Z3

This page gives you information about z^3 language, operators, functions etc.

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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-0.2608063395600766,0.3107987651601434,-0.36583504383452237,-0.34252223931252956,0.16313816863112152,-0.386728432495147,-0.4420854849740863,-0.0289194923825562,0.4190911327023059	-0.41857722331769764,-0.3457936530467123,0.3407129691913724,0.17490631970576942,0.4740190056618303,0.33442569547332823,-0.4021838700864464,0.01767508266493678,0.19617761834524572	-0.005285372259095311,0.2860999288968742,0.2895744510460645,-0.42999060708098114,-0.2451291240286082,0.46434784517623484,-0.06909980205819011,0.016562352422624826,-0.41358066350221634	-0.143253271933645,-0.17276814603246748,-0.34271695581264794,0.42872798326425254,-0.3591233992483467,-0.3483293631579727,0.2119363124947995,-0.43084264802746475,0.4917781667318195	-0.4926239042542875,0.47259499062784016,0.2176911027636379,0.4266858506016433,-0.3561588164884597,-0.18736131326295435,0.34525797073729336,0.07538306643255055,0.4284512938465923	0.2962957404088229,-0.19573178025893867,0.0802487323526293,0.43155232118442655,-0.3102017848286778,-0.3444714401848614,0.25591936474666,0.37851681909523904,0.33791361656039953	-0.3690603149589151,-0.16680384473875165,0.12651539221405983,0.042686946922913194,0.4994191285222769,-0.04251782689243555,0.4586381970439106,-0.013901118887588382,-0.4791243502404541	-0.04867852199822664,0.2621756491716951,0.08170396974310279,-0.161636077798903,-0.15682890987955034,0.023121989564970136,0.17740983609110117,0.20641399989835918,0.43295700242742896	0.30700156721286476,0.09756432077847421,0.2700566719286144,0.2743928460404277,-0.07327439147047698,0.07790404907427728,-0.1943378746509552,-0.16528425505384803,0.49998670746572316
-0.2022708582226187,-0.47838392690755427,-0.0903228900860995,-0.29938447126187384,-0.38560304301790893,-0.007816316559910774,-0.32445228099823,0.15714373532682657,-0.4018373831640929	0.07826365740038455,0.1967176734469831,0.2824950881768018,0.47379933670163155,0.2517655179835856,0.0695308344438672,0.19463025103323162,0.42969443020410836,-0.3645740863867104	-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.

• z^3 Editor and Keys

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.

• z^3 Commands and Operators

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 Addition
<->    - 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

• z^3 Language Documentation

Operators

@: Function Apply Operator

1..100@SIN

~: Transpose Operator

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

↑ and ↓: Ascending and Descending Operator

	
	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

Logical Statements

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*/
        	  /*Break is automatically added. */
        	  /*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)
	

z^3 Array Manipulation

Refer z^3 Array Manipulation

Fractions

Refer Fractions

z^3 Units

Refer z^3 Units page

z^3 Constants

Constants	Value	Abbreviations
Acceleration Of Gravity- Gee	9.80665 m·s−2	%gee
Acceleration Of Gravity (Gee, Free-Fall On Earth)	9.80665 m·s−2	%g
Atomic Mass Constant	1.66053892173e−27 kg	%atomic
Avogadro'S Number	6.0221412927e23 mol−1	%avogadro
Bohr Magneton	9.2740096820e−24 J·T−1	%bohr
Bohr Radius	5.291772109217e−11 m	%bohrradius
Boltzmann Constant	1.380648813e−23 J·K−1	%boltzmann
Characteristic Impedance Of Vacuum	376.730313461 Ω	%characteristic
Classical Electron Radius	2.817940326727e−15 m	%classical
Conductance Quantum	7.748091734625e−5 S	%conductance
Conventional Value Of Josephson Constant	4.835979e14 Hz·V−1	%conventional
Conventional Value Of Von Klitzing Constant	25812.807 Ω
Coulomb'S Constant	8.987551787e9 N·m2·C−2
Efimov Factor	22.7	%efimov
Electric Constant Vacuum Permittivity	8.854187817e−12 F·m−1	%electric
Electron Mass	9.1093829140e−31 kg	%electronmass
Elementary Charge	1.60217656535e−19 C	%elementary
Faraday Constant	96485.336521C·mol−1	%faraday
Fermi Coupling Constant	1.1663645e−5 GeV−2	%fermi
Fine-Structure Constant	7.297352569824e−3	%fine
First Radiation Constant	3.7417715317e−16 W·m2	%first
First Radiation Constant For Spectral Radiance	1.19104286953e−16 W·m2·sr−1
Gas Constant	8.314462175 J·K−1·mol−1	%gas
Hartree Energy	4.3597443419e−18 J	%hartree
Inverse Conductance Quantum	12906.403721742 Ω	%inverse
Josephson Constant	4.8359787011e14 Hz·V−1	%josephson
Loschmidt Constant	2.686780524e25 m−3	%loschmidt
Magnetic Constant Vacuum Permeability	1.256637061e−6 N·A−2
Magnetic Flux Quantum	2.06783375846e−15 Wb
Molar Mass Constant	1e−3 kg·mol−1	%molarmass
Molar Mass Constant Of Carbon-12	1.2e−2 kg·mol−1
Molar Planck Constant	3.990312717628e−10 J·s·mol−1	%molar
Molar Volume Of An Ideal Gas At T=273.15K And P=100Kpa	2.271095321e−2 m3·mol−1	%molarvolume
Molar Volume Of An Ideal Gas At T=273.15K And P=101.325 Kpa	2.241396820e−2 m3·mol−1
Newtonian Constant Of Gravitation	6.6740831e−11 m3·kg−1·s−2	%newtonian
Nuclear Magneton	5.0507835311e−27 J·T−1	%nuclear
Planck Charge	1.87554595641e−18 C	%planckcharge
Planck Constant	6.62607004081e−34 J·s	%planck
Planck Length	1.61619997e−35 m	%plancklength
Planck Mass	2.1765113e−8 kg	%planckmass
Planck Temperature	1.41683385e32 K	%plancktemperature
Planck Time	5.3910632e−44 s	%plancktime
Proton Mass	1.67262177774e−27 kg	%proton
Quantum Of Circulation	3.636947552024e−4 m2 s−1	%quantumof
Reduced Planck Constant	1.05457180013e−34 J·s
Rydberg Constant	10973731.56853955 m−1	%rydberg
Sackur-Tetrode Constant At T=1 K And P=100Kpa	−1.151707823	%sackur
Sackur-Tetrode Constant At T=1 K And P=101.325 Kpa	−1.164870823
Second Radiation Constant	1.438777013e−2 m·K	%second
Speed Of Light In Vacuum	299792458 m·s−1	%speed
Speed Of Sound In Dry Air	343.2 m·s−1
Standard Atmosphere	101325 Pa	%atm
Stefan–Boltzmann Constant	5.67037321e−8 W·m−2·K−4	%stefan
Thomson Cross Section	6.65245873413e−29 m2	%thomson
Von Klitzing Constant	25812.807443484 Ω	%von
Weak Mixing Angle	0.222321	%weak
Wien Displacement Law Constant	2.897772126e−3 m·K	%wien

ZOS and Calci functions Categorywise

Refer ZOS and Calci functions Categorywise

z^3 API functions

Refer z^3 API Functions page

z3 Language Test

Check z^3 language skills

Z3_Exercises

List of few z^3 exercises for you to try out

• <<Back to ZCubes Home