Difference between revisions of "Units"

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/* TO GET PRINTED RIGHT */
 
/* TO GET PRINTED RIGHT */
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{| class="wikitable"
 
{| class="wikitable"

Revision as of 12:41, 13 June 2016

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);

/* TO GET PRINTED RIGHT */


(1..100)<>m

Numeric,Units UNITSOF
1
m
1m
2
m
2m
3
m
3m
4
m
4m
5
m
5m
6
m
6m
7
m
7m
8
m
8m
9
m
9m
10
m
10m
11
m
11m
12
m
12m
13
m
13m
14
m
14m
15
m
15m
16
m
16m
17
m
17m
18
m
18m
19
m
19m
20
m
20m
21
m
21m
22
m
22m
23
m
23m
24
m
24m
25
m
25m
26
m
26m
27
m
27m
28
m
28m
29
m
29m
30
m
30m
31
m
31m
32
m
32m
33
m
33m
34
m
34m
35
m
35m
36
m
36m
37
m
37m
38
m
38m
39
m
39m
40
m
40m
41
m
41m
42
m
42m
43
m
43m
44
m
44m
45
m
45m
46
m
46m
47
m
47m
48
m
48m
49
m
49m
50
m
50m
51
m
51m
52
m
52m
53
m
53m
54
m
54m
55
m
55m
56
m
56m
57
m
57m
58
m
58m
59
m
59m
60
m
60m
61
m
61m
62
m
62m
63
m
63m
64
m
64m
65
m
65m
66
m
66m
67
m
67m
68
m
68m
69
m
69m
70
m
70m
71
m
71m
72
m
72m
73
m
73m
74
m
74m
75
m
75m
76
m
76m
77
m
77m
78
m
78m
79
m
79m
80
m
80m
81
m
81m
82
m
82m
83
m
83m
84
m
84m
85
m
85m
86
m
86m
87
m
87m
88
m
88m
89
m
89m
90
m
90m
91
m
91m
92
m
92m
93
m
93m
94
m
94m
95
m
95m
96
m
96m
97
m
97m
98
m
98m
99
m
99m
100
m
100m


Numeric,Units UNITSOF
1,m 1m
2,m 2m
3,m 3m
4,m 4m
5,m 5m
6,m 6m
7,m 7m
8,m 8m
9,m 9m
10,m 10m


Numeric,Units UNITSOF
1,mi 1
2,mi 2
3,mi 3
4,mi 4
5,mi 5
6,mi 6
7,mi 7
8,mi 8
9,mi 9
10,mi 10

Now b has the values 1..100 in miles.

Let us convert all of these values to km. b<>km;

The answer is given as:

Numeric,Units UNITSOF
1,km 1.6093439999999999
2,km 3.2186879999999998
3,km 4.828031999999999
4,km 6.4373759999999995
5,km 8.046719999999999
6,km 9.656063999999999
7,km 11.265407999999999
8,km 12.874751999999999
9,km 14.484096
10,km 16.093439999999998



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

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