# Difference between revisions of "Z3"

## Introduction

Why another programming language? Do we not have enough of them?

Well, let us try this real world experiment. Go to the best programmer you know. Pick the simplest formula you can think of: E=mc2. Ask how the Energy (E) can be calculated, for a mass (m) of 1kg, 2kg, 3kg,… 10kg and for a constant Speed of Light (3x10^8m/s). And let us just watch the programmer for what happens next. Yes, go ahead and start a stop watch!

Likely that the programmer would pull up a spreadsheet and type formulae notation such as shown below, to do this, within a minute or so.

 C =3*10^8 M Energy 1 =D5*\$E\$3^2 =D5+1 =D6*\$E\$3^2 =D6+1 =D7*\$E\$3^2 =D7+1 =D8*\$E\$3^2 =D8+1 =D9*\$E\$3^2 =D9+1 =D10*\$E\$3^2 =D10+1 =D11*\$E\$3^2 =D11+1 =D12*\$E\$3^2 =D12+1 =D13*\$E\$3^2 =D13+1 =D14*\$E\$3^2

Or maybe, the programmer would make a program, in a computer language to do this, and will come back to you in about an hour!

Well, this shows the poor state of the current state of the art computer human interaction. Today, an ordinary computer can do billions of operations per second. And even with the best techniques, translating from our human language to computer language takes minutes or hours!

Now, what if, if we could just say:

Energy:=m*(3*10^8)^2

Energy@1..10

And the results come out:

 m Energy 1 90000000000000000 2 180000000000000000 3 270000000000000000 4 360000000000000000 5 450000000000000000 6 540000000000000000 7 630000000000000000 8 720000000000000000 9 810000000000000000 10 900000000000000000

Or let us imagine you wanted to create an array of 9 rows and 9 columns and with 9 cells each in 3 dimensions, and z^3 would give this to you with the command:

|9x9x9|

 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0 0,0,0,0,0,0,0,0,0

What if you could fill it with random numbers and assign it to A using:

A=RANDOM(|9x9x9|)

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-0.027604628819972277,-0.022821340011432767,-0.3781412618700415,0.4142134212888777,0.12101718713529408,-0.008385246619582176,-0.3361411860678345,0.438513757660985,0.4385419557802379 -0.06667872029356658,0.06350918905809522,-0.1931271613575518,-0.3754569529555738,0.4396738887298852,0.3152043076697737,-0.10245247255079448,-0.23103816714137793,-0.22935058921575546 -0.24598459526896477,-0.20915936143137515,-0.226813254179433,0.41752541926689446,-0.4017587248235941,-0.45505133643746376,-0.1271870033815503,-0.41925627854652703,-0.4875814290717244 0.20632574148476124,0.20196053222753108,-0.34814507188275456,0.2960397240240127,-0.08257539756596088,-0.3015523599460721,0.37208341457881033,-0.1326182004995644,0.34098264505155385 0.04407765343785286,0.420143665978685,-0.08965241932310164,-0.4079979187808931,-0.3565519633702934,-0.018076440319418907,0.4534321865066886,-0.2951448289677501,-0.1633545272052288 -0.21133289858698845,-0.07556938286870718,0.1189079019241035,-0.1346991437021643,-0.370825408725068,-0.1300838114693761,-0.09347013221122324,-0.12794372951611876,0.36772827967070043 -0.03696576110087335,0.4258665544912219,-0.13509223307482898,-0.3952769173774868,-0.3180696666240692,0.24897645460441709,0.1436553478706628,0.13836245937272906,0.21769006550312042 0.23965330887585878,-0.3712375834584236,0.44605221855454147,0.3071361028123647,-0.15616067801602185,-0.414444058900699,-0.1781746146734804,0.3204122583847493,0.4556370184291154 -0.11982318083755672,-0.21459656162187457,0.05913971993140876,0.39466725406236947,-0.37277397280558944,-0.3931461414322257,-0.07019152771681547,-0.29783264151774347,-0.009687110083177686 0.33500119112432003,0.2673738191369921,0.1282032411545515,-0.30506192496977746,-0.11686063115485013,-0.33484474173747003,0.411201735958457,0.041212135925889015,-0.4215310923755169 0.29349666088819504,0.40313133667223155,-0.04813785175792873,0.47613331652246416,-0.38947859266772866,0.1780794879887253,0.4989867629483342,0.1881732391193509,0.46752460254356265 0.3259336925111711,0.2213933274615556,-0.3023625467903912,0.47005707561038435,0.05567215685732663,0.22283329139463603,0.1105746019165963,0.1529993456788361,0.2278926013968885 -0.43219304690137506,0.0294269397854805,0.46398221468552947,-0.3116440454032272,-0.47513903118669987,-0.07985166111029685,-0.443554509896785,0.15013995114713907,0.09688317100517452 0.16715386998839676,-0.4456294975243509,-0.07369275717064738,-0.3025795437861234,-0.027793404879048467,-0.0484570418484509,-0.22052075434476137,-0.4531863001175225,-0.12990865157917142 -0.21291427174583077,-0.20333527983166277,0.3869544540066272,0.2600411137100309,-0.4836206557229161,-0.15566928149200976,-0.08516661822795868,-0.38520910614170134,-0.0015736056957393885 0.08731097495183349,0.09316025790758431,-0.18632080289535224,-0.2906111949123442,-0.461293478962034,-0.18076600949279964,-0.023019180865958333,-0.4638032771181315,0.2364378476049751

Wow!

That is why we created a simple Language for you and the machine called: z^3.

## Editor and Short cut Keys

In the code editor, generally, you can type the function name (case sensitive), and Shift+Enter will give you parameter expansion. Say CUBEROOT and Shift+Enter will give you CUBEROOT(Number)

or PMT Shift+Enter will give you PMT(Rate,NoPaymentPeriods,PresentValue,FutureValue,Type)

Generally z^3 Editor automatically shows a listbox with likely functions that you could use given a few letters.

Code expansion also works with things like for, ifelse, switch, zswitch, zif, etc. Simply press Shift+Enter after you type the term.

Say, type FOR and then press Shift+Enter.

Errors are highlighted immediately to give you help with typing things in correctly.

Most functions are Combanatorial. That means you can run them as: PMT((12..20)%,12,1000) or SQRT(1..100) or COMBIN(10..100..10,2..3) etc.

# List of Operators

+,  -,  *,  /, ^, %	 - Arithmetic Operators
| |    - Array Function and Creation Operator
..     - Arithmetic and Geometric Series Creation
...    - Arithmetic and Geometric Series Creation
@      - apply to
#      - Series or Special Case Qualifier for Dates, Calci  Cells, and Sequences, etc.
<<<    - Member or Variable Assignment
<>     - Unit Conversion
<->    - Unit Substraction
<*>    - Unit Multiplication
</>    - Unit Division
()     - Function Call
[]     - Set Creation
- Object Set
- Set Object Membership
.      - Member Function Dereferencing.
. mf   - Member Function
.\$ mf(function, parameters)   - Element-wise Function Application
.\$\$ mf (special	        – Row-wise Function Application
.\$\$\$ mf (special) 	– Column-wise Function Application
.\$_ mf (special)	- Cumulative Function Application (all)

::     - If
:::    - switch

# Short Cut Keys

CTRL+G - to convert into Greek Code
CTRL+U - Converts SIGMA to Σ
SHIFT+ENTER- Gives Parameter Expansion
Double tap SHIFT - Toggle Capital and Small Letter [Ex: Convert FRACTAL to fractal and vice verse]
CTRL+SPACE - Function Listing

# Operators

1..100@SIN

[[[1..10]~]~]~

MAGICSQUARE(5)!
(1..100)↓
(1..100)↑

## ⧓,⧒,⧒ and ⋈: Between Operators

a=-1;
⧓(1,a,30)
a=29;
⧓(1,a,30) //between g

a=31;
⧒(1,a,30) //xlbetween g
a=30;
⧒(1,a,30) //xlbetween g

⧒(1,2,30) // xlb g
⧒(1,1,30)

a=29;
⋈(1,-1..31,30);

⧓(1,-1..5,4);

[
⧓(1,1,30),
⧓(1,0,30),
⧓(1,10,30),
⧓(1,31,30),
⧑(1,29,30),
⧑(1,30,30),
⧑(1,1,30),
⧑(1,30,30),
⋈(1,1,30),
⋈(1,3,30)
]

## √: Square Root, Cube Root, Fourth Root and Nth Root Operators

√(3+34)
∛(27.01)
√√64
ROOTNTH(1..10,4)
// root is first parameter
NTHROOT(1..10,4)
// root is second parameter

NTHROOT(1..100,2)
NTHROOT(1..100,4)
ROOTNTH(1..100,2)
ROOTNTH(1..100,4)
3√81

## If Statements

a=3;
(a<0)::{"whatever"},
{
!(a>4)::
{"whateverelse"},
{"whateverelseleft"}
}

(a>4)::
{"whateverelse"},
{"whateverelseleft"}

## Switch Statements

Apart from the conventional Javascript switch statement syntax, z^3 enhances language simplicity with a new style.

The new z^3 switch statements syntax is as follows.

discriminant:::
{
x, y::
/*statements to be executed if x or y is true*/
/*Simply add an empty statement using a simple extra semicolon (;)) */
,
z::
/*statements to be executed if z is true*/
,
default::
}
For example,
b=0;
c=343;
fruits="mango";
fruits:::
{
"apple","tomato"::
b++;
c=3.4;
,
"mango"::
b=34905;

,
default::

b=45.6;

}
[b,c];

switch(a)
{
case b:
case c:
break;
default:
break;
}

## Loops

a=1;
do
{
a++
}
until(a>20); // do while(!condition)
a; // here this will be 21, since !condition is checked like a do while loop.

a=11;
b=45;
because(a<b)
{
a++
OUTPUT(a)
}

a=11;
do
{
a++
}
unless(a==11);
a;

# Function Declarations

function y(x)
{
∵(x<345)
{
∴(x+3434)
}
∵(x>345)
{
∴(x-3434)
}
}
y(13);

The letter Ƒ can also be used instead of the full term function.

Ƒ y(x)
{
∵(x<345)
{
∴(x+3434)
}
∵(x>345)
{
∴(x-3434)
}
}
y(13);

# Existential Quantification

a=1..100;
∀a("x<810")
∃a("x<810")
∄a("x<810")

a=1..100;
[∀a("x<810"),∃a("x<810"),∄a("x<810")]
a=1..100;
[∀a("x<810"),∃a("x<810"),(!∄a("x<0"))]

a=1..100;
b= ∀a("y*2<200");
b.result

a=1..100;
b= ∀a("y*2<=50");
a.pick(b.result)

//make a pick operator based on a similar array of true false. or non-existant to get the values out.
//PICK

a=1..100;
b= ∀a("y*2<50");
a.pick(b.result)