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<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN"><!Converted with LaTeX2HTML 95.1 (Fri Jan 20 1995) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds ><HEAD><TITLE>Collaborative Mathematics Environments</TITLE></HEAD><BODY><meta name="description" value="Collaborative Mathematics Environments"><meta name="keywords" value="it"><meta name="resource-type" value="document"><meta name="distribution" value="global"><P> <BR> <HR><A NAME=tex2html1 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="next" SRC="http://www.cs.cornell.edu/Info/Projects/NuPrl/icons/next_motif.gif"></A> <IMG ALIGN=BOTTOM ALT="up" SRC="http://www.cs.cornell.edu/Info/Projects/NuPrl/icons/up_motif_gr.gif"> <IMG ALIGN=BOTTOM ALT="previous" SRC="http://www.cs.cornell.edu/Info/Projects/NuPrl/icons/previous_motif_gr.gif"> <BR><B> Next:</B> <A NAME=tex2html2 HREF="node1.html"> Introduction</A><BR> <HR> <P><P><H4> <b> PROJECT SUMMARY</b></H4> <BR><H4> <b> Collaborative Mathematics Environments</b></H4> <BR>Paul Chew, Robert L. Constable, Keshav Pingali, Steve Vavasis, Richard Zippel<P><em> Computational science</em> will be the dominant paradigm for sciencein the next century. This proposal addresses one of the majorchallenges facing this new kind of science---the demand for bettersoftware support for computational mathematics. The task of providingthis support is sufficiently central to the national interest andsufficiently comprehensive that it could serve as a Grand Challengeproblem for computer science.<P>A strategy for meeting this challenge has evolved from inter-projectcooperation at Cornell on the elements of scientific computing. Thisproposal represents a collaboration among five computer scientistswith diverse backgrounds: scientific computing, computationalgeometry, computer algebra, applied logic, and programming languages.In various combinations these people have worked together, andsoftware from their separate projects has been linked. Theirexperience with the difficulty of this linking process has led to theidentification and to the prospective solutions of three majorproblems: the <em> connectivity problem</em>, the <em> code generationproblem</em>, and the <em> explanation problem</em>. The problems and theirsolutions are briefly explained below. This proposal outlines a planto design and implement an open system architecture that willintegrate a variety of computational science tools into an environmentthat supports collaborative activity.<P>Many interesting and powerful tools exist to support computationalmathematics (for example, Matlab, Lapack, Mathematica, Axiom, Ellpack,PLTMG, Autocad, and LEDA), but most of these are focused on onespecific area or on one specific style of computation. These systemsare largely self-contained and <em> closed</em>, connecting to othersoftware only at a very low level of abstraction, using, for instance,string-to-string communication. They do not have a common semanticbase that would allow one system to ``collaborate'' with another.This is the <em> connectivity problem</em>. To address the connectivityproblem, a common <em> mathematical bus</em> (the <em> MathBus</em>) willserve as the backbone of the system. Its communication protocols willbe based on a typed formal language which provides the semantics forcollaboration. A major design objective is to raise the level ofcommunication among software tools, allowing the communication ofmathematical objects instead of being restricted to simple strings.<P>Although existing software has contributed substantially to scientificprogramming productivity, the time taken to generate code remains amajor impediment to progress in computational science. This is the<em> code creation problem</em>. In part, this problem is due to thedifficulty of expressing certain mathematical techniques assubroutines. The problem of code creation is addressed with a methodof transformation and refinement, allowing the transformation ofhigh-level mathematical expressions into more-traditional code.<P>One of the reasons that sharing code with a colleague is difficult isbecause there is no common language for explaining what a program doesand for precisely giving the conditions necessary to apply it. Thisis the <em> explanation problem</em>. The solution to the connectivityproblem also provides an approach to explanation, namely to provideformal and semi-formal semantic standards for communications andlinkage on the proposed MathBus.<P>The problem solutions outlined here lead to an additional opportunity.Once tools can inter-operate and mathematical models can be shared, itbecomes possible to create collections of mathematical theorems,explanations, and examples and counterexamples. Such a mathematicaldatabase could capture an important part of mathematical knowledgethat is at best poorly represented by books and journals.<P><P><H1>Collaborative Mathematics Environments</H1><P><STRONG>Paul Chew, Robert L. Constable, Keshav Pingali, Steve Vavasis, Richard Zippel</STRONG><P><P><P><BR> <HR><UL> <LI> <A NAME=tex2html3 HREF="node1.html#SECTION00010000000000000000"> Introduction</A><UL> <LI> <A NAME=tex2html4 HREF="node2.html#SECTION00011000000000000000"> The Basic Problems</A><LI> <A NAME=tex2html5 HREF="node3.html#SECTION00012000000000000000"> Research Program</A></UL> <LI> <A NAME=tex2html6 HREF="node4.html#SECTION00020000000000000000"> The Connectivity Problem</A><UL> <LI> <A NAME=tex2html7 HREF="node5.html#SECTION00021000000000000000"> Mesh Generation</A><LI> <A NAME=tex2html8 HREF="node6.html#SECTION00022000000000000000"> Numerical Linear Algebra</A><LI> <A NAME=tex2html9 HREF="node7.html#SECTION00023000000000000000"> Weyl/Nuprl</A><LI> <A NAME=tex2html10 HREF="node8.html#SECTION00024000000000000000"> Mathematical Bus</A></UL> <LI> <A NAME=tex2html11 HREF="node9.html#SECTION00030000000000000000"> The Code Creation Problem</A><UL> <LI> <A NAME=tex2html12 HREF="node10.html#SECTION00031000000000000000"> Quadratic Formula</A><LI> <A NAME=tex2html13 HREF="node11.html#SECTION00032000000000000000"> Sparse Matrices</A><LI> <A NAME=tex2html14 HREF="node12.html#SECTION00033000000000000000"> Ongoing Activities</A></UL> <LI> <A NAME=tex2html15 HREF="node13.html#SECTION00040000000000000000"> The Explanation Problem</A><UL> <LI> <A NAME=tex2html16 HREF="node14.html#SECTION00041000000000000000"> Symbolic Computations and the Explanation Problem</A><LI> <A NAME=tex2html17 HREF="node15.html#SECTION00042000000000000000"> Geometry and the Explanation Problem</A><LI> <A NAME=tex2html18 HREF="node16.html#SECTION00043000000000000000"> Access to Libraries</A><LI> <A NAME=tex2html19 HREF="node17.html#SECTION00044000000000000000"> Value of Precise Mathematical Language</A><UL> <LI> <A NAME=tex2html20 HREF="node18.html#SECTION00044010000000000000"> Conditions on Transformations.</A><LI> <A NAME=tex2html21 HREF="node19.html#SECTION00044020000000000000"> Geometry.</A></UL> <LI> <A NAME=tex2html22 HREF="node20.html#SECTION00045000000000000000"> Summary</A></UL> <LI> <A NAME=tex2html23 HREF="node21.html#SECTION00050000000000000000"> The Mathematical Database Opportunity</A><LI> <A NAME=tex2html24 HREF="node22.html#SECTION00060000000000000000"> Milestones</A><UL> <LI> <A NAME=tex2html25 HREF="node23.html#SECTION00060010000000000000"> Year 1</A><LI> <A NAME=tex2html26 HREF="node24.html#SECTION00060020000000000000"> Year 2</A><LI> <A NAME=tex2html27 HREF="node25.html#SECTION00060030000000000000"> Year 3</A><LI> <A NAME=tex2html28 HREF="node26.html#SECTION00060040000000000000"> Year 4</A><LI> <A NAME=tex2html29 HREF="node27.html#SECTION00060050000000000000"> Year 5</A></UL> <LI> <A NAME=tex2html30 HREF="node28.html#SECTION00070000000000000000"> Results from Prior NSF Support</A><UL> <LI> <A NAME=tex2html31 HREF="node29.html#SECTION00071000000000000000"> Constable</A><LI> <A NAME=tex2html32 HREF="node30.html#SECTION00072000000000000000"> Pingali</A><UL> <LI> <A NAME=tex2html33 HREF="node31.html#SECTION00072100000000000000"> Partial List of Publications</A><LI> <A NAME=tex2html34 HREF="node32.html#SECTION00072200000000000000"> Development of Human Resources</A></UL> <LI> <A NAME=tex2html35 HREF="node33.html#SECTION00073000000000000000"> Vavasis</A></UL> <LI> <A NAME=tex2html36 HREF="node34.html#SECTION01000000000000000000">References</A><UL> <LI> <A NAME=tex2html37 HREF="node35.html#SECTION01010000000000000000"> Biographical Sketches</A><UL> <LI> <A NAME=tex2html38 HREF="node36.html#SECTION01011000000000000000"> L. Paul Chew</A><LI> <A NAME=tex2html39 HREF="node37.html#SECTION01012000000000000000"> Robert L. Constable</A><LI> <A NAME=tex2html40 HREF="node38.html#SECTION01013000000000000000"> Keshav K. Pingali</A><LI> <A NAME=tex2html41 HREF="node39.html#SECTION01014000000000000000"> Stephen A. Vavasis</A><LI> <A NAME=tex2html42 HREF="node40.html#SECTION01015000000000000000"> Richard E. Zippel</A></UL> </UL> <LI> <A NAME=tex2html43 HREF="node41.html#SECTION02000000000000000000"> Budget</A><UL> <LI> <A NAME=tex2html44 HREF="node42.html#SECTION02000100000000000000"> Salaries and wages for senior personnel</A><LI> <A NAME=tex2html45 HREF="node43.html#SECTION02000200000000000000"> Postdoctoral research associate</A><LI> <A NAME=tex2html46 HREF="node44.html#SECTION02000300000000000000"> Equipment</A><LI> <A NAME=tex2html47 HREF="node45.html#SECTION02000400000000000000"> Travel</A></UL> <LI> <A NAME=tex2html48 HREF="node46.html#SECTION03000000000000000000"> Current and Pending Support</A><LI> <A NAME=tex2html49 HREF="node47.html#SECTION04000000000000000000"> Facilities, Equipment and Other Resources</A><LI> <A NAME=tex2html50 HREF="node48.html#SECTION05000000000000000000"> About this document ... </A></UL><BR> <HR><A NAME=tex2html1 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="next" SRC="http://www.cs.cornell.edu/Info/Projects/NuPrl/icons/next_motif.gif"></A> <IMG ALIGN=BOTTOM ALT="up" SRC="http://www.cs.cornell.edu/Info/Projects/NuPrl/icons/up_motif_gr.gif"> <IMG ALIGN=BOTTOM ALT="previous" SRC="http://www.cs.cornell.edu/Info/Projects/NuPrl/icons/previous_motif_gr.gif"> <BR><B> Next:</B> <A NAME=tex2html2 HREF="node1.html"> Introduction</A><BR> <HR> <P><BR> <HR><P><ADDRESS><I>nuprl project <BR>Tue Nov 21 08:50:14 EST 1995</I></ADDRESS></BODY>⌨️ 快捷键说明
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