Mathematics in the internet
description
Transcript of Mathematics in the internet
Mathematics in the internet
Mika Seppälä
University of Helsinki and
Florida State University
We need to be able to
• Cut and paste mathematical objects
• Search information using the context of a formula as a key word
• Exchange scientific data so that the meaning gets understood automatically
• Produce scientific web material with live formulae
Proper standard encoding helps to avoid costly mistakes
• Ariane V explosion
• Mars orbiter
Standard encoding of mathematics
Needed for proper educational web material used for a virtual university
OpenMath and MathML
• Languages to define the meaning of mathematical formulae
• MathML covers K12 mathematics
• OpenMath extends MathML to all areas of mathematics (via extensible content dictionaries)
OpenMath solution
OpenMath language as defined by CD’s
Maple
Mathem.
Editor
Database
Browser
Translation between OM and proprietary presentations by phrasebooks
Preamble of an OpenMath CD
OpenMath Content Dictionary: arith1
Preamble of an OpenMath CD
OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd
Preamble of an OpenMath CD
OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd
Preamble of an OpenMath CD
OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd Defines: abs, divide, gcd, lcm, minus, plus, power, product, root, sum, times, unary_minus
Preamble of an OpenMath CD
OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd Defines: abs, divide, gcd, lcm, minus, plus, power, product, root, sum, times, unary_minus Date: 2001-03-12 Version: 2 Review Date: 2003-04-01
Preamble of an OpenMath CD
OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd Defines: abs, divide, gcd, lcm, minus, plus, power, product, root, sum, times, unary_minus Date: 2001-03-12 Version: 2 Review Date: 2003-04-01 Status: official Uses CD: alg1, fns1, integer1, interval1, linalg2, logic1, quant1, relation1, set1, setname1, transc1
OpenMath CD definitions
lcm The symbol to represent the n-ary function to return the least common multiple of its arguments. Commented Mathematical property (CMP): lcm(a,b) = a*b/gcd(a,b)
OpenMath CD definitions
Formal Mathematical property (FMP): <OMOBJ> <OMA> <OMS cd="relation1" name="eq"/> <OMA> <OMS cd="arith1" name="lcm"/> <OMV name="a"/> <OMV name="b"/> </OMA> <OMA> <OMS cd="arith1" name="divide"/> <OMA> <OMS cd="arith1" name="times"/>
<OMV name="a"/><OMV name="b"/>
</OMA> <OMA> <OMS cd="arith1" name="gcd"/> <OMV name="a"/> <OMV name="b"/> </OMA> </OMA> </OMA></OMOBJ>eq (lcm ( a, b) , divide (times ( a, b) , gcd ( a, b) ) )
OM definition of sin(x2+1)
x2
<OMOBJ>………. <OMS cd="arith1" name="power"/> <OMV name="x"/> <OMI>2</OMI>……….
</OMOBJ>
OM definition of sin(x2+1)
x2+1
<OMOBJ>………. <OMA> <OMS cd = "arith1" name="plus"/> <OMA> <OMS cd="arith1" name="power"/> <OMV name="x"/> <OMI>2</OMI> </OMA> <OMI>1</OMI> </OMA>……….
</OMOBJ>
OM definition of sin(x2+1)
(x2+1)
<OMOBJ>…… <OMATP> <OMS cd="presentation" name="left"/> <OMSTR>(</OMSTR> <OMS cd="presentation" name="right"/> <OMSTR>)</OMSTR> </OMATP> <OMA> <OMS cd = "arith1" name="plus"/> <OMA> <OMS cd="arith1" name="power"/> <OMV name="x"/> <OMI>2</OMI> </OMA> <OMI>1</OMI> </OMA> </OMATTR> </OMA></OMOBJ>
OM definition of sin(x2+1)
sin(x2+1)
<OMOBJ><OMA> <OMS cd="transc1" name="sin"/> <OMATTR> <OMATP> <OMS cd="presentation" name="left"/> <OMSTR>(</OMSTR> <OMS cd="presentation" name="right"/> <OMSTR>)</OMSTR> </OMATP> <OMA> <OMS cd = "arith1" name="plus"/> <OMA> <OMS cd="arith1" name="power"/> <OMV name="x"/> <OMI>2</OMI> </OMA> <OMI>1</OMI> </OMA> </OMATTR> </OMA></OMOBJ>
OpenMath and MathML Organizations
• W3 Math working group (chaired by A. Diaz and P. Ion)
• NAOMI
• OpenMath Society
• OpenMath Esprit project
NAOMI
• North American OpenMath Initiative
• Started by S. Braham (SFU) and R. Sutor (IBM)
• Partner organizations include FSU, NCS, Drexel, UC Berkeley
OpenMath Society
• Registered international society in Helsinki
• President: A. Cohen (Eindhoven, The Netherlands)
• Executive committee: A. Cohen, G. Gonnet, M. Seppälä, S. Watt, S. Braham, M. Dewar, M. Gaetano
• openmath.org hosted by FSU
OpenMath Esprit project
• Coordinated by M. Dewar (NAG, Oxford)
• Funding over 3 M$ for 1997-2000
• Included several academic and industrial partners in Europe
• Produced the OM standard, phrasebooks and tools to create and edit OM objects
Industrial partners of the OpenMath projects
• IBM (techexplorer group)
• Waterloo Maple
• Springer Verlag
• Other European partners
• North American partners
Example of a next generation OM application
Cellular telephone as a scientific calculator(following slides provided by mofile.com, inc.)