** “msharpmath”, **The Simple is the Best

[100] 001 Tutorial introduction introduction

Click the above button for full-text tutorial of introduction.

**m#math **works in an **expression-look-alike** style, and is easy to use. The core grammar has been developed at Seoul National University, and the product is released by Msharpmath Inc. The beta Version of m#math is free-of-charge for personal users.

As can be seen in our logo, a novel concept of ‘**Umbrella**‘ is innovated to realize an *‘expression-look-alike’* grammar. For example, the following m#math commands are almost the same as their relevant mathematical problems.

#> ( 1/2 + 1/3 + 1/5 ).ratio ; // ans=(31/30) with integer denomenator

#> 77.f ; // 77 Fahrenheit to other temperatures

#> 3’4” * 5’6” ; // area in square meter of 3’4” wide 5’6” high plate

#> (a,b,c)=(1,2,3); (b,c,a)=(a,b,c); // exchange values via tuples

#> [ 1,2,3 ; 4,5,6 ] .solve ; // x+2y = 3, 4x+5y = 6

#> .[ 1,2,3 ] .solve ; // x^2 + 2x + 3 = 0 (a leading dot for poly)

#> .[ 1,0,0,0 ].~ ; // sum_{x=1}^{x=n} x^3 = [(1/2)n(n+1)]^2

#> .[ 1,0,0,0 ].’ ; // p(x)-p(x-1)=x^3-(x-1)^3=3x^2-3x+1

#> [ 1,2,3 ] .roots ; // (x-1)(x-2)(x-3) = x^3 -6x^2 + 11x -6

#> s=0; for.n(1,10) s+=n; // s = 1+2+3+4+5+6+7+8+9+10

#> solve .x ( exp(x) = 5 ); // single nonlinear equation

#> solve .a.b ( a+b = 3, a*b = 2 ); // coupled nonlinear equations

#> plot .x( 0,pi ) ( |x|*sin(x) ); // plot 2d curve

#> int .x( 1,2 ) .y(x,2*x+1) ( exp(-x-y)*sin(x+y) ); // double integration

#> ode .t( 0,1 ) ( y’ = t*y+1, y = 1 ).plot; // ODE (Ordinary Differential Equation)

#> plot .r[21](0,1).t[61](0,6*pi) ( (r^(1/3)+t!/3) .cyl .y ) .cyl; // figure shown below

%> force-balance equation between springs

(k1,k2,k3,k4) = (100,50,75,200);;

F = 2000;;

solve .x1 .x2 .x3 .x4 (

k2*(x2-x1) = k1*x1,

k3*(x3-x2) = k2*(x2-x1),

k4*(x4-x3) = k3*(x3-x2),

F = k4*(x4-x3)

);

ans =

[ 20 ]

[ 60 ]

[ 86.6667 ]

[ 96.6667 ]

Also, consider multiple operations as in PV/T where

pressure : P = 300 torr = 39.9967 kPa

volume : V = 3.2 barrel = 0.5088 m^3

temperature : T = 30 C = 303.15 K

With these mixed units, we have

#> 300.torr * 3.2.bbl / 30.c ; // units as given

ans = 0.06712956

which is exactly the same as

#> 39.9967 * 0.5088 / 303.15 ; // in SI unit [kPa.m^3/K]

ans = 0.067129543

In many calculations involving unit conversions, all units are automatically converted into MKS unit. This would help scientists and engineers to avoid headache in unit conversions.

Our products are provided both in **Window** PC and **iOS** devices (iPad, iPhone and iPod touch). The iOS version can be downloaded from the Appstore by searching ‘msharpmath’. However, some of grammars have been changed and will be upgraded based on the Window-version in future.

One of the most striking features of Cemmath is its simple and concise grammar. Also, a small size (only a few megabyte) provides quick response for use.

m#math handles a number of data types including :

- double (real numbers)
- complex (complex numbers)
- poly (polynomial)
- matrix
- vertex (good for treating 3D space)
- csys (coordinate system)
- char
- string
- array of double, complex, poly, matrix, vertex, csys, char, string
- signal

Some of the standard C-language are implemented :

- if
- else
- do
- for
- while
- break
- continue
- goto
- switch
- case (only for interger value in cemnamu)
- default
- return
- void
- double

m#math covers a variety of fields including

- Unit conversions

Triangle ABC

2D graph

3D graph

Sequence and series

Coordinate system

mathematical functions

integration

differentiation

gradient, divergence, curl, Laplacian

Finding roots and minimum - interpolation and curve fitting

Initial Value Problems (IVP)

Boundary Value Problems (BVP)

Eigenvalue Problems

Parabolic Partial Differential Equations (PDE)

Elliptic PDE

Digital Signal Processing

Please support us to improve m#math** **by reporting any bugs or comments. We will continue to upgrade m#math. Thanks a lot.