“Project Trinity” Mathematical Computation Environment Supports Program Proposal

Sage-Math Development Project

2009.10.21

Duk-Sun Kimmass@skku.edu

Background

- Jan. 2008 - JMMC Conference in San Diego, Sage-Math has a good presentation.

(Introduction for the Sage-Math and its usage)

- Jun. 2008- First Sage-Math server was prepared in the department of mathemat-

ics. (http://math1.skku.ac.kr) under the guidance of Prof. Sang-Gu Lee

- Version : 2.5 / A PC server was donated by Prof. Sang-Gu Lee - For other testing, we prepared one tentative server on the old-PC.

(http://galois10.skku.ac.kr) : Now it was not available.

- Sep. 2008- Prof. Dan Drake showed his interest on our service of Gage-Math and

informed a warning for the security

- Throughout this communication, we made a connection with Prof. W. Stein who is a leader of the development team for Sage-Math.

Background

- Jan. 2009 - With J.-Y. Bak, we made some outcome with our Sage-Math.

(published at the JKSME, Series E)

- Apr. 2009 - Prof. Dan Drake gave an invited talk on his Sage-Math at

Sungkyunkwan University.

- Jun. 2009- First step for Korean version of Sage-Math was completed.

(with J.-Y. Bak, http://math1.skku.ac.kr)- In spring, we had made some outcome with our Sage-Math in our Lin-

ear Algebra classes (with J.-Y. Bak and R.-Y. Koh)

- Sep. 2009- Prof. Dan Drake was invited to introduce Sage-Math at KSME fall con-

ference.- We developed the Mobile Service on the Sage-Math (with J.Y. Park)

Situation

Sage-Math

Service (Dept. of Math.)

http://math1.skku.ac.kr• Main Sage-Math Server• Mobile Service Implemented• Educational Implements con-

tained (LA)• Secured• Based on the Fedora 9 Linux

Operating System

http://math2.skku.ac.kr• Tentative Server (for

developers)• Not secured• Experimental Use ONLY• Fedora 11 Linux will be

used

http://galois09.skku.ac.kr• Support the web-

based functions• PHP, Python Support• XML-RPC Platform

developed

Math1 Re-Design

Useful Functions in our classes

Explanatory example: Taylor Series

This is the code and a mockup animation of the interact command. It defines a slider, seen on

top, that can be dragged. Once dragged, it changes the value of the variable "order" and the whole block of code gets evaluated. This

principle can be seen in various examples pre-sented on the pages above!

Useful Functions in our classes: CalculusDirectional Derivatives

This interact displays graphically a tangent line to a function, illustrating a directional derivative (the slope of the tangent line).

3D graph with points and curvesBy Robert Marik This sagelet is handy when showing local, con-strained and absolute maxima and minima in two variables

Useful Functions in our classes: Linear Algebra

Gerschgorin Circle Theorem

by Marshall Hampton. This animated ver-sion requires convert (imagemagick) to be installed, but it can easily be modified to a static version. The animation illustrates the idea behind the stronger version of Gerschgorin's theorem, which says that if the disks around the eigenvalues are dis-joint then there is one eigenvalue per disk. The proof is by continuity of the eigenval-ues under a homotopy to a diagonal ma-trix.

Useful Functions in our classes

http://wiki.sagemath.org/interact

Future PlanMake the “Trinity Structure” for the persistency

Math2

Support Main

ServerLecture

Dominator

Math1

Main Server

Math3

Research ServerWAP

RPGS

Ga-lois09

Load-Balancer(Distribution of all loads)

(Parallel Algorithm Support)

Support Classes: Calculus and LA

For the research

SpecificationsAll system will be constructed with PC-Server

Math2

Support Main

ServerLecture

Dominator

Math1

Main Server

Math3

Research ServerWAP

RPGS

Ga-lois09

Load-Balancer(Distribution of all loads)

(Parallel Algorithm Support)

CPU: Intel E6400(Dual-Core)RAM : 2Gbyte(Already Prepared)

CPU : P-IV 2.4G (Built in 1999)RAM : 512Mbyte(Already Prepared)

CPU : P-IV 2.4G (Built in 1999)RAM : 512Mbyte(Already Prepared)

CPU : P-IV 2.4G (Built in 1999)RAM : 512Mbyte(Not prepared)

CPU: Intel E6600(Dual-Core)RAM : 2Gbyte(Already Prepared)

CPU: Intel E6600(Dual-Core)RAM : 2Gbyte(Not prepared)

SchedulesDetail schedule with server groups

Math2

Support Main

ServerLecture

Dominator

Math1

Main Server

Math3

Research ServerWAP

RPGS

Ga-lois09

Load-Balancer(Distribution of all loads)

(Parallel Algorithm Support)

Already Completed

Nov. 2009 : TBA

Dec. 2009 : TBA

Continuous Proceeding(Support Web-Functions)

RPG with Sage-Math : Oct. 2009Mobile RPG with Sage-Math : Nov. 2009

Dynamic Multimedia Contents with RPG and Sage-Math : Dec. 2009

Feb. 2010 : LBS will be appeared

Effectiveness

- Cost - Sage-Math is a free software which have similar functions with the Mathematica, MATLAB and Maple.

- It will reduce our cost to buy expensive softwares for our class.

- Connectivity- Sage-Math is based on our internet environment.- When researchers want to do computation in any place, we can make

them to find the result whenever they have internet connection. (We offer our pub-lication system in our Sage-Math server.)

- Teaching- Students obtain chance to use a good mathematical software without

any cost.- We can solve problems involving large size computation over simple

text-book problems and students can think of proper mathematical models in real world problems.

Thank you for your interesting in my proposal.