Schyper

ABOUT

Dennis Gabil It becomes half-imaginary to write about something one sets out to do with only a fraction of it achieved. A glance at the menu of available functions on the home page or at the bottom of this page conveys the same; it's suggestive of what it is supposed to be, and yet, it's not the whole.

This project/web application is a concomitant of the fascination I had with the legendary MACSYMA program that I happened to read about in George B. Thomas Jr. and Ross L. Finney’s book Calculus and Analytic Geometry (6th Ed.) during my earliest days at St. Edmund’s College, Shillong. Back then, I had just started writing simple programs in Pascal during practical classes, like swapping two numbers or finding the sum of the first 10 natural numbers. The subsequent programming assignments in ascending complexity, like summing up the sine series for some x upto some n or approximating the roots of some equations using the Newton-Raphson method, gave me a feeling of doing something useful related to mathematics. Those programs were but confined to obtaining numerical results. But what I read of MACSYMA was different. In the aforementioned book, it was described as the program with the ability to evaluate “indefinite integrals by symbolic manipulation.” It made sense, as the answers we seek to mathematical problems aren't always numerical. When we factorize or expand algebraic expressions, or multiply polynomials, or prove trigonometric identities, the solutions we seek are generally algebraic expressions with an x or a \theta or some other variable in it. The MACSYMA math engine, written in a dialect of the language much older than those I was learning, came across as a reminder of the sublime things that can be achieved through programming, the hows of which I do not know yet.

In the days that followed I learned that there also exists other applications as well capable of doing symbolic manipulation and that they are collectively known as Computer Algebra Systems. I also learned of programs which do numerical computations, known as Numerical Software Packages, and those that create and manipulate geometric constructions, known as Interactive Geometry Softwares.

Some of the first Computer Algebra Systems I tried out were Maxima, PARI/GP, Fermat and Mathomatic (glad they are still around) and the initial impressions they made on me were deep. For example, I was at awe how strikingly fast the factorial of 10000 was computed and displayed in the console in the wink of an eye while the parallel versions we wrote for the same in our Pascal/C/C++ practical classes can barely hold the correct value upto the factorial of 12.

All these years, the urge to create a CAS of my own has stayed in the back of my mind, albeit dormantly. And although initially I had conceived of it as a desktop application (that of course was around 1999), now caught up in the Information Age, it has become only logical to create it as a web application. And so I begin this as a confluence of bits and pieces of those forgotten programs in the pages of my ageing college note books I wrote long ago and I have named it the Symbolic Computational HyperScriptorium, shortened to SCHYPER. It is a modest collection for a start and I have also made use of some PHP/JS browser-specific built-in objects/functions to total up to 36 computational functions. More functions will be added in the next sprint and in the sprint after that and so on. I also intend to include articles, biographies, games, infographics, jokes and quotes related to mathematics in the coming days.

SCHYPER will be a lifetime project; I will be appending features to it and refining existing ones, slowly expanding it over time.

Dennis Gabil

+91 9742 869379

P.S. The logo is an 'allegory' of Euler's famous equation e^{i\pi} = -1 in the Cartesian Plane.

FUNCTIONS