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Using Macaulay2 Effectively in Practice
Using Macaulay2 effectively in practice Mike Stillman ([email protected]) Department of Mathematics Cornell 22 July 2019 / IMA Sage/M2 Macaulay2: at a glance Project started in 1993, Dan Grayson and Mike Stillman. Open source. Key computations: Gr¨obnerbases, free resolutions, Hilbert functions and applications of these. Rings, Modules and Chain Complexes are first class objects. Language which is comfortable for mathematicians, yet powerful, expressive, and fun to program in. Now a community project Journal of Software for Algebra and Geometry (started in 2009. Now we handle: Macaulay2, Singular, Gap, Cocoa) (original editors: Greg Smith, Amelia Taylor). Strong community: including about 2 workshops per year. User contributed packages (about 200 so far). Each has doc and tests, is tested every night, and is distributed with M2. Lots of activity Over 2000 math papers refer to Macaulay2. History: 1976-1978 (My undergrad years at Urbana) E. Graham Evans: asked me to write a program to compute syzygies, from Hilbert's algorithm from 1890. Really didn't work on computers of the day (probably might still be an issue!). Instead: Did computation degree by degree, no finishing condition. Used Buchsbaum-Eisenbud \What makes a complex exact" (by hand!) to see if the resulting complex was exact. Winfried Bruns was there too. Very exciting time. History: 1978-1983 (My grad years, with Dave Bayer, at Harvard) History: 1978-1983 (My grad years, with Dave Bayer, at Harvard) I tried to do \real mathematics" but Dave Bayer (basically) rediscovered Groebner bases, and saw that they gave an algorithm for computing all syzygies. I got excited, dropped what I was doing, and we programmed (in Pascal), in less than one week, the first version of what would be Macaulay. -
Luis David Garcıa Puente
Luis David Garc´ıa Puente Department of Mathematics and Statistics (936) 294-1581 Sam Houston State University [email protected] Huntsville, TX 77341–2206 http://www.shsu.edu/ldg005/ Professional Preparation Universidad Nacional Autonoma´ de Mexico´ (UNAM) Mexico City, Mexico´ B.S. Mathematics (with Honors) 1999 Virginia Polytechnic Institute and State University Blacksburg, VA Ph.D. Mathematics 2004 – Advisor: Reinhard Laubenbacher – Dissertation: Algebraic Geometry of Bayesian Networks University of California, Berkeley Berkeley, CA Postdoctoral Fellow Summer 2004 – Mentor: Lior Pachter Mathematical Sciences Research Institute (MSRI) Berkeley, CA Postdoctoral Fellow Fall 2004 – Mentor: Bernd Sturmfels Texas A&M University College Station, TX Visiting Assistant Professor 2005 – 2007 – Mentor: Frank Sottile Appointments Colorado College Colorado Springs, CO Professor of Mathematics and Computer Science 2021 – Sam Houston State University Huntsville, TX Professor of Mathematics 2019 – 2021 Sam Houston State University Huntsville, TX Associate Department Chair Fall 2017 – 2021 Sam Houston State University Huntsville, TX Associate Professor of Mathematics 2013 – 2019 Statistical and Applied Mathematical Sciences Institute Research Triangle Park, NC SAMSI New Researcher fellowship Spring 2009 Sam Houston State University Huntsville, TX Assistant Professor of Mathematics 2007 – 2013 Virginia Bioinformatics Institute (Virginia Tech) Blacksburg, VA Graduate Research Assistant Spring 2004 Virginia Polytechnic Institute and State University Blacksburg, -
Chapter 1. Origins of Mac OS X
1 Chapter 1. Origins of Mac OS X "Most ideas come from previous ideas." Alan Curtis Kay The Mac OS X operating system represents a rather successful coming together of paradigms, ideologies, and technologies that have often resisted each other in the past. A good example is the cordial relationship that exists between the command-line and graphical interfaces in Mac OS X. The system is a result of the trials and tribulations of Apple and NeXT, as well as their user and developer communities. Mac OS X exemplifies how a capable system can result from the direct or indirect efforts of corporations, academic and research communities, the Open Source and Free Software movements, and, of course, individuals. Apple has been around since 1976, and many accounts of its history have been told. If the story of Apple as a company is fascinating, so is the technical history of Apple's operating systems. In this chapter,[1] we will trace the history of Mac OS X, discussing several technologies whose confluence eventually led to the modern-day Apple operating system. [1] This book's accompanying web site (www.osxbook.com) provides a more detailed technical history of all of Apple's operating systems. 1 2 2 1 1.1. Apple's Quest for the[2] Operating System [2] Whereas the word "the" is used here to designate prominence and desirability, it is an interesting coincidence that "THE" was the name of a multiprogramming system described by Edsger W. Dijkstra in a 1968 paper. It was March 1988. The Macintosh had been around for four years. -
Mac OS X and PDF: the Real Story
Mac OS X and PDF The Real Story Leonard Rosenthol Lazerware, Inc. Copyright©1999-2001, Lazerware, Inc. Overview •Mac OS X •PDF • Where’s the overlap? Copyright©1999-2001, Lazerware, Inc. You are here because… • You’re currently working with Mac OS and are interested in what Mac OS X brings to the table. • You’re curious about what Apple’s latest hype is all about. • You’re already awake and had to find something to kill time. • You’re a friend of mine and wanted to heckle Copyright©1999-2001, Lazerware, Inc. How I do things • You should all have copies of the presentation that you received when you walked in. • There is also an electronic copy of this presentation (PDF format, of course!) on my website at http://www.lazerware.com/ • I’ve left time at the end for Q&A, but please feel free to ask questions at any time! Copyright©1999-2001, Lazerware, Inc. Mac OS X Overview Copyright©1999-2001, Lazerware, Inc. Darwin • “Core OS” (Kernel) – Solid Unix foundation • FreeBSD 3.2 & Mach 3.0 • Memory protection, preemptive multitasking, etc. – High performance I/O • Firewire, USB, etc. • Open source Copyright©1999-2001, Lazerware, Inc. Graphics •Quartz – Adobe Imaging Model (PDF) • Includes full anti-aliasing and opacity/transparency • OpenGL – Industry standard 3D engine used by Quake & Maya • QuickTime Copyright©1999-2001, Lazerware, Inc. Graphics Demos - Quartz Copyright©1999-2001, Lazerware, Inc. Graphics Demos – OpenGL Copyright©1999-2001, Lazerware, Inc. Application Frameworks • Classic – Compatibility “box” for existing Mac OS applications. • Carbon – Modern versions of Mac OS applications prepared for Mac OS X. -
An Alternative Algorithm for Computing the Betti Table of a Monomial Ideal 3
AN ALTERNATIVE ALGORITHM FOR COMPUTING THE BETTI TABLE OF A MONOMIAL IDEAL MARIA-LAURA TORRENTE AND MATTEO VARBARO Abstract. In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the way of describing the method, we also prove new constraints on the shape of the possible Betti tables of a monomial ideal. 1. Introduction Since many years syzygies, and more generally free resolutions, are central in purely theo- retical aspects of algebraic geometry; more recently, after the connection between algebra and statistics have been initiated by Diaconis and Sturmfels in [DS98], free resolutions have also become an important tool in statistics (for instance, see [D11, SW09]). As a consequence, it is fundamental to have efficient algorithms to compute them. The usual approach uses Gr¨obner bases and exploits a result of Schreyer (for more details see [Sc80, Sc91] or [Ei95, Chapter 15, Section 5]). The packages for free resolutions of the most used computer algebra systems, like [Macaulay2, Singular, CoCoA], are based on these techniques. In this paper, we introduce a new algorithmic method to compute the minimal graded free resolution of any finitely generated graded module over a polynomial ring such that some (possibly non- minimal) graded free resolution is known a priori. We describe this method and we present the resulting algorithm in the case of monomial ideals in a polynomial ring, in which situ- ation we always have a starting nonminimal graded free resolution. -
Computations in Algebraic Geometry with Macaulay 2
Computations in algebraic geometry with Macaulay 2 Editors: D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels Preface Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re- cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith- mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv- ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi- mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. -
A Simplified Introduction to Virus Propagation Using Maple's Turtle Graphics Package
E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package A simplified introduction to virus propagation using Maple's Turtle Graphics package Eugenio Roanes-Lozano Instituto de Matemática Interdisciplinar & Departamento de Didáctica de las Ciencias Experimentales, Sociales y Matemáticas Facultad de Educación, Universidad Complutense de Madrid, Spain Carmen Solano-Macías Departamento de Información y Comunicación Facultad de CC. de la Documentación y Comunicación, Universidad de Extremadura, Spain Eugenio Roanes-Macías Departamento de Álgebra, Universidad Complutense de Madrid, Spain [email protected] ; [email protected] ; [email protected] Partially funded by the research project PGC2018-096509-B-100 (Government of Spain) 1 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package 1. INTRODUCTION: TURTLE GEOMETRY AND LOGO • Logo language: developed at the end of the ‘60s • Characterized by the use of Turtle Geometry (a.k.a. as Turtle Graphics). • Oriented to introduce kids to programming (Papert, 1980). • Basic movements of the turtle (graphic cursor): FD, BK RT, LT. • It is not based on a Cartesian Coordinate system. 2 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package • Initially robots were used to plot the trail of the turtle. http://cyberneticzoo.com/cyberneticanimals/1969-the-logo-turtle-seymour-papert-marvin-minsky-et-al-american/ 3 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package • IBM Logo / LCSI Logo (’80) 4 E. -
What Can Computer Algebraic Geometry Do Today?
What can computer Algebraic Geometry do today? Gregory G. Smith Wolfram Decker Mike Stillman 14 July 2015 Essential Questions ̭ What can be computed? ̭ What software is currently available? ̭ What would you like to compute? ̭ How should software advance your research? Basic Mathematical Types ̭ Polynomial Rings, Ideals, Modules, ̭ Varieties (affine, projective, toric, abstract), ̭ Sheaves, Divisors, Intersection Rings, ̭ Maps, Chain Complexes, Homology, ̭ Polyhedra, Graphs, Matroids, ̯ Established Geometric Tools ̭ Elimination, Blowups, Normalization, ̭ Rational maps, Working with divisors, ̭ Components, Parametrizing curves, ̭ Sheaf Cohomology, ঠ-modules, ̯ Emerging Geometric Tools ̭ Classification of singularities, ̭ Numerical algebraic geometry, ̭ ैक़௴Ь, Derived equivalences, ̭ Deformation theory,Positivity, ̯ Some Geometric Successes ̭ GEOGRAPHY OF SURFACES: exhibiting surfaces with given invariants ̭ BOIJ-SÖDERBERG: examples lead to new conjectures and theorems ̭ MODULI SPACES: computer aided proofs of unirationality Some Existing Software ̭ GAP,Macaulay2, SINGULAR, ̭ CoCoA, Magma, Sage, PARI, RISA/ASIR, ̭ Gfan, Polymake, Normaliz, 4ti2, ̭ Bertini, PHCpack, Schubert, Bergman, an idiosyncratic and incomplete list Effective Software ̭ USEABLE: documented examples ̭ MAINTAINABLE: includes tests, part of a larger distribution ̭ PUBLISHABLE: Journal of Software for Algebra and Geometry; www.j-sag.org ̭ CITATIONS: reference software Recent Developments in Singular Wolfram Decker Janko B¨ohm, Hans Sch¨onemann, Mathias Schulze Mohamed Barakat TU Kaiserslautern July 14, 2015 Wolfram Decker (TU-KL) Recent Developments in Singular July 14, 2015 1 / 24 commutative and non-commutative algebra, singularity theory, and with packages for convex and tropical geometry. It is free and open-source under the GNU General Public Licence. -
Darwin: Mac OS X's Core OS
ADC April 2001 3/8/01 1:57 PM Page 1 Apple Developer Connection Direct Darwin: Mac OS X’s Core OS eneath Mac OS X’s user-friendly and attractive user interface, Most of the reference documents can be Aqua, and the application frameworks (Classic, Carbon and found in the /Developer/Documentation/ BCocoa) is Darwin: Mac OS X’s core OS. Unseen by users, Kernel directory on any Mac OS X system Darwin provides a strong yet flexible foundation with features like with the Mac OS X Developer Tools package preemptive multitasking, protected memory and real-time support installed. that make Mac OS X a truly modern operating system. The focus of this article is to provide a brief overview of Components of Darwin Darwin and its components as well as give an introduction to Just like in the old Reese’s Peanut Butter developing kernel extensions—modules that extend Darwin’s Cups commercials (“You’ve got chocolate in functionality. For more in-depth information, you should read my peanut butter… No, you’ve got peanut butter on my choco- Inside Mac OS X: Kernel Environment which is available, along late!”), Darwin blends a mixture of mature industry standard com- with other documents referred to in this article, on the Apple ponents such as Mach and BSD with Apple-engineered components Developer Connection (ADC) web site in the Mac OS X to provide Mac OS X with a stable, reliable and extensible founda- Documentation section: tion. Darwin consists of five main components: Mach, I/O Kit, File http://developer.apple.com/techpubs/macosx/macosx.html System, Networking and BSD. -
Managing OS X with Configuration Profiles
Apple Technical White Paper Managing OS X with Configuration Profiles Apple Technical White Paper Managing OS X with Configuration Profiles OS X Lion v 10.7.3 1 Apple Technical White Paper Managing OS X with Configuration Profiles Table of Contents About Configuration Profiles .......................................................................................3 Creating Configuration Profiles ..................................................................................8 Deploying Configuration Profiles ...............................................................................13 Appendix A: Profile Reference .....................................................................................25 Appendix B: Service Port Reference ..........................................................................28 Appendix C: Example Profiles ......................................................................................29 2 Apple Technical White Paper Managing OS X with Configuration Profiles About Configuration Profiles Introduction On iOS devices, preferences and preconfigured settings are managed with Mobile Device Management (MDM) technologies and configuration profiles. Beginning with OS X Lion, Apple has brought the configuration profile and MDM technologies from iOS to OS X. Configuration profiles not only allow for the same preference policies to be deployed as the Managed Preferences system, but they also bring powerful new configuration options such as directory service binding, 802.1X configuration, and certificate -
Lecture 7 Mac OS X and Ios Operating Systems Saving Data In
Mac OS X and iOS operating systems Lecture 7 Saving data in iOS Tomasz Idzi Agenda NSString and NSData NSFileManager Property List JSON Core Data Mac OS X and iOS operating systems Tomasz Idzi iOS Directories App Documents Inbox Library Caches temp Mac OS X and iOS operating systems Tomasz Idzi iOS Directories Directory Description Backed up by iTunes AppName.app This directory contains the app and all of its resources. NO Documents/ Use this directory to store user-generated content. YES Use this directory to access files that your app was asked to open Documents/Inbox YES by outside entities. Such as mail’s attachments. This is the top-level directory for any files that are not user data Library YES files. Library/Caches Subfolder of Library for any caching files. NO Use this directory to write temporary files that don’t need to persist Tmp/ NO between launches of your app. Mac OS X and iOS operating systems Tomasz Idzi Accessing File Paths NSArray *paths = NSSearchPathForDirectoriesInDomains (NSDocumentDirectory, NSUserDomainMask, YES); NSString *docPath = [paths firstObject]; NSString *path = [docPath stringByAppendingComponent:@”myFile.txt”]; Mac OS X and iOS operating systems Tomasz Idzi Writing NSData BOOL success = [data writeToFile:path options:NSDataWritingAtomic error:&error]; NSDataWritingAtomic - create temp file first NSDataWritingWithoutOverwriting - prevent overwriting an existing file Mac OS X and iOS operating systems Tomasz Idzi Reading NSData [NSData alloc] initWithContentsOfFile: path options:NSDataReadingMappedIfSafe error:&error]; NSDataReadingMappedIfSafe - file should be mapped into virtual memory, if possible and safe NSDataReadingUncached - file should not be stored in the file-system caches NSDataReadingMappedAlways - map the file, if possible. -
Dell Encryption Enterprise for Mac Administrator Guide V10.9
Dell Encryption Enterprise for Mac Administrator Guide v10.9 March 2021 Rev. A02 Notes, cautions, and warnings NOTE: A NOTE indicates important information that helps you make better use of your product. CAUTION: A CAUTION indicates either potential damage to hardware or loss of data and tells you how to avoid the problem. WARNING: A WARNING indicates a potential for property damage, personal injury, or death. © 2012-2021 Dell Inc. All rights reserved. Registered trademarks and trademarks used in the Dell Encryption and Endpoint Security Suite Enterprise suite of documents: Dell™ and the Dell logo, Dell Precision™, OptiPlex™, ControlVault™, Latitude™, XPS®, and KACE™ are trademarks of Dell Inc. Cylance®, CylancePROTECT, and the Cylance logo are registered trademarks of Cylance, Inc. in the U.S. and other countries. McAfee® and the McAfee logo are trademarks or registered trademarks of McAfee, Inc. in the US and other countries. Intel®, Pentium®, Intel Core Inside Duo®, Itanium®, and Xeon® are registered trademarks of Intel Corporation in the U.S. and other countries. Adobe®, Acrobat®, and Flash® are registered trademarks of Adobe Systems Incorporated. Authen tec® and Eikon® are registered trademarks of Authen tec. AMD® is a registered trademark of Advanced Micro Devices, Inc. Microsoft®, Windows®, and Windows Server®, Windows Vista®, Windows 7®, Windows 10®, Active Directory®, Access®, BitLocker®, BitLocker To Go®, Excel®, Hyper-V®, Outlook®, PowerPoint®, Word®, OneDrive®, SQL Server®, and Visual C++® are either trademarks or registered trademarks of Microsoft Corporation in the United States and/or other countries. VMware® is a registered trademark or trademark of VMware, Inc. in the United States or other countries.