doi           = {10.1145/120694.120700},
    location      = adr:bonn,
    keywords      = {selection strategy, groebner bases},
}

@article{Almqvist1990under,
    author        = {G. Almqvist and D. Zeilberger},
    title         = {{T}he {M}ethod of {D}ifferentiating {U}nder the {I}ntegral {S}ign},
    journal       = j:symb_comp,
    volume        = {10},
    pages         = {571--591},
    year          = {1990},
    publisher     = pub:academic,
    address       = adr:new_york,
    keywords      = {symbolic, differentiation, integration},
}

@incollection{Cherry1984special,
    author        = {G. W. Cherry and B. F. Caviness},
    title         = {{I}ntegration in {F}inite {T}erms with {S}pecial {F}unctions: {A} {P}rogress {R}eport},
    booktitle     = {Lecture Notes in Computer Science},
    volume        = {174},
    pages         = {351--358},
    year          = {1984},
    publisher     = pub:springer,
    address       = adr:heidelberg,
    issn          = {0302-9743},
    isbn          = {978-3-540-13350-6},
    doi           = {10.1007/BFb0032823},
    keywords      = {symbolic, integration, special functions},
}

@book{Li1993kolmogorov,
    author        = {Ming Li and Paul Vit\'{a}nyi},
    title         = {{A}n {I}ntroduction to {K}olmogorov {C}omplexity and its {A}pplications},
    year          = {1993},
    publisher     = pub:springer,
    address       = adr:new_york,
    isbn          = {0-387-94053-7},
    keywords      = {kolmogorov, complexity, introduction},
}

@incollection{Gianni1985groebner,
    author        = {Patrizia Gianni and Barry Trager},
    title         = {{GCD's} and {F}actoring {M}ultivariate {P}olynomials using {G}r\"{o}bner {B}ases},
    booktitle     = {Lecture Notes in Computer Science},
    volume        = {204},
    pages         = {409--410},
    year          = {1985},
    publisher     = pub:springer,
    address       = adr:heidelberg,
    issn          = {0302-9743},
    isbn          = {978-3-540-15984-1},
    doi           = {10.1007/3-540-15984-3},
    keywords      = {polynomial, GCD, factorization, groebner bases},
}

@inproceedings{Knowles1986liouvillian,
    author        = {Paul. H. Knowles},
    title         = {{I}ntegration of {L}iouvillian {F}unctions with {S}pecial {F}unctions},
    booktitle     = pro:symsac:86,
    pages         = {179--184},
    year          = {1986},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-199-7},
    doi           = {10.1145/32439.32475},
    location      = adr:waterloo,
    keywords      = {symbolic, integration, liouvillian},
}

@article{Knowles1993transcendental,
    author        = {Paul H. Knowles},
    title         = {{I}ntegration of a {C}lass of {T}ranscendental {L}iouvillian {F}unctions with {E}rror--{F}unctions},
    journal       = j:symb_comp,
    volume        = {16},
    number        = {3},
    year          = {1993},
    pages         = {227--241},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1993.1042},
    keywords      = {symbolic, integration, transcendental},
}

@proceedings{Lakshman1996issac,
    editor        = {Y. N. Lakshman},
    note          = {chairman: Erwin Engeler and Bob F. Caviness},
    title         = pro:issac:96,
    year          = {1996},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {0-89791-796-0},
    location      = adr:zurich,
    keywords      = {issac, proceedings},
}

@book{Adams1994intro,
    author        = {William Wells Adams and Philippe Loustaunau},
    title         = {{A}n {I}ntroduction to {G}r\"{o}bner {B}ases},
    pages         = {289+},
    month         = {July},
    year          = {1994},
    publisher     = pub:ams,
    address       = adr:boston,
    isbn          = {0-821-83804-0},
    keywords      = {groebner bases, introduction},
}

@manual{Tantau2008tikz,
    author        = {Till Tantau},
    title         = {{T}he {TikZ} and {PGF} {P}ackages},
    edition       = {2.0.0},
    month         = {February},
    year          = {2008},
    url           = {http://www.ctan.org/tex-archive/graphics/pgf/base/doc/generic/pgf/pgfmanual.pdf},
    keywords      = {tikz, pgf, manual},
}

@misc{Stegers2006f5,
    author        = {Till Stegers},
    title         = {{F}aug\`{e}re's {F5} {A}lgorithm {R}evisited},
    howpublished  = {Cryptology ePrint Archive, Report 2006/404},
    year          = {2006},
    note          = {http://eprint.iacr.org/},
    keywords      = {groebner bases, F5, algorithm},
}

@book{Wolfram2003book,
    author        = {Stephen Wolfram},
    title         = {{T}he {M}athematica {B}ook},
    edition       = edt:fifth,
    pages         = {1488+},
    year          = {2003},
    publisher     = pub:wolfram:media,
    address       = adr:champaign,
    isbn          = {1-579-55022-3},
    keywords      = {mathematica, manual},
}

@manual{Souza2004book,
    author        = {Paulo Ney de Souza and Richard J. Fateman and Joel Moses and Cliff Yap},
    title         = {{T}he {M}axima {B}ook},
    month         = {September},
    year          = {2004},
    url           = {http://maxima.sourceforge.net/docs/maximabook/maximabook-19-Sept-2004.pdf},
    keywords      = {maxima, manual},
}

@book{Cox2015ideals,
    author        = {David Cox and John Little and Donald O'Shea},
    title         = {{I}deals, {V}arieties and {A}lgorithms},
    edition       = edt:fourth,
    pages         = {650+},
    year          = {2015},
    series        = {Undergraduate Texts in Mathematics},
    publisher     = pub:springer,
    address       = adr:new_york,
    isbn          = {978-3-319-16720-6},
    keywords      = {ideals, varieties, groebner bases},
}

@techreport{Jirstrand1995cylindrical,
    author        = {Mats Jirstrand},
    title         = {{C}ylindrical {A}lgebraic {D}ecomposition --- {A}n {I}ntroduction},
    institution   = {Link\"{o}ping University},
    address       = {Link\"{o}ping, Sweden},
    month         = {October},
    year          = {1995},
    keywords      = {cylindrical algebraic decompostion},
}

@book{MacLane1972categories,
    author        = {Saunders Mac Lane},
    title         = {{C}ategories for the {W}orking {M}athematician},
    edition       = edt:first,
    pages         = {132+},
    year          = {1972},
    series        = {Graduate Texts in Mathematics},
    publisher     = pub:springer,
    address       = adr:new_york,
    isbn          = {0-387-98403-8},
    keywords      = {},
}

@inproceedings{deKleine2005nonmonic,
    author        = {Jennifer de Kleine and Michael Monagan and Allan Wittkopf},
    title         = {{A}lgorithms for the {N}on--{M}onic {C}ase of the {S}parse {M}odular {GCD} {A}lgorithm},
    booktitle     = pro:issac:05,
    pages         = {124--131},
    year          = {2005},
    publisher     = pub:acm,
    address       = adr:new_york,
    isbn          = {1-59593-095-7},
    doi           = {10.1145/1073884.1073903},
    location      = {Beijing, China},
    keywords      = {},
}

@article{Kozen1989decomposition,
    author        = {Dexter Kozen and Susan Landau},
    title         = {{P}olynomial {D}ecomposition {A}lgorithms},
    journal       = j:symb_comp,
    volume        = {7},
    number        = {5},
    pages         = {445--456},
    year          = {1989},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1016/S0747-7171(89)80027-6},
    keywords      = {},
}

@inproceedings{Rump1976sign,
    author        = {Siegfried Rump},
    title         = {{O}n the {S}ign of a {R}eal {A}lgebraic {N}umber},
    booktitle     = pro:symsac:76,
    pages         = {238--241},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/800205.806341},
    location      = adr:yorktown,
    keywords      = {},
}

@article{Strzebonski1997computing,
    author        = {Adam Wojciech Strzebo\'{n}ski},
    title         = {{C}omputing in the {F}ield of {C}omplex {A}lgebraic {N}umbers},
    journal       = j:symb_comp,
    volume        = {24},
    number        = {6},
    pages         = {647--656},
    year          = {1997},
    publisher     = pub:academic,
    address       = adr:duluth,
    issn          = {0747-7171},
    doi           = {10.1006/jsco.1997.0158},
    keywords      = {},
}

@article{Barnett2002sciences,
    author        = {Michael P. Barnett},
    title         = {{C}omputer algebra in life sciences},
    journal       = j:sigsam_bulletin,
    volume        = {36},
    number        = {4},
    year          = {2002},
    publisher     = pub:acm,
    address       = adr:new_york,
    keywords      = {computer algebra, applications, science},
}

@inproceedings{Yun1976padic,
    author        = {David Y. Y. Yun},
    title         = {{A}lgebraic {A}gorithms using p--adic {C}onstructions},
    booktitle     = pro:symsac:76,
    pages         = {},
    year          = {1976},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {},
    location      = adr:yorktown,
    keywords      = {modular, p-adic, zassenhaus construction, gcd, factoring},
}

@article{Zippel1996zero,
    author        = {Richard Zippel},
    title         = {{Z}ero testing of algebraic functions},
    journal       = j:info_proc_letters,
    volume        = {61},
    number        = {},
    pages         = {63-67},
    year          = {1996},
    publisher     = pub:elsevier,
    address       = adr:oxford,
    keywords      = {algebraic functions, zero equivalence, polynomials},
}

@misc{Buchberger2007talk,
    author        = {Bruno Buchberger},
    title         = {{I}ntroduction to {G}r\"{o}bner {B}ases},
    year          = {2007},
    publisher     = {Emerging Topics in Cryptographic Design and Cryptanalysis},
    address       = {Samos, Greece},
    keywords      = {groebner bases, introduction, talk, applications, history},
}

@misc{Watt2006symbolic,
    author        = {Stephen M. Watt},
    title         = {{M}aking {C}omputer {A}lgebra {M}ore {S}ymbolic},
    year          = {2006},
}

@book{Sturmfels2008invariant,
    author        = {Bernd Sturmfels},
    title         = {{A}lgorithms in {I}nvariant {T}heory},
    series        = {Texts and Monographs in Symbolic Computation},
    year          = {2008},
    isbn          = {978-3-211-77416-8},
    publisher     = pub:springer,
    address       = adr:wien,
}

@book{Kubale2004color,
    editor        = {Marek Kubale},
    title         = {{G}raph {C}olorings},
    series        = {Contemporary Mathematics},
    pages         = {208+},
    year          = {2004},
    isbn          = {978-0821834589},
    publisher     = pub:ams,
}

@inproceedings{Traverso1991integer,
    author        = {Carlo Traverson and Pasqualina Conti},
    title         = {{B}uchberger {A}lgorithm and {I}nteger {P}rogramming},
    booktitle     = {AAECC--9: Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes},
    year          = {1991},
    pages         = {130--139},
    isbn          = {3-540-54522-0},
    publisher     = pub:springer,
    address       = adr:london,
}

@article{Abramson2009history,
    author        = {Michael P. Abramson},
    title         = {{H}istorical background to {G}r\"{o}bner's paper},
    journal       = j:sigsam_bulletin,
    volume        = {43},
    number        = {1/2},
    year          = {2009},
    pages         = {22--23},
    issn          = {0163-5824},
    publisher     = pub:acm,
    address       = adr:new_york,
    doi           = {10.1145/1610296.1610301},
}

@phdthesis{Buchberger1965thesis,
    author        = {Bruno Buchberger},
    title         = {{E}in {A}lgorithmus zum {A}uffinden der {B}asis {E}lemente des {R}estklassenrings nach einem nulldimensionalen {P}olynomideal},
    year          = {1965},
    school        = {University of Innsbruck},
    address       = adr:innsbruck,
    keywords      = {groebner bases, thesis},
}

@article{Abramson2006translation,
    author        = {Michael P. Abramson},
    title         = {{B}runo {B}uchberger's {PhD} thesis 1965: {A}n {A}lgorithm for {F}inding the {B}asis {E}lements of the {R}esidue {C}lass {R}ing of a {Z}ero--{D}imensional {P}olynomial {I}deal},
    journal       = j:symb_comp,
    volume        = {41},
    number        = {3--4},
    year          = {2006},
    pages         = {475--511},
    publisher     = pub:academic,
    address       = adr:new_york,
    issn          = {0747-7171},
    doi           = {10.1016/j.jsc.2005.09.007},
    keywords      = {translation, Buchberger, thesis, groebner, bases},
}

@article{Winkler1990geometry,
    author        = {Franz Winkler},
    title         = {{G}r\"{o}bner {B}ases in {G}eometry {T}heorem {P}roving and {S}implest {D}egeneracy {C}onditions},
    journal       = j:pannonica,
    volume        = {1},
    number        = {1},
    year          = {1990},
    pages         = {15--32},
    keywords      = {groebner bases, geometry, theorem, proving},
}

@book{Buchberger1998applications,
    editor        = {Bruno Buchberger, Franz Winkler},
    title         = {{G}r\"{o}bner {B}ases and {A}pplications},
    publisher     = pub:cambridge,
    pages         = {564+},
    year          = {1998},
    isbn          = {978-0521632980},
}

@book{Sturmfels1996lectures,
    author        = {Bernd Sturmfels},
    title         = {{G}\"{o}rbner {B}ases and {C}onvex {P}olytopes},
    series        = {University Lecture Series},
    year          = {1996},
    publisher     = pub:ams,
}

@book{Grabmeier2003algebra,
    editor        = {Johannes Grabmeier and Erich Kaltofen and Volker Weispfenning},
    title         = {{C}omputer {A}lgebra {H}andbook},
    year          = {2003},
    publisher     = pub:springer,
    address       = adr:new_york,
    isbn          = {3-540-65466-6},
}

@book{Graham1994concrete,
    author        = {Ronald L. Graham and Donald E. Knuth and Oren Patashnik},
    title         = {{C}oncrete {M}athematics: {A} {F}oundation for {C}omputer {S}cience},
    edition       = edt:second,
    pages         = {672+},
    year          = {1994},
    publisher     = pub:addison,
    isbn          = {978-0201558029},
}

@inproceedings{Decker1999parallel,
    author        = {Thomas Decker and Werner Krandick},
    title         = {{P}arallel {R}eal {R}oot {I}solation {U}sing the {D}escartes {M}ethod},
    booktitle     = {HiPC '99: Proceedings of the 6th International Conference on High Performance Computing},
    pages         = {261--268},
    year          = {1999},
    isbn          = {3-540-66907-8},
    publisher     = pub:springer,
    address       = adr:london,
}

@inproceedings{Decker2001isoefficiency,
    author        = {Thomas Decker and Werner Krandick},
    title         = {{O}n the {I}soefficiency of the {P}arallel {D}escartes {M}ethod},
    editor        = {G\"{o}tz Alefeld and Jiri Rohn and Siegfried M. Rump and Tetsuro Yamamoto},
    booktitle     = {Symbolic Algebraic Methods and Verification Methods},
    pages         = {55--67},
    year          = {2001},
    publisher     = pub:springer,
    address       = adr:london,
}

@book{Hamming1987numerical,
    author        = {Richard Hamming},
    title         = {{N}umerical {M}ethods for {S}cientists and {E}ngineers},
    edition       = edt:second,
    year          = {1987},
    publisher     = pub:dover,
}

@manual{Poll1999types,
    author        = {E. Poll and S. Thompson},
    title         = {{T}he {T}ype {S}ystem of {A}ldor},
    year          = {1999},
    publisher     = {University of Kent at Canterbury},
    address       = adr:kent,
}

@manual{Rossum2009python,
    author        = {Guido van Rossum},
    title         = {{P}ython a {D}ynamic {O}bject--oriented {P}rogramming {L}anguage},
    year          = {1991--2009},
    url           = {http://www.python.org},
}

@manual{Stein2009sage,
    author        = {William Stein},
    title         = {SAGE Mathematics Software (Version 3.2)},
    year          = {2007--2009},
    publisher     = {The SAGE Group},
    url           = {http://www.sagemath.org},
}

@misc{Dijkstra1982zero,
    author        = {Edsgar Dijkstra},
    title         = {\url{http://userweb.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html}},
    year          = {1982},
}

@misc{SymPyGSoC2010,
    author        = {SymPyGSoC2010},
    title         = {\url{http://wiki.sympy.org/wiki/GSoC2010Ideas}},
}

@misc{PlanetMathSymmetric,
    author        = {PlanetMathSymmetric},
    title         = {\url{http://planetmath.org/encyclopedia/ReductionAlgorithmForSymmetricPolynomials.html}},
}

@misc{MaximaGroebner,
    author        = {MaximaGroebner},
    title         = {\url{http://maxima.sourceforge.net/docs/manual/en/maxima_54.html}},
}

@misc{MathematicaGroebner,
    author        = {MathematicaGroebner},
    title         = {\url{http://reference.wolfram.com/mathematica/tutorial/ComplexPolynomialSystems.html}},
}

@misc{MathematicaInternal,
    author        = {MathematicaInternal},
    title         = {\url{http://reference.wolfram.com/mathematica/note/SomeNotesOnInternalImplementation.html}},
}

@misc{PythonModules,
    author        = {PythonModules},
    title         = {\url{http://docs.python.org/tutorial/modules.html}},
}

@misc{PythonIssue1771,
    author        = {PythonModules},
    title         = {\url{http://bugs.python.org/issue1771}},
}

@misc{UnladenSwallow,
    author        = {UnladenSwallow},
    title         = {\url{http://code.google.com/p/unladen-swallow}},
}

@misc{PyPy,
    author        = {PyPy},
    title         = {\url{http://codespeak.net/pypy}},
}

@misc{KNS2009,
    author        = {Mateusz Paprocki},
    title         = {{SymPy} --- {A} {S}ystem {F}or {E}ploring {S}ymbolic {M}athematics},
    howpublished  = {KNS~'09: Annual Scientific Conference for Students},
    month         = {May},
    year          = {2009},
    location      = adr:wroclaw,
    url           = {http://sympy.googlecode.com/svn/materials/presentations/kns2009.pdf},
    keywords      = {sympy, slides},
}

@misc{EuroSciPy2009,
    author        = {Mateusz Paprocki},
    title         = {{SymPy} --- a library for doing symbolic mathematics in pure {P}ython},
    howpublished  = {EuroScipy~'09: 2nd European Conference for Scientists using Python},
    month         = {July},
    year          = {2009},
    location      = adr:leipzig,
    url           = {http://sympy.googlecode.com/svn/materials/presentations/euroscipy2009.pdf},
    keywords      = {sympy, slides},
}

@misc{Py4Science2010,
    author        = {Mateusz Paprocki},
    title         = {{S}ymbolic {M}anipulation in {P}ure {P}ython. {I}s it {F}easible?},
    howpublished  = {Py4Science~'10: Python for Science Group Meeting},
    month         = {May},
    year          = {2010},
    location      = adr:berkeley,
    url           = {http://sympy.googlecode.com/svn/materials/presentations/py4science2010.pdf},
    keywords      = {sympy, polynomials, slides},
}

@misc{EuroSciPy2010,
    author        = {Mateusz Paprocki},
    title         = {{C}omputing with {P}olynomials in {SymPy}},
    howpublished  = {EuroScipy~'10: 3nd European Conference for Scientists using Python},
    month         = {July},
    year          = {2010},
    location      = adr:paris,
    url           = {http://www.euroscipy.org/talk/1984},
    keywords      = {sympy, polynomials, slides},
}

@misc{Haigh2005interview,
    author        = {T. Haigh},
    title         = {{G}aston {G}onnet {O}ral history interview},
    howpublished  = {Society for Industrial and Applied Mathematics},
    month         = {March},
    year          = {2005},
    location      = adr:zurich,
}

@article{Nakos1997fractionfree,
    author        = {George C. Nakos and Peter R. Turner and Robert M. Williams},
    title         = {{F}raction--{F}ree {A}lgorithms for {L}inear and {P}olynomial {E}quations},
    journal       = j:sigsam_bulletin,
    volume        = {31},
    number        = {3},
    pages         = {11--19},
    year          = {1997},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {0163-5824},
    doi           = {10.1145/271130.271133},
}

@article{Stoutemyer2008partial,
    author        = {David R. Stoutemyer},
    title         = {{M}ultivariate {P}artial {F}raction {E}xpansion},
    journal       = j:acm_comm_comp_algebra,
    volume        = {42},
    number        = {4},
    pages         = {206--210},
    year          = {2008},
    publisher     = pub:acm,
    address       = adr:new_york,
    issn          = {1932-2240},
    doi           = {10.1145/1504341.1504346},
}

@misc{MathWorld-Cyclotomic-Poly,
    title         = {Cyclotomic Polynomial},
    howpublished  = {\url{https://mathworld.wolfram.com/CyclotomicPolynomial.html}},
}

@book{NivenZuckerman,
    author        = {I. Niven and H. S. Zuckerman},
    title         = {An Introduction to the Theory of Numbers},
    year          = {1991},
    publisher     = pub:wiley,
}

@book{BeckerWeispfenning93,
    author        = {Thomas Becker and Volker Weispfenning},
    title         = {Gr\"obner Bases: A Computational Approach to Commutative Algebra},
    series        = {Graduate Texts in Mathematics},
    volume        = {141},
    year          = {1993},
    note          = {In Cooperation with Heinz Kredel},
    address       = adr:new_york,
    publisher     = pub:springer,
    pages         = {xxii+574},
    isbn          = {0-387-97971-9},
}

@book{Koepf98,
    title         = {Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities},
    author        = {W. Koepf},
    publisher     = {Braunschweig},
    year          = {1998},
}

@book{Bose03,
    author        = {N.K. Bose, B. Buchberger and J.P. Guiver},
    title         = {Multidimensional Systems Theory and Applications},
    year          = {2003},
    edition       = edt:second,
    publisher     = {Springer},
}

@techreport{Bostan02,
    author        = {A. Bostan, P. Flajolet, B. Salvy and E. Schost},
    title         = {Fast Computation with Two Algebraic Numbers},
    number        = {4579},
    institution   = {Institut National de Recherche en Informatique et en Automatique},
    year          = {2002},
    keywords      = {},
}

@book{Luke1969,
    author        = {Yudell L. Luke},
    title         = {The Special Functions and Their Approximations},
    volume        = {1},
    publisher     = pub:academic,
    address       = adr:new_york,
    year          = {1969},
}

@inproceedings{Roach1996,
    author        = {Roach, Kelly},
    title         = {Hypergeometric Function Representations},
    booktitle     = {Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation},
    series        = {ISSAC '96},
    year          = {1996},
    isbn          = {0-89791-796-0},
    location      = adr:zurich,
    pages         = {301--308},
    numpages      = {8},
    url           = {https://dl.acm.org/citation.cfm?doid=236869.237088},
    doi           = {10.1145/236869.237088},
    acmid         = {237088},
    publisher     = pub:acm,
    address       = adr:new_york,
}

@inproceedings{Roach1997,
    author        = {Roach, Kelly},
    title         = {Meijer G Function Representations},
    booktitle     = {Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation},
    series        = {ISSAC '97},
    year          = {1997},
    isbn          = {0-89791-875-4},
    location      = adr:kihei,
    pages         = {205--211},
    numpages      = {7},
    url           = {https://dl.acm.org/citation.cfm?doid=258726.258784},
    doi           = {10.1145/258726.258784},
    acmid         = {258784},
    publisher     = pub:acm,
    address       = adr:new_york,
}

@book{Prudnikov1990,
    author        = {A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev},
    year          = {1990},
    series        = {Integrals and Series},
    title         = {More Special Functions},
    volume        = {3},
    publisher     = {Gordon and Breach},
}

@article{Collins1967subr,
    author        = {Collins, George E.},
    title         = {Subresultants and Reduced Polynomial Remainder Sequences},
    journal       = j:acm,
    issue_date    = {Jan. 1967},
    volume        = {14},
    number        = {1},
    month         = jan,
    year          = {1967},
    issn          = {0004-5411},
    pages         = {128--142},
    numpages      = {15},
    url           = {https://dl.acm.org/citation.cfm?doid=321371.321381},
    doi           = {10.1145/321371.321381},
    acmid         = {321381},
    publisher     = pub:acm,
    address       = adr:new_york,
}

@article{Alkiviadis2005comp,
    author        = {Strzebonski, Adam and Akritas, Alkiviadis},
    year          = {2005},
    month         = {01},
    pages         = {297-304},
    title         = {A Comparative Study of Two Real Root Isolation Methods},
    volume        = {10},
    journal       = {Nonlinear Analysis: Modelling and Control}
}

@article{Alkiviadis2008cf,
    author        = {Akritas, Alkiviadis and Strzebonski, Adam and Vigklas, Panagiotis},
    year          = {2008},
    month         = {08},
    pages         = {},
    title         = {Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots},
    volume        = {3},
    journal       = {Nonlinear Analysis. Modelling and Control}
}

@article{Alkiviadis2009bounds,
    author        = {Akritas, Alkiviadis},
    year          = {2009},
    month         = {01},
    pages         = {523-537},
    title         = {Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials},
    volume        = {15},
    journal       = {J. UCS}
}

@inproceedings{Man1994disp,
    author        = {Man, Yiu-Kwong and Wright, Francis J.},
    title         = {Fast Polynomial Dispersion Computation and Its Application to Indefinite Summation},
    booktitle     = {Proceedings of the International Symposium on Symbolic and Algebraic Computation},
    series        = {ISSAC '94},
    year          = {1994},
    isbn          = {0-89791-638-7},
    location      = adr:oxford,
    pages         = {175--180},
    numpages      = {6},
    url           = {https://dl.acm.org/citation.cfm?doid=190347.190413},
    doi           = {10.1145/190347.190413},
    acmid         = {190413},
    publisher     = pub:acm,
    address       = adr:new_york,
}

@article{Man1993indefsum,
    author        = {Man, Yiu-Kwong},
    title         = {On Computing Closed Forms for Indefinite Summations},
    journal       = j:symb_comp,
    issue_date    = {Oct. 1993},
    volume        = {16},
    number        = {4},
    month         = oct,
    year          = {1993},
    issn          = {0747-7171},
    pages         = {355--376},
    numpages      = {22},
    url           = {https://www.sciencedirect.com/science/article/pii/S0747717183710539},
    doi           = {10.1006/jsco.1993.1053},
    acmid         = {181787},
    publisher     = pub:academic,
    address       = adr:duluth,
}

@inproceedings{Ben-Or1981ff,
    author        = {Ben-Or, Michael},
    title         = {Probabilistic Algorithms in Finite Fields},
    booktitle     = {Proceedings of the 22Nd Annual Symposium on Foundations of Computer Science},
    series        = {SFCS '81},
    year          = {1981},
    pages         = {394--398},
    numpages      = {5},
    url           = {https://doi.org/10.1109/SFCS.1981.37},
    doi           = {10.1109/SFCS.1981.37},
    acmid         = {1382740},
    publisher     = {IEEE Computer Society},
    address       = {Washington, DC, USA},
}

@article{Kredel1988indep,
    title         = {Computing dimension and independent sets for polynomial ideals},
    journal       = j:symb_comp,
    volume        = {6},
    number        = {2},
    pages         = {231--247},
    year          = {1988},
    issn          = {0747-7171},
    doi           = {10.1016/S0747-7171(88)80045-2},
    url           = {https://www.sciencedirect.com/science/article/pii/S0747717188800452},
    author        = {Heinz Kredel and Volker Weispfenning},
}

@inproceedings{Monagan2000Brown,
    author        = {Monagan, Michael B. and Wittkopf, Allan D.},
    title         = {On the Design and Implementation of Brown's Algorithm over the Integers and Number Fields},
    booktitle     = {Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation},
    series        = {ISSAC '00},
    year          = {2000},
    isbn          = {1-58113-218-2},
    location      = {St. Andrews, Scotland},
    pages         = {225--233},
    numpages      = {9},
    url           = {https://dl.acm.org/citation.cfm?doid=345542.345639},
    doi           = {10.1145/345542.345639},
    acmid         = {345639},
    publisher     = pub:acm,
    address       = adr:new_york,
}

@article{Faugere1993groebner,
    author        = {Faug\`{e}re, J.C. and Gianni, P. and Lazard, D. and Mora, T.},
    title         = {Efficient Computation of Zero-dimensional Gr\"{o}Bner Bases by Change of Ordering},
    journal       = j:symb_comp,
    issue_date    = {Oct. 1993},
    volume        = {16},
    number        = {4},
    month         = oct,
    year          = {1993},
    issn          = {0747-7171},
    pages         = {329--344},
    numpages      = {16},
    url           = {https://www.sciencedirect.com/science/article/pii/S0747717183710515},
    doi           = {10.1006/jsco.1993.1051},
    acmid         = {181785},
    publisher     = pub:academic,
    address       = adr:duluth,
}

@article{SunWang2010f5,
    author        = {Yao Sun and Dingkang Wang},
    title         = {A New Proof of the {F5} Algorithm},
    journal       = {CoRR},
    volume        = {abs/1004.0084},
    year          = {2010},
    url           = {https://arxiv.org/abs/1004.0084},
    archivePrefix = {arXiv},
    eprint        = {1004.0084},
    timestamp     = {Mon, 13 Aug 2018 16:47:47 +0200},
    biburl        = {https://dblp.org/rec/bib/journals/corr/abs-1004-0084},
    bibsource     = {dblp computer science bibliography, https://dblp.org}
}

@article{Yokoyama1989primitive,
    title         = {Computing primitive elements of extension fields},
    journal       = j:symb_comp,
    volume        = {8},
    number        = {6},
    pages         = {553--580},
    year          = {1989},
    issn          = {0747-7171},
    doi           = {10.1016/S0747-7171(89)80061-6},
    url           = {https://www.sciencedirect.com/science/article/pii/S0747717189800616},
    author        = {Kazuhiro Yokoyama and Masayuki Noro and Taku Takeshima},
}

@inproceedings{Shoup1991ffactor,
    author        = {Shoup, Victor},
    title         = {A Fast Deterministic Algorithm for Factoring Polynomials over Finite Fields of Small Characteristic},
    booktitle     = {Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation},
    series        = {ISSAC '91},
    year          = {1991},
    isbn          = {0-89791-437-6},
    location      = adr:bonn,
    pages         = {14--21},
    numpages      = {8},
    url           = {https://dl.acm.org/citation.cfm?doid=120694.120697},
    doi           = {10.1145/120694.120697},
    acmid         = {120697},
    publisher     = pub:acm,
    address       = adr:new_york,
}

@article{Kaltofen1998subquadratic,
    author        = {Kaltofen, Erich and Shoup, Victor},
    title         = {Subquadratic-time Factoring of Polynomials over Finite Fields},
    journal       = {Math. Comput.},
    issue_date    = {July 1, 1998},
    volume        = {67},
    number        = {223},
    month         = jul,
    year          = {1998},
    issn          = {0025-5718},
    pages         = {1179--1197},
    numpages      = {19},
    url           = {http://www.ams.org/journals/mcom/1998-67-223/S0025-5718-98-00944-2/home.html},
    doi           = {10.1090/S0025-5718-98-00944-2},
    acmid         = {294748},
    publisher     = pub:ams,
    address       = adr:boston,
}

@article{Abramov71rat,
    title         = {On the summation of rational functions},
    journal       = {USSR Computational Mathematics and Mathematical Physics},
    volume        = {11},
    number        = {4},
    pages         = {324--330},
    year          = {1971},
    issn          = {0041-5553},
    doi           = {10.1016/0041-5553(71)90028-0},
    url           = {https://www.sciencedirect.com/science/article/abs/pii/0041555371900280},
    author        = {S.A. Abramov}
}

@article{Arno1996alg,
    title         = {On Denominators of Algebraic Numbers and Integer Polynomials},
    journal       = {Journal of Number Theory},
    volume        = {57},
    number        = {2},
    pages         = {292--302},
    year          = {1996},
    issn          = {0022-314X},
    doi           = {10.1006/jnth.1996.0049},
    url           = {https://www.sciencedirect.com/science/article/pii/S0022314X96900499},
    author        = {Steven Arno and M.L. Robinson and Ferell S. Wheeler},
}

@phdthesis{LeeM2013factor,
    author        = {M M-D Lee},
    title         = {Factorization of multivariate polynomials},
    year          = {2013},
    school        = {University of Kaiserslautern},
}

@article{Brown1978prs,
    author        = {Brown, W. S.},
    title         = {The Subresultant PRS Algorithm},
    journal       = j:acm_tran_math_soft,
    issue_date    = {Sept. 1978},
    volume        = {4},
    number        = {3},
    month         = sep,
    year          = {1978},
    issn          = {0098-3500},
    pages         = {237--249},
    numpages      = {13},
    url           = {https://dl.acm.org/doi/10.1145/355791.355795},
    doi           = {10.1145/355791.355795},
    acmid         = {355795},
    publisher     = pub:acm,
    address       = adr:new_york,
}

@article{Hoeven02,
    author        = {Van der Hoeven, Joris},
    title         = {Relax, but Don'T Be Too Lazy},
    journal       = j:symb_comp,
    issue_date    = {December 2002},
    volume        = {34},
    number        = {6},
    month         = dec,
    year          = {2002},
    issn          = {0747-7171},
    pages         = {479--542},
    numpages      = {64},
    url           = {https://www.sciencedirect.com/science/article/pii/S0747717102905626},
    doi           = {10.1006/jsco.2002.0562},
    acmid         = {766453},
    publisher     = pub:academic,
    address       = adr:duluth,
}

@book{Menezes97,
    author        = {Menezes, A. J. and Van, O. P. C. and Vanstone, S. A.},
    year          = {1997},
    title         = {Handbook of applied cryptography},
    publisher     = pub:crc,
    address       = adr:boca,
}

@book{Andreescu15,
    author        = {Andreescu, T. and Andrica, D.},
    title         = {Quadratic Diophantine Equations},
    year          = {2015},
    publisher     = pub:springer,
}

@book{TenenbaumPollard63,
	author    = {Tenenbaum, M. and Pollard, H.},
	title     = {Ordinary Differential Equations},
	year      = {1963},
	publisher = pub:dover,
}

@book{polyanin2006handbook,
    title     = {Handbook of Mathematics for Engineers and Scientists},
    author    = {Polyanin, A.D. and Manzhirov, A.V.},
    isbn      = {9781584885023},
    year      = {2006},
    publisher = pub:taylor,
}

@book{simmons2016differential,
    title     = {Differential Equations with Applications and Historical Notes, Third Edition},
    author    = {Simmons, G.F.},
    isbn      = {9781498702621},
    series    = {Textbooks in Mathematics},
    year      = {2016},
    publisher = pub:crc,
}

@book{goldstein1973advanced,
    title     = {Advanced Methods for the Solution of Differential Equations},
    author    = {Goldstein, M.E. and Braun, W.H.},
    series    = {NASA (United States. National Aeronautics and Space Administration)},
    year      = {1973},
    publisher = {Scientific and Technical Information Office, National Aeronautics and Space Administration},
}

@book{hairer2014solving,
    title     = {Solving Ordinary Differential Equations I: Nonstiff Problems},
    author    = {Hairer, E. and N{\o}rsett, S.P. and Wanner, G.},
    isbn      = {9783642052330},
    series    = {Springer Series in Computational Mathematics},
    year      = {2014},
    publisher = pub:springer,
}

@article{Collins1971mod,
    author     = {Collins, George E.},
    title      = {The Calculation of Multivariate Polynomial Resultants},
    year       = {1971},
    issue_date = {October 1971},
    publisher  = pub:acm,
    address    = adr:new_york,
    volume     = {18},
    number     = {4},
    issn       = {0004-5411},
    url        = {https://doi.org/10.1145/321662.321666},
    doi        = {10.1145/321662.321666},
    journal    = j:acm,
    month      = oct,
    pages      = {515--532},
    numpages  = {18},
}
