Creation of Sets/Array in z^3

Tricks and Shortcuts

Description

*Creating an Array

• Comma(,) has to be used to separate the elements(especially when negative numbers are in an array). This removes the ambiguity.

For example:(without comma)
a = [1 2 3; -4*5 -4 6; 7 8 10]
This gives the answer as:
a =  1 2  3
   -24 6
     7 8 10

with comma:
a = [1 2 3; -4*5, -4 6; 7 8 10]
a =  1  2 3
   -20 -4 6
     7  8 10

*Notations

• The unit operators work for simple or matrix parameters on both sides. This makes |-| be available for non-unit based subtraction. This is possibly a better notation.
• To do unit based subtractions, do

A=[1m 2m];
B=[4m 5m];
c=A<->B
c = [-3m -3m]

• Matrix subtraction, without units.

A=[1m 2m];
B=[4m 5m];
c=A|-|B
c = [-3 -3]

*Creating an Array within an interval

• An array can be created within a given interval using this notation. Brackets() are important.

var x = [];
xmin = 1
xmax = 2
dx = 0.2
x = (xmin-dx)..(xmax+dx)..(dx);
x = [0.8 1 1.2000000000000002 1.4000000000000001 1.6 1.8 2 2.2]

• To get the inverse of a matrix, add ~ to the array.

x = ((xmin-dx)..(xmax+dx)..(dx))
n = x~
n = 0.8
    1
    1.2000000000000002
    1.4000000000000001
    1.6
    1.8
    2
    2.2

*Evaluating a Function

• Calculating the value of function "u0" with corresponding values of x.

var x = [];
var u0 = [];
xmin = 1
xmax = 2
dx = 0.2
x = (xmin-dx)..(xmax+dx)..(dx);
u0 = EXP(-2<*>(x|-|0.25)<^>2);
u0 = [0.5460744266397094 0.32465246735834974 0.16447445657715493 0.07100535373963703 0.026121409853918226 0.008188701014374078 0.002187491118182886 0.0004979554215032733]

*PLOT

• Graph of x vs u0: Merge x and u0~ arrays using "mergerows" and include .graphin() to plot.

var x =[];
var u0 = [];
xmin = 1
xmax = 2
dx = 0.2
x = (xmin-dx)..(xmax+dx)..(dx);
u0 = EXP(-2<*>(x<->0.25)<^>2);
m = (x).mergerows(u0~).graphin()

The graph looks as shown below.