Units

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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.

Metricscales.png

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