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Ponencia Algebra Computacional.Pdf DESARROLLO DEL ALGEBRA ELEMENTAL A TRAVÉS DE LOS SISTEMAS DE COMPUTACIÓN SIMBÓLICO Rene Viveros Gutierrez Universidad Surcolombiana QUE ES LA COMPUTACIÓN SIMBÓLICA? • Intuitivamente hablando se puede decir que la computación simbólica consiste en el desarrollo de algoritmos que permiten manipular expresiones y símbolos matemáticos, tal y como se suele hacer en papel. Esta metodología de computación ha dado lugar a un campo interdisciplinar de investigación que, como resultado de su evolución y éxitos alcanzados, proporciona herramientas algorítmicas y métodos que, por una parte, sirven de apoyo para la enseñanza y comprensión de las Matemáticas y, por otra, contribuyen a la resolución de aspectos computacionales que surgen en investigación. COMO NACE LA COMPUTACION SIMBOLICA? En 1955, John McCarthy acuñó el término "Inteligencia Artificial" en su propuesta para el "Darmouth Summer Research Conference on Artificial Intelligence", un evento organizado por el propio McCarthy, Marvin Minsky, Nathalien Rochester y Claude Shannon fue un adelantado a su tiempo y gran parte de sus contribuciones forman parte de los pilares básicos de la Inteligencia Artificial. McCarthy lideró la investigación en lógica matemática para la Inteliencia Artificial. De hecho, en 1958, en su artículo "Programs with Common Sense" [McCarthy 1958], propuso la utilización de la lógica para representar la información en una computadora. En este artículo, McCarthy proponía "...programas que manipulen en un lenguaje formal (a ser posible una parte del cálculo de predicados) instrucciones comunes. El programa básico será capaz de extraer conclusiones automáticas a partir de una serie de premisas. Estas conclusiones serán o bien declarativas o bien sentencias imperativas. Cuándo se deduzca una sentencia imperativa, el programa realizará la acción correspondiente a la misma". Este trabajo seminal inspiraría una gran cantidad de trabajo posterior en "question-answering" y programación lógica.. • 1958 - El primer lenguaje funcional en aparecer fue LISP, diseñado en 1958 por John McCarthy en el entorno de la computación simbólica. A este lenguaje siguieron otros como ML, el Miranda y el Haskell. • En 1960, publicó la especificación del lenguaje LISP ("List Processing Language")[McCarthy 1960], un lenguaje basado en el Cálculo Lambda y que fue, durante muchos años, un lenguaje de referencia para las aplicaciones de Inteligencia Artificial. De hecho LISP se sigue utilizando todavía hoy en muchos sitios, siendo el segundo lenguaje de programación de alto nivel en uso más viejo, después de Fortran. Como ejemplo de uso,Emacs, uno de los editores de textos más conocidos y populares, sobre todo en ámbitos Unix, está enteramente programado en LISP. APARICION DE LOS SISTEMAS DE COMPUTACION SIMBOLICA Los sistemas de álgebra computacional aparecieron al principio de la década de los 70, y evolucionaron a partir de la investigación en inteligencia artificial, aunque hoy en día constituyen campos ampliamente separados. Los primeros trabajos fueron dirigidos por el Premio Nobel Martin Veltman, quien diseñó en 1963 un programa para matemática simbólica, llamado Schoonship, especializado en Física de Altas Energías. Los primeros sistemas populares fueron Reduce y Macsyma. Hoy en día, una versión copyleft de Macsyma llamada Maxima es mantenida activamente. LOS PRIMEROS • REDUCE es un programa de uso general de álgebra computacional (CAS) encaminado hacia usos en física. Comenzó a ser desarrollado desde la década de 1960 por Anthony Hearn, desde entonces, muchos científicos de todo el mundo han contribuido a su desarrollo. Está escrito completamente en su propio dialecto del lenguaje de programación LISP, llamado Standard LISP, sus sintaxis llamada RLISP es similar a Algol • muMATH es un programa de álgebra computacional desarrollado a finales de la década de 1970, y principios de la década de 1980, por Albert Rich y David Stoutemyer en la empresa Soft Warehouse en Honolulu, Hawaii, EE. UU. Fue creado en el lenguaje de programación muSIMP, el cual a su vez fue diseñado basándose en un dialecto de LISP, llamado muLISP. Las plataformas soportadas eran CP/M y TRS- DOS (desde muMATH-79), Apple II (desde muMATH-80) y MS-DOS (en muMATH-83, la última versión) • Maple es un programa matemático de propósito general capaz de realizar cálculos simbólicos, algebraicos y de álgebra computacional. Fue desarrollado originalmente en 1981 por el Grupo de Cálculo Simbólico en la Universidad de Waterloo en Waterloo, Ontario, Canadá. Maple 13: Abril, 2009 Maple V R3: Marzo, 1994 Maple 3.0: Mayo, 1983 Maple 12: Junio, 2008 Maple V R2: Noviembre 1992 Maple 2.2: Diciembre, 1982 Maple 11: Febrero, 2007 Maple V: Agosto, 1990 Maple 2.15: Agosto, 1982 Maple 10: Mayo, 2005 Maple 4.3: Marzo, 1989 Maple 2.1: Junio, 1982 Maple 9.5: Abril, 2004 Maple 4.2: Diciembre, 1987 Maple 2.0: Mayo, 1982 Maple 9: Junio, 2003 Maple 4.1: Mayo, 1987 Maple 1.1: Enero, 1982 Maple 8: Abril, 2002 Maple 4.0: Abril, 1986 Maple 1.0: Enero, 1982 Maple 7: Julio, 2001 Maple 3.3: Marzo, 1985 (primera Maple 6: Diciembre, 1999 versión disponible públicamente) Maple V R5: Noviembre, 1997 Maple 3.2: Abril, 1984 Maple V R4: Enero, 1996 Maple 3.1: Octubre, 1983 • Mathematica es un programa utilizado en áreas científicas, de ingeniería, matemáticas y áreas computacionales. Originalmente fue concebido por Stephen Wolfram quien continua siendo el líder del grupo de matemáticos y programadores que desarrollan el producto en Wolfram Research, compañía ubicada en Champaign, Illinois. Comúnmente considerado como un sistema de álgebra computacional, Mathematica es también un poderoso lenguaje de programación de propósito general. La primera versión de Mathematica fue liberada en 1988. La versión 7, la más reciente fue liberada el 18 de noviembre de 2008 y se encuentra disponible para una gran variedad de sistemas operativos. • Wolfram ha lanzado al mercado las siguientes versiones: [2] Mathematica 1.0 (1988) Mathematica 4.1 (2000) [3] Mathematica 1.2 (1989) Mathematica 4.2 (2002)[9] [4] Mathematica 2.0 (1991) Mathematica 5.0 (2003)[10] [5] Mathematica 2.1 (1992) Mathematica 5.1 (2004)[11] [6] Mathematica 2.2 (1993) Mathematica 5.2 (2005)[12] [7] Mathematica 3.0 (1996) Mathematica 6.0 (2007)[13] [8] Mathematica 4.0 (1999) Mathematica 7.0 (2008)[14 • Derive fue un programa de álgebra computacional (CAS) desarrollado como un sucesor de muMATH por Soft Warehouse en Honolulu, Hawaii, EE. UU., actualmente es propiedad de Texas Instruments. Derive fue creado en muLISP. La primera versión en el mercado fue en 1988. • En la evolución de DERIVE a TI-CAS, pasó de ser una aplicación de ordenador a estar incluido en las calculadoras TI-89 y TI-Nspire CAS de Texas Instruments. • Derive se encuentra disponible para las plataformas Windows y DOS, y es usado ampliamente con propósitos educativos. • A fecha de 2009, la última versión es Derive 6.5. • Actualmente Texas Instruments ya no comercializa Derive, cuyo desarrollo paso ahora como un nuevo producto el TI-Nspire CAS • MATLAB (abreviatura de MATrix LABoratory, "laboratorio de matrices") es un software matemático que ofrece un entorno de desarrollo integrado (IDE) con un lenguaje de programación propio (lenguaje M). Está disponible para las plataformas Unix, Windows y Apple Mac OS X. • Entre sus prestaciones básicas se hallan: la manipulación de matrices, la representación de datos y funciones, la implementación de algoritmos, la creación de interfaces de usuario (GUI) y la comunicación con programas en otros lenguajes y con otros dispositivos hardware. El paquete MATLAB dispone de dos herramientas adicionales que expanden sus prestaciones, a saber, Simulink (plataforma de simulación multidominio) y GUIDE (editor de interfaces de usuario - GUI). Además, se pueden ampliar las capacidades de MATLAB con las cajas de herramientas (toolboxes); y las de Simulink con los paquetes de bloques (blocksets). [1] Nombre de Versión Año la versión MATLAB 5.2 R10 MATLAB 7.0.4 R14SP2 1998 2005 MATLAB 1.0 R? 1984 MATLAB 5.2.1 R10.1 MATLAB 7.1 R14SP3 MATLAB 2 R? 1986 MATLAB 5.3 R11 MATLAB 7.2 R2006a 1999 2006 MATLAB 3 R? 1987 MATLAB 5.3.1 R11.1 MATLAB 7.3 R2006b MATLAB 3.5 R? 1990 MATLAB 6.0 R12 2000 MATLAB 7.4 R2007a 2007 MATLAB 4 R? 1992 MATLAB 6.1 R12.1 2001 MATLAB 7.5 R2007b MATLAB 4.2c R7 1994 MATLAB 6.5 R13 2002 MATLAB 7.6 R2008a 2008 MATLAB 5.0 R8 1996 MATLAB 6.5.1 R13SP1 MATLAB 7.7 R2008b 2003 MATLAB 5.1 R9 MATLAB 6.5.2 R13SP2 MATLAB 7.8 R2009a 2009 MATLAB 1997 MATLAB 7 R14 R9.1 2004 5.1.1 MATLAB 7.0.1 R14SP1 ESPECIALIZADOS EN ALGEBRA • MAXIMA es un programa para Álgebra (Matemáticas) que te permite crear fórmulas matemáticas, gráficos y realizar múltiples operaciones inclusive con símbolos, desde polinomios hasta análisis de Fourier por ejemplo. Se puede crear gráficos 2D y 3D. Usa la interfaz llamada wxMaxima que brinda el uso de menús y cuadros. Las fórmulas se guardan en formato TeX o como imagen; las gráficas en formato postscript. • Lo mejor de todo es gratuito (GPL). College Algebra Solved! • Este Programa te resuelve de una manera sencilla ejercicios del álgebra dándote como resultado todo el procedimiento del ejercicio ya resuelto.Soluciona su ejercicios más difíciles de álgebra, proporcionando las respuestas que usted quiere con todo el procedimiento, paso a paso y explicaciones que usted necesita.así de fácil podrás resolver todo de una manera fácil y sencilla, una versión mas reciente la 2008 • ALGEBRATOR Programa que resuelve ecuaciones matemáticas, desigualdades, logarítmica y exponencial compleja. El cálculo es desglosado paso a paso para que el estudiante pueda entender como se resuelve dicho problema.
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