## Contents Open Source Mathematical Software:

Citations: | 4 - 1 self |

### BibTeX

@MISC{Joyner_contentsopen,

author = {D. Joyner and W. Stein},

title = {Contents Open Source Mathematical Software:},

year = {}

}

### OpenURL

### Abstract

### Citations

295 |
Every Planar map is Four Colorable
- Appel, Haken, et al.
- 1977
(Show Context)
Citation Context ...g extensive data for conjectures. Perhaps three of the most well-known applications of computation to mathematical research are resolution of the four-color conjecture by Appel and Haken in 1976 (see =-=[AH]-=-, [AHK], though it is now reproven in [RSST]), Hales’s proof [H] of the Kepler’s conjecture, and the formulation of the Birch and Swinnerton-Dyer conjecture [BSD] which grew out of extensive numerical... |

119 | The four-colour theorem
- Robertson, Sanders, et al.
- 1997
(Show Context)
Citation Context ...three of the most well-known applications of computation to mathematical research are resolution of the four-color conjecture by Appel and Haken in 1976 (see [AH], [AHK], though it is now reproven in =-=[RSST]-=-), Hales’s proof [H] of the Kepler’s conjecture, and the formulation of the Birch and Swinnerton-Dyer conjecture [BSD] which grew out of extensive numerical computation. To give a concrete flavor of h... |

65 |
Λ-rings and the representation theory of the symmetric group
- Knutson
- 1973
(Show Context)
Citation Context ...JK] used it to understand which representations of SL2(GF(p)) occur in the decomposition of H 1 (X(p), C), where X(p) is a modular curve and p > 5 is a prime. 1.2 Character theory Knutson’s 1973 book =-=[K]-=- contains the following conjecture: 4sConjecture. Let G be a finite group, ρ the right regular representation of G and π any irreducible representation. There is a π ′ in the Grothendieck ring R(G) su... |

39 | Hurwitz monodromy, spin separation and higher levels of a modular tower
- Bailey, Fried
- 1999
(Show Context)
Citation Context ...urfaces. This is not the only use of GAP in Riemann surface theory. Indeed, Paul Bailey, in his Ph.D. thesis [Ba], computed a Hurwitz space using GAP. Then he and his advisor Mike Fried wrote a paper =-=[BaF]-=- based on a different Hurwitz space, where they also used GAP to compute the number of components and their genus. Joyner and Ksir [JK] used it to understand which representations of SL2(GF(p)) occur ... |

36 |
Characters and automorphism groups of compact Riemann surfaces
- BREUER
(Show Context)
Citation Context ...it is not surprising that GAP – primarily a group 3stheory package – is very helpful in the investigation of Riemann surfaces and curves with “large” automorphism groups. Thomas Breuer’s Ph.D. thesis =-=[B1]-=- initiated a computational program to exploit this connection using GAP. His thesis focues on the following two problems: (1) Classify all groups of automorphisms of compact Riemann surfaces X of fixe... |

16 |
Computer Construction of the Monster
- Linton, Parker, et al.
- 1998
(Show Context)
Citation Context ...s, especially the large ones, which are difficult to analyze “by hand”. Two examples are A. Hulpke and S. Linton [HL], who investigate the group Co3, and S. Linton, R. Parker, P. Walsh, and R. Wilson =-=[LPWW]-=-, who investigate the Monster simple group. 2 Rigor and design principles In mathematics, correctness and verifiability rule with an iron fist. This holds true for scholarly papers, and should hold as... |

11 | Toric codes over finite fields
- Joyner
(Show Context)
Citation Context ... k, the code C that has the largest possible d. Using GUAVA and some additional GAP programming, a code C over GF(8) with previously unknown parameters [49, 11, 28] was discovered by the first author =-=[J]-=-. This illustrates the wide variety of applications that GAP has to not only pure mathematics but also in applied mathematics. Of even more significance, GUAVA was also useful in the classification of... |

8 |
Elliptic curves over Q: A progress report, 1969 Number Theory Institute (Proc
- Birch
- 1969
(Show Context)
Citation Context ...ecture by Appel and Haken in 1976 (see [AH], [AHK], though it is now reproven in [RSST]), Hales’s proof [H] of the Kepler’s conjecture, and the formulation of the Birch and Swinnerton-Dyer conjecture =-=[BSD]-=- which grew out of extensive numerical computation. To give a concrete flavor of how open source mathematical software contribute to research, we will focus in the rest of this section on the 20-year ... |

8 | A GAP package for braid orbit computation, and applications
- Magaard, Shpectorov, et al.
(Show Context)
Citation Context ...or genus 2 ≤ g ≤ 48. (Only classifications for 2 ≤ g ≤ 5 had been achieved earlier.) Considering (2), for example, he obtained full classifications for arbitrary dihedral and abelian groups. The work =-=[MSV]-=- using the GAP package BRAID was inspired by Thomas Breuer’s earlier work. Let G be a finite group. By Riemann’s Existence Theorem, braid orbits of generating systems of G with product 1 correspond to... |

6 |
On the classification of extremal even formally self-dual codes. Des
- Fields, Gaborit, et al.
- 1999
(Show Context)
Citation Context ...s the wide variety of applications that GAP has to not only pure mathematics but also in applied mathematics. Of even more significance, GUAVA was also useful in the classification of self-dual codes =-=[FGHP]-=-. Coding theory is not the only applied area of mathematics on which GAP has had an impact. For example, several applications of GAP to chemistry (via the theory of crystallographic groups) are indica... |

4 | An invitation to Computational Group Theory
- Neubüser
- 1993
(Show Context)
Citation Context ...athematica/tutorial/ WhyYouDoNotUsuallyNeedToKnowAboutInternals.html Increasingly, proprietary software and the algorithms used are an essential part of mathematical proofs. To quote Joachim Neubüser =-=[N]-=-, the “father” of GAP, “with this situation two of the most basic rules of conduct in mathematics are violated: In mathematics information is passed on free of charge and everything is laid open for c... |

3 |
Incremental Ascent of a Modular Tower via Branch Cycle Designs, unpublished thesis from UC at Irvine, at http://math.uci.edu/˜mfried/paplistmt/pBaileyThesis2002.pdf
- Bailey
(Show Context)
Citation Context ...klein use BRAID to deal with other questions in the theory of monodromy groups of Riemann surfaces. This is not the only use of GAP in Riemann surface theory. Indeed, Paul Bailey, in his Ph.D. thesis =-=[Ba]-=-, computed a Hurwitz space using GAP. Then he and his advisor Mike Fried wrote a paper [BaF] based on a different Hurwitz space, where they also used GAP to compute the number of components and their ... |

3 | Modular representations on some Riemann-Roch spaces of modular curves X(N), preprint 2005. Available at http://front.math.ucdavis.edu/math.AG/0502586
- Ksir
(Show Context)
Citation Context ...ace using GAP. Then he and his advisor Mike Fried wrote a paper [BaF] based on a different Hurwitz space, where they also used GAP to compute the number of components and their genus. Joyner and Ksir =-=[JK]-=- used it to understand which representations of SL2(GF(p)) occur in the decomposition of H 1 (X(p), C), where X(p) is a modular curve and p > 5 is a prime. 1.2 Character theory Knutson’s 1973 book [K]... |

2 | GUAVA: An error-correcting codes package
- Joyner
- 2005
(Show Context)
Citation Context ...1990’s by Jasper Cramwinckel, Erik Roijackers, and Reinald Baart as a final project at Delft University of Technology, Department of Pure Mathematics, under the direction of Professor Juriaan Simonis =-=[GU]-=-. Regarding a code C as a vector subspace of F n (F a finite field) with a fixed basis, the key “parameters” of C are its length n, its dimension k, and the smallest number d of nonzero coordinates of... |

2 |
The Kepler Conjecture, preprint math.MG/9811078
- Hales
(Show Context)
Citation Context ...known applications of computation to mathematical research are resolution of the four-color conjecture by Appel and Haken in 1976 (see [AH], [AHK], though it is now reproven in [RSST]), Hales’s proof =-=[H]-=- of the Kepler’s conjecture, and the formulation of the Birch and Swinnerton-Dyer conjecture [BSD] which grew out of extensive numerical computation. To give a concrete flavor of how open source mathe... |

2 | Construction of Co3. An example of the use of an integrated system for Computational Group Theory
- Hulpke, Linton
- 1999
(Show Context)
Citation Context ...f all finite simple groups. GAP has been used by many to investigate the sporadic groups, especially the large ones, which are difficult to analyze “by hand”. Two examples are A. Hulpke and S. Linton =-=[HL]-=-, who investigate the group Co3, and S. Linton, R. Parker, P. Walsh, and R. Wilson [LPWW], who investigate the Monster simple group. 2 Rigor and design principles In mathematics, correctness and verif... |

2 |
Extended Rate, more GFUN, preprint 2007. Available at: http://front.math.ucdavis.edu/math.CO/0702086
- Rubey
(Show Context)
Citation Context ...nAxiom page http://www.open-axiom.org/index.html. For example, Axiom is a leader in “reverse computation” (guessing formulas for a sequence given its first few terms; see Martin Rubey’s package GUESS =-=[R]-=-). 13s• CoCoALib 5 (“Computations in Commutative Algebra”) Its web page is: http://cocoa.dima.unige.it/ (at the time of this writing, CoCoALib 5 is still in development version). • GAP is a system for... |

1 |
post to SAGE-support email list: http://thread.gmane.org/gmane.comp.mathematics.sage
- Kosan
(Show Context)
Citation Context ...d open source software. Ted Kosan is currently developing teaching materials for computer technology for distance learning courses taught to high-schoolers in Ohio. He selected SAGE. In his own words =-=[Ko]-=-: “As part of this process, I have been searching for open source mathematics software that has a modern programming environment intimately integrated into it. I also wanted it to be alive and 16swell... |

1 |
Interviews with Three Fields Medalists
- Muñoz, Persson
- 2007
(Show Context)
Citation Context ...ibraries, etc. One can learn from the success of TEX and more specialized software like Macaulay2. I do hope that funding agencies are looking into this.” – Andrei Okounkov, 2006 Fields Medalist (see =-=[MP]-=-). By mathematical software we mean a collection of specific implementations of algorithms and data structures for computation with mathematical objects such as matrices, functions, groups, rings, gra... |