Units

How to specify units

Units are a unique, inherent and simple feature of the z^3 language.

Using units is simple and easy. For example:

a=1m;

indicates that a is now a variable containing the value of 1 meter. For more complex units we can enclose them in brackets as in 3(m/sec).

If a variable needs to be specified in specific units, simply use the <> operator. Such as: a<>(m/sec);

In z^3 language, <> is the unit conversion operator. Also, any arithmetic operator such as +, -, *, /, ^, % etc. should be enclosed within < and > to allow unit conversions to propagate through these operations. These conversion operations can be done on arrays as parameters also. Hence to add a meter to 2 centimeters, do the following: a=1m<+>2cm; and z^3 will give the answer: 102 cm.

Note, that this result now carries the units with it for further operations. For example: a=(1m<+>2cm)<^>3; gives the answer as 1061208 cm3.

To convert the current value of a variable to a different unit, simply use the <> operator: a<>cm;

Notice that if a already had a unit, it will be appropriately converted using the units. If it did not have units inherently, it will simply be given the units. $> a=1 1 $> a<>cm; 1 cm.

$> a=1m; 1 m. $> a<>cm; 100 cm.

In the second case, 1m is converted to 100cm.

Unit Prefixes

Similarly, scales such as milli, mega, etc. are supported using conventional SI units. a=1m; 1 m. a<>ym; 1.0000000000000001e+24 ym.

Here a now has the unit yoctometer.

Using uppercase Y, we get the answer in Yottameter. a=1m; 1 m. a<>Ym; 1.0000000000000001e-24 Ym.

These conversions of scale follow the SI unit prefix standards.

Conversion among Unit Systems

z^3 supports conversion among unit systems, such as SI Units and FPS systems.

For example:

a=1mi; 1 mi.

a<>km; 1.6093439999999999 km.

Notice that the mi (miles) unit of variable a is converted to km.

Units on Array of Values

Units work on variables as simple numerical values or as arrays.

Let us consider numbers 1 to 100. a=1..100;

b=a<>(mi);

b<>mi<>km b<>mi<>km

Numeric	Units	UNITSOF
1mi	km	1.6093439999999999km
2mi	km	3.2186879999999998km
3mi	km	4.828031999999999km
4mi	km	6.4373759999999995km
5mi	km	8.046719999999999km
6mi	km	9.656063999999999km
7mi	km	11.265407999999999km
8mi	km	12.874751999999999km
9mi	km	14.484096km
10mi	km	16.093439999999998km
11mi	km	17.702783999999998km
12mi	km	19.312127999999998km
13mi	km	20.921471999999998km
14mi	km	22.530815999999998km
15mi	km	24.140159999999998km
16mi	km	25.749503999999998km
17mi	km	27.358848km
18mi	km	28.968192km
19mi	km	30.577536km
20mi	km	32.186879999999995km
21mi	km	33.796223999999995km
22mi	km	35.405567999999995km
23mi	km	37.014911999999995km
24mi	km	38.624255999999995km
25mi	km	40.233599999999996km
26mi	km	41.842943999999996km
27mi	km	43.452287999999996km
28mi	km	45.061631999999996km
29mi	km	46.670975999999996km
30mi	km	48.280319999999996km
31mi	km	49.889663999999996km
32mi	km	51.499007999999996km
33mi	km	53.108352km
34mi	km	54.717696km
35mi	km	56.32704km
36mi	km	57.936384km
37mi	km	59.545728km
38mi	km	61.155072km
39mi	km	62.764416km
40mi	km	64.37375999999999km
41mi	km	65.983104km
42mi	km	67.59244799999999km
43mi	km	69.201792km
44mi	km	70.81113599999999km
45mi	km	72.42048km
46mi	km	74.02982399999999km
47mi	km	75.639168km
48mi	km	77.24851199999999km
49mi	km	78.857856km
50mi	km	80.46719999999999km
51mi	km	82.076544km
52mi	km	83.68588799999999km
53mi	km	85.295232km
54mi	km	86.90457599999999km
55mi	km	88.51392km
56mi	km	90.12326399999999km
57mi	km	91.732608km
58mi	km	93.34195199999999km
59mi	km	94.951296km
60mi	km	96.56063999999999km
61mi	km	98.169984km
62mi	km	99.77932799999999km
63mi	km	101.388672km
64mi	km	102.99801599999999km
65mi	km	104.60735999999999km
66mi	km	106.216704km
67mi	km	107.82604799999999km
68mi	km	109.435392km
69mi	km	111.04473599999999km
70mi	km	112.65408km
71mi	km	114.26342399999999km
72mi	km	115.872768km
73mi	km	117.48211199999999km
74mi	km	119.091456km
75mi	km	120.70079999999999km
76mi	km	122.310144km
77mi	km	123.91948799999999km
78mi	km	125.528832km
79mi	km	127.13817599999999km
80mi	km	128.74751999999998km
81mi	km	130.356864km
82mi	km	131.966208km
83mi	km	133.575552km
84mi	km	135.18489599999998km
85mi	km	136.79424km
86mi	km	138.403584km
87mi	km	140.012928km
88mi	km	141.62227199999998km
89mi	km	143.231616km
90mi	km	144.84096km
91mi	km	146.450304km
92mi	km	148.05964799999998km
93mi	km	149.668992km
94mi	km	151.278336km
95mi	km	152.88768km
96mi	km	154.49702399999998km
97mi	km	156.10636799999997km
98mi	km	157.715712km
99mi	km	159.325056km
100mi	km	160.93439999999998km

---

a=(1..100)<>℃ b=a<>℉

E:=(m<>kg)*(SPEEDOFLIGHT()<^>2); E(2kg)

a=1mi; b=10km; [a,b,(a<+>b)<>mi]

10mi<>km

Pi seems to be obfuscated.

SIN(90<>deg)

(rad2piby10)<>rad<>deg

((rad2piby10)<>rad<>deg)@SIN .graphin() //did not work in safari. (1..10)<>kg

b=(100$<+>3020¢); b<>$;

SETCONVERSION(1<>euro,1<>dollar,1.1)

SETCONVERSION(1$,1€,0.9); PRINTCONVERSION(); 345$<>€

1$<>1₹ // without conversion will fail.

(1..100)<>℃<>℉

SETCONVERSION(1<>€,1<>$,1.1); (1..100)<>€<>$

SETCONVERSION(1<>€,1<>$,1.10); (1..1000..10)<>€<>$

SETCONVERSION(1<>€,1<>$,1.10); (0..1000..20)<>€<>$

UNITIFY([1m,2m,3cm])

SUM(UNITIFY([1m,2m,3mm]))

(100$<+>300¢<+>30¢)<>$ PMT(4%,12,1000$,120000¢,0)

PMT(4%,12,1000$,1200.00¢,0) PMT(4%,12,1000$,120000¢,0)

1<>gal<>l 1<>l<>oz

(1..100)<>l<>ul 1Pa<>atm

E:=(m<>kg)<*>(SPEEDOFLIGHT()<^>2); b=E(2g); ConvertToUnitOfNature(b,"energy")

1m<>>1cm;

[1m,2m]<>>[1cm,200cm];

[1m,2m]<>=>[1cm,200cm];

[1m,2m]<<>[1cm,200cm];

[1m,2m]<<>[1cm,200cm];

[1m,2m]<==>[1cm,200cm];

[1m,2m]<!=>[1cm,200cm];

[1m,2m]<<=>[1cm,199.99cm];

[1m,2m]<<=>[1cm,200.01cm];

((1..10)<>m)<>>3m;

((0.1..10)<>m)<>>30cm

CONSTANT("G") CONSTANT("G")<*>1kg<*>110kg</>(6000m<^>2) // did not work.

(CONSTANT("G")<*>1kg<*>110kg)</>((6000m)<^>2) // how to bracket the units to be inside and ignore < etc? // ## can be used to name variables with spaces in them. // the actual variable is named by removing the spaces. // otherwise it goes into code as it is. ##weight of zone=3m; ++(##weight of zone);

##weight of zone=3m; a=3.4mm<+>(##weight of zone);

//%G is gravitational constant GF:=%G*m1*m2/r^2; GF(1,2,300)

v:=u+%g*t; // this uses %g as default g value v(1,2)

%planck %boltzmann; %planck length;

PRINTCONVERSIONS() CONSTANTS() CONVERT()

A¹=34; A=[23,4,5,5]; /* no array indexing on subscript yet. Will decide on that later. */ A¹=[23,4,5,5] A¹[2]

a=%gravit; b=30<*>a

a=%gravit; b=(1..10)<*>a

E:=m<>kg<*>%c<^>2; E(1000kg) E(1000kg<>lbm) // - will gave same result as 1000kg E(1000lbm) //lbm is used for units of lb mass.

// %G<*>1kg<*>110kg(6000m<^>2) // %G<*>1kg<*>110kg((6000m)<^>2) // -did not work. Said 7.34149141e-9Nm3UNITPOWERUNITSOF %G<*>1kg<*>110kg<*>((6000m)<^>2)

%G<*>1kg<*>110kg</>((6000m)<^>2)

// make this work. 1..100 @> x.txt; // send output to a <@ x.txt; // read input from a;

1.3J<>GeV 1.3J<>eV

1J<>l.atm; // 0.0098692latm 1J<>(l.atm-1) // this should fail. and will keep original units. maybe safer. 1m2<>in2 1m²<>in²

10m2<>are 1m2<>are

100m2<>acre

E:=m<>kg<*>%c<^>2; b=E(1000kg)<>J

   c=b<>eV;

[b,c]

1..100.$("[SIN(x),COS(x),TAN(x)]") 1..100.$([SIN,COS,TAN]) worked. 1..100.$("[x,x^2,x^3,x^4,x^3+x^4,SIN(x)]") works 1..100.$("[SIN(x),COS(x),TAN(x)]") 1..100.$([SIN,COS,TAN]) x=SERIESOF("1/x",9,10) //this is to from in parameter sequence. x=SERIESOF("1/x",19,10) SERIESOF("1/x",10,5) x=SERIESOF "1/LOG(x,2)" 100 1 x=SERIESOF "1/log2x" 100 91 //removed: 1..10.$_([+,-]) 1..10.$_([SUM,MINUS]) //removed: 1..10.$_|+| EXPOF(5) [SIN,COS]@[1..100] 1..10.$_("+") 1..10.$_("+") 1..10@["+"] 1..10@"+"

(1..100)<>m<+>10cm

MAGICSQUARE(3).$$(SUM) MAGICSQUARE(3).$$$(SUM) MAGICSQUARE(3).$_(SUM)

a=1m<>mm<+>400km 1m<>eor // should give nothing as there is no such conversion. (((1..100)<>m)<^>2)<>are

(1..1000)<>$ (((1..100)<>m)<^>2)<>km2 // why chinese headers here?

(1..100)m<>cm

F=%G<*>100kg<*>10g</>((100km)<^>2);

1.3J<>GeV //check this

velocity=3<>(m/sec); time=1hr; velocity<*>time;

1(g.m)<>(mg.cm)

a=LAZYRANGE(1,100) a(1..100) // generate numbers in the range at that interval, without having to generate the array ahead of time. Useful in things like INTEGRALS etc. a() a=LAZYOBJECT(1,100,1000) // can even take a(0.1); a.islazyrange()

1(kg.m2s-2)<>(N.m) 1(kg.m2s-2)<>J 1(kg.m2s-2)<>(N) // also should work as we want to get rid of the /s here in this case. 1(kg.m2s-2)<>(N.m2) // should fail. 1(kg.m2s-2)<>(J/s) // should fail. 1(kg.m2s-3)<>(J/s) 1(kg.m2.s)<>(J/s) // should this fail? it works now.

12(g.m-1/s)<>(g.cm) // should fail. 12(g.m)<>(g.mm) // should not fail. 12(g.m)<>(g.cm) // should not fail.

12(g.m)<>(g.s) // should fail. original should be returned. 12(g.m)<>(g.mm) 12(g.m)<>(g.s) 12(g.m-1)<>(g.mm-1) 12(g.m-1/s)<>(g.cm-1) // converts, but this is ok, since /s on left sometimes we want to get rid off for some reason for using it on another calculation. Say N/s but you only want to use the N on it. 1(kg.m2/s2)<>e // how to make this conversion?

1(kg.m2/s2)<>J<>e

1.3(kg.m2/s2)<>Jo // would fail and original will be kept.

(((1..100)<>m)<^>2)<>are (1..100)<>are [1cm2,2m2]<>are %pi*34; %e; %avo;

q=1(mol/s); heat=%avo<*>q;

1Pa<>atm 1atm<>psi 1atm<>hPa

a=1<>(kg/m.s-2)<>Pa<>torr 1J<>BTU 1ly<>m 10ly<>m<>km

1atm<>inHg<>mmHg

1atm<+>1bar (1atm<+>1bar)<>atm 1km<>m<>lightyear

1lightyear<>km

1lightyear<>pc

1m<>ly

1km<>ly //seemed off. this is possibly correct. (1km<+>1ly)<>km

1Å<>km

1Å<>m

(1..100)<>AU<>m

1degree<>arcminute

1Tsec<>sec

1(m/s)<>(km/hr) 1(km/s)<>(km/hr)

1(cal/mn)<>(J/sec) // d

1(kg/m3)<>(slug.ft-3)

2(rad/sec)<>rpm // did not convert. not sure why.

(1..100)<>USD<>EUR

SUPPORTEDUNITS()

1nibble<>bit 102400000000bit<>MB 1kB<>MB // seems wrong. 1kB<>Mb 1(kb)<>(bit) Pi<>(rad/sec)<>rpm 1(rad/sec)<>rpm 1(rad/mn)<>rpm (1(rad/mn)<>rpm)*2*Pi // should give 1. 1(rotation/mn)<>rpm 1(cycle/mn)<>(rad/mn)

1(cycle/mn)<>rpm

60rad<>deg 60rad<>deg<>rotation

1MB<>kB 1B<>kB 1MB<>B 1kB<>B

a=1(kg/m/s-2/t3) a=1(kg/m/s-2/t3) a=1(kg/m/s-2/t3) a=1(kg/m/s-2/t3) a=1<>(kg/m.s-2) // this worked though.

1(kg/m3)<>(slug/ft^3) // will not work due to ^. 1(kg/m3)<>(slug/ft3) //works 1(kg/m3)<>(slug.ft-3) //works

1(s-1)<>Hz 1(mn-1)<>Hz

velocity=3<>(m/s); time=1hr; velocity<*>time;

(((1..100)<>m)<^>2)<>acre

((1..100)<>m)<^>2