1(1) insect - scientific calculator (1)
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6 insect - interactive scientific calculator
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9 insect [EXPR]
10
12 insect is a high-precision scientific calculator with full support for
13 physical units.
14 It can be used in interactive mode by simply calling insect. This mode
16 can also be used to read from a file, by simply piping the file con‐
17 tents via insect < my-calculation.ins. If you want to evaluate just a
18 single expression, pass it as an argument: insect '70mph to km/h'.
19 Documentation
21 · Evaluate mathematical expressions:
22 1920/16*9
24 2^32
25 sqrt(1.4^2 + 1.5^2) * cos(pi/3)^2
26 · Operators: addition (+), subtraction (-), multiplication (*, ·, ×),
28 division (/, ÷, per), exponentiation (^, **). Full list: see Ref‐
29 erence below.
30 · Mathematical functions: abs, acos, acosh, asin, asinh, atan, atan2,
32 atanh, ceil, cos, cosh, exp, floor, fromCelsius, fromFahrenheit,
33 gamma, ln, log, log10, maximum, minimum, mean, round, sin, sinh,
34 sqrt, tan, tanh, toCelsius, toFahrenheit.
35 · High-precision numeric type with 30 significant digits that can
37 handle very large (or small) exponents like 10^(10^10).
38 · Exponential notation: 6.022e23.
40 · Physical units: parsing and handling, including metric prefixes:
42 2 min + 30 s
44 40 kg * 9.8 m/s^2 * 150 cm
45 sin(30°)
46 · Supported units: see Reference section below.
48 · Implicit conversions: 15 km/h * 30 min evaluates to 7.5 km.
50 · Useful error messages:
52 > 2 watts + 4 newton meter
54 Conversion error:
56 Cannot convert unit N·m (base units: kg·m²·s⁻²)
57 to unit W (base units: kg·m²·s⁻³)
58 · Explicit unit conversions: the -> conversion operator (aliases: →, ➞,
60 to):
61 60 mph -> m/s
63 500 km/day -> km/h
64 1 mrad -> degree
65 52 weeks -> days
66 5 in + 2 ft -> cm
67 atan(30 cm / 2 m) -> degree
68 6 Mbit/s * 1.5 h -> GB
69 · Variable assignments:
71 Example: mass of the earth
73 r = 6000km
75 vol = 4/3 * pi * r^3
76 density = 5 g/cm^3
77 vol * density -> kg
78 Example: oscillation period of a pendulum
80 len = 20 cm
82 2pi*sqrt(len/g0) -> ms
83 · Predefined constants (type list to see them all): speed of light
85 (c), Planck's constant (h_bar), electron mass (electronMass), ele‐
86 mentary charge (elementaryCharge), magnetic constant (µ0), electric
87 constant (eps0), Bohr magneton (µ_B), Avogadro's constant (N_A),
88 Boltzmann constant (k_B), gravitational acceleration (g0), ideal
89 gas constant (R), ...
90 · Last result: you can use ans (answer) to refer to the result of the
92 last calculation.
93 · User-defined functions:
95 Example: kinetic energy
97 kineticEnergy(mass, speed) = 0.5 * mass * speed^2 -> kJ
99 kineticEnergy(800 kg, 120 km/h)
101 Example: barometric formula
103 P0 = 1 atm
105 T0 = fromCelsius(15)
106 tempGradient = 0.65 K / 100 m
107 pressure(height) = P0 * (1 - tempGradient * height / T0)^5.255 -> hPa
109 pressure(1500 m)
111 · Sums and products:
113 Syntax:
115 sum(<expression>, <index-variable>, <from>, <to>)
117 product(<expression>, <index-variable>, <from>, <to>)
118 Examples:
120 # sum of the first ten squares
122 sum(k^2, k, 1, 10)
123 # the factorial of n as the product 1 × 2 × ... × n
125 myFactorial(n) = product(k, k, 1, n)
126 · Unicode support:
128 λ = 2 × 300 µm
130 ν = c/λ → GHz
131 · And more: tab completion, command history (arrow keys, Ctrl+R), pret‐
133 ty printing, syntax highlighting, ...
134 Reference
136 · Operators (ordered by precedence: high to low)
137 Operator Syntax
139 ──────────────────────────────────────────
140 factorial !
141 square, cube, ... ², ³, ⁻¹, ...
142 exponentiation ^, **
143 multiplication (implicit) whitespace
144 modulo %
145 division per
146 division /, ÷
147 multiplication (explicit) *, ·, ×
148 subtraction -
149 addition +
150 unit conversion ->, →, ➞, to
151 assignment =
152 Note that implicit multiplication has a higher precedence than divi‐
154 sion, i.e. 50 cm / 2 m will be parsed as 50 cm / (2 m).
155 · Commands
157 Command Syntax
159 ─────────────────────────────────
160 help text help, ?
161 list of variables list, ls, ll
162 reset environment reset
163 clear screen clear, cls
164 quit (CLI) quit, exit
165 FAQ
167 · Why are Celsius and Fahrenheit not supported?
168 Compared to the SI unit Kelvin (https://en.wikipedia.org/wiki/Kelvin)
170 and in contrast to all other units, Celsius and Fahrenheit require an
171 additive offset when converting into and from other temperature
172 units. This additive offset leads to all kinds of ambiguities when
173 performing calculations in these units. Adding two temperatures in
174 Celsius, for example, is only meaningful if one of them is seen as an
175 offset value (rather than an absolute temperature). Insect is pri‐
176 marily a scientific calculator (as opposed to a unit conversion tool)
177 and therefore focuses on getting physical calculations right.
178 Even though °C and °F are not supported as built-in units, there are
180 helper functions to convert to and from Celsius (and Fahrenheit):
181 · fromCelsius takes a scalar value that represents a temperature in
183 Celsius and returns a corresponding temperature in Kelvin:
184 > fromCelsius(0)
186 = 273.15 K
188 > k_B * fromCelsius(23) to meV
190 = 25.5202 meV
192 · toCelsius takes a temperature in Kelvin and returns a scalar value
194 that represents the corresponding temperature in Celsius:
195 > toCelsius(70 K)
197 = -203.15
199 > toCelsius(25 meV / k_B)
201 = 16.963
203 · Why is 1/2 x parsed as 1/(2x)?
205 Implicit multiplication (without an explicit multiplication sign) has
207 a higher precedence than division (see operator precedence rules).
208 This is by design, in order to parse inputs like 50 cm / 2 m as
209 (50 cm) / (2 m). If you meant ½ · x, write 1/2 * x.
210 · What is the internal numerical precision?
212 By default, Insect shows 6 significant digits in the result of the
214 calculation. However, the internal numerical precision is much high‐
215 er (30 digits).
216 · How does the conversion operator work?
218 The conversion operator -> attempts to convert the physical quantity
220 on its left hand side to the unit of the expression on its right hand
221 side. This means that you can write an arbitrary expression on the
222 right hand side (but only the unit part will be extracted). For ex‐
223 ample:
224 # simple unit conversion:
226 > 120 km/h -> mph
227 = 74.5645 mi/h
229 # expression on the right hand side:
231 > 120 m^3 -> km * m^2
232 = 0.12 m²·km
234 # convert x1 to the same unit as x2:
236 > x1 = 50 km / h
237 > x2 = 3 m/s -> x1
238 x2 = 10.8 km/h
240
242 Written by David Peter <mail@david-peter.de>.
243
245 Please report bugs on GitHub: <https://github.com/sharkdp/insect>.
246
248 insect is MIT-licensed. For details, see
249 <https://github.com/sharkdp/insect>.
250
252 · Full documentation at <https://github.com/sharkdp/insect>.
253 · Web-version at <https://insect.sh>.
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