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qalc - Powerful and easy to use command line calculator
Contents
Bugs
Please report any bugs at https://github.com/Qalculate/libqalculate/issuesCommands
approximate
Equivalent to set approximation try exact.
assumeassumptions
Set default assumptions for unknown variables (unknown, non-zero, positive, negative, non-
positive, non-negative + number, real, rational, integer, boolean).
basebase
Sets the result number base (equivalent to set base).
clear Clears the screen.
clearhistory
Clears the expression history.
deletename
Removes the user-defined variable or function with the specified name.
Example: delete var1.
exact Equivalent to set approximation exact.
expand Expands the current result.
exrates Downloads current exchange rates from the Internet.
factor Factorizes the current result.
find,list[name]
Displays a list of variables, functions and units. Enter with argument 'currencies',
'functions', 'variables', 'units', or 'prefixes' to show a list of all currencies, functions,
variables, units, or prefixes. Enter a search term to find matching variables, functions, units,
and/or prefixes. If command is called with no argument all user-definied objects are listed.
Example: list functions.
Example: find dinar.
Example: find variables planck.
functionnameexpression
Creates a function with the specified name and expression. Use '\x', '\y', '\z', '\a', etc. for
arguments in the expression. The function is persistent unless the command is invoked from file
or in result only mode.
Example: function func1 5*\x.
help[command]history Lists the expression history.
infoname
Displays information about a function, variable, unit, or prefix.
Example: info sin.
keep/unkeepname
Make the temporary user-defined variable or function with the specified name non-temporary.
Example: keep var1.
MC/MS/M+/M-
Memory operations (memory clear, memory store, memory plus, memory minus). Recall the memory
using the MR/MRC variable.
mode Displays the current mode.
partialfraction
Applies partial fraction decomposition to the current result.
save,storename[category][title]
Saves the current result in a variable with the specified name. You may optionally also provide a
category (default "Temporary") and a title. If name equals "mode" or "definitions", the current
mode and definitions, respectively, will be saved.
Example: store var1.
savedefinitionssavemodesetoptionvalueto,convert,->unit/"to"-command
Converts the previous result. Equivalent to using "to" at the end of an expression. Example: to
m/s
Example: to bin
variablenameexpression
Create a variable with the specified name and expression. The variable is persistent unless the
command is invoked from file or in result only mode.
Example: variable var1 pi / 2.
quit/exit
Terminates the program.
Commands for RPN mode:
rpnstate
(De)activates the Reverse Polish Notation stack and syntax. "syntax" activates only the RPN
syntax and "stack" enables the RPN stack. "on" (1) and "off" (0) (de)activates both.
stack Displays the RPN stack.
clearstack
Clears the entire RPN stack.
copy[index]
Duplicates a value on the RPN stack to the top of the stack. If no index is specified, the top of
the stack is duplicated. Index 1 is the top of stack and negative index values count from the
bottom of the stack.
moveindex1[index2]
Changes the position of a value on the RPN stack. Index 1 is the top of stack and negative index
values count from the bottom of the stack.
Example: move 2 4
pop[index]
Removes the top of the RPN stack or the value at the specified index. Index 1 is the top of stack
and negative index values count from the bottom of the stack.
rotate[direction]
Rotates the RPN stack up (default) or down.
swap[index1][index2]
Swaps position of values on the RPN stack. If no index is specified, the values on the top of the
stack (index 1 and index 2) will be swapped and if only one index is specified, the value at this
index will be swapped with the top value. Index 1 is the top of stack and negative index values
count from the bottom of the stack.
Example: swap 2 4
When a line begins with '/', the text that follows is always interpreted as a command.
Description
Qalculate! is a multi-purpose cross-platform desktop calculator. It is simple to use but provides power
and versatility normally reserved for complicated math packages, as well as useful tools for everyday
needs (such as currency conversion and percent calculation). Features include a large library of
customizable functions, unit calculations and conversion, physical constants, symbolic calculations
(including integrals and equations), arbitrary precision, uncertainty propagation, interval arithmetic,
plotting, and a user-friendly interface. qalc is the command line interface of Qalculate!.
Examples
Note that semicolon can be replaced with comma, if comma is not used as decimal or thousands separator.
Basicfunctionsandoperators
sqrt 4 = sqrt(4)
= 4^(0.5)
= 4^(1/2)
= 2
sqrt(25; 16; 9; 4)
= [5 4 3 2]
sqrt(32)
= 4 * sqrt(2) (inexactmode)
cbrt(-27)
= root(-27; 3)
= -3 (realroot)
(-27)^(1/3)
= 1.5 + 2.5980762i (principalroot)
ln 25 = log(25; e)
= 3.2188758
log2(4)/log10(100)
= log(4; 2)/log(100; 10)
= 1
5! = 1 * 2 * 3 * 4 * 5
= 120
5\2 (integerdivision)
= 5//2
= trunc(5/2)
= 2
5 mod 3 = mod(5; 3)
= 2
52 to factors
= 2^2 * 13
25/4 * 3/5 to fraction
= 3 + 3/4
gcd(63; 27)
= 9
sin(pi/2) - cos(pi)
= sin(90 deg) - cos(180 deg)
= 2
sum(x; 1; 5)
= 1 + 2 + 3 + 4 + 5 = 15
sum(\i^2+sin(\i); 1; 5; \i)
= 1^2 + sin(1) + 2^2 + sin(2) + ... = 55.176162
product(x; 1; 5)
= 1 * 2 * 3 * 4 * 5 = 120
var1:=5 store value 5 in variable var1
5^2 #this is a comment
= 25
sinh(0.5) where sinh()=cosh()
= cosh(0.5) = 1.1276260
plot(x^2; -5; 5)
plots the function y=x^2 from -5 to 5
Units
5 dm3 to L = 5 dm^3 to L
= 5 L
20 miles / 2h to km/h
= 16.09344 km/h
1.74 to ft = 1.74 m to ft
= 5 ft + 8.5039370 in
1.74 m to -ft
= 5.7086614 ft
100 lbf * 60 mph to hp
= 16 hp
50 Ω * 2 A
= 100 V
50 Ω * 2 A to base
= 100 kg*m^2*s^-3*A^-1
10 N / 5 Pa
= (10 N)/(5 Pa) = 2 m^2
5 m/s to s/m
= 0.2 s/m
500 EUR - 20% to USD
= 451.04 USD
500 megabit/s * 2 h to b?byte
= 419.09516 gibibytes
Physicalconstants
k_e / G * a_0
= (coulombs_constant / newtonian_constant) * bohr_radius
= 7.126e9 kg*H*m^-1
planck ∕ (compton_wavelength * c)
= 9.1093837e-31 kg
5 ns * rydberg to c
= 6.0793194E-8c
atom(Hg; weight) + atom(C; weight) * 4 to g
= 4.129e-22 g
(G * planet(earth; mass) * planet(mars; mass))/(54.6e6 km)^2
= 8.58e16 N (gravitationalattractionbetweenearthandmars)Uncertaintyandintervalarithmeticresultwithintervalarithmeticactivatedisshowninparenthesis
sin(5+/-0.2)^2/2+/-0.3
= 0.460±0.088 (0.46+/-0.12)
(2+/-0.02 J)/(523+/-5 W)
= 3.824+/-0.053 ms (3.82+/-±0.075 ms)
interval(-2; 5)^2
= interval(-8.2500000; 12.750000) (interval(0; 25))
Algebra
(5x^2 + 2)/(x - 3)
= 5x + 15 + 47/(x - 3)
(\a + \b)(\a - \b) = ("a" + "b")("a" - "b")
= 'a'^2 - 'b'^2
(x + 2)(x - 3)^3
= x^4 - 7x^3 + 9x^2 + 27x - 54
factorize x^4 - 7x^3 + 9x^2 + 27x - 54
= x^4 - 7x^3 + 9x^2 + 27x - 54 to factors
= (x + 2)(x - 3)^3
cos(x)+3y^2 where x=pi and y=2
= 11
gcd(25x; 5x^2)
= 5x
1/(x^2+2x-3) to partial fraction
= 1/(4x - 4) - 1/(4x + 12)
x+x^2+4 = 16
x = 3 or x = -4
x^2/(5 m) - hypot(x; 4 m) = 2 m where x > 0
x = 7.1340411 m
cylinder(20cm; x) = 20L
x = (1 / (2pi)) m
x = 16 cm (heightof20Lcylinderwithradius20cm)
asin(sqrt(x)) = 0.2
x = sin(0.2)^2
x = 0.039469503
x^2 > 25x
= x > 25 or x < 0
solve(x = y+ln(y); y)
= lambertw(e^x)
solve2(5x=2y^2; sqrt(y)=2; x; y)
= 32/5
multisolve([5x=2y+32, y=2z, z=2x]; [x, y, z])
= [-32/3 -128/3 -64/3]
dsolve(diff(y; x) - 2y = 4x; 5)
= 6e^(2x) - 2x - 1
Calculus
diff(6x^2)
= 12x
diff(sinh(x^2)/(5x) + 3xy/sqrt(x))
= (2/5) * cosh(x^2) - sinh(x^2)/(5x^2) + (3y)/(2 * sqrt(x))
integrate(6x^2)
= 2x^3 + C
integrate(6x^2; 1; 5)
= 248
integrate(sinh(x^2)/(5x) + 3xy/sqrt(x))
= 2x * sqrt(x) * y + Shi(x^2) / 10 + C
integrate(sinh(x^2)/(5x) + 3xy/sqrt(x); 1; 2)
= 3.6568542y + 0.87600760
limit(ln(1 + 4x)/(3^x - 1); 0)
= 4 / ln(3)
Matricesandvectors
[1, 2, 3; 4, 5, 6]
= ((1; 2; 3); (4; 5; 6))
= [1 2 3; 4 5 6] (2x3matrix)
1...5 = (1:5) = (1:1:5)
= [1 2 3 4 5]
(1; 2; 3) * 2 - 2
= [(1 * 2 - 2), (2 * 2 - 2), (3 * 2 - 2)]
= [0 2 4]
[1 2 3].[4 5 6]
= dot([1 2 3]; [4 5 6])
= 32 (dotproduct)
cross([1 2 3]; [4 5 6])
= [-3 6 -3] (crossproduct)
[1 2 3; 4 5 6].*[7 8 9; 10 11 12]
= hadamard([1 2 3; 4 5 6]; [7 8 9; 10 11 12])
= [7 16 27; 40 55 72] (hadamardproduct)
[1 2 3; 4 5 6] * [7 8; 9 10; 11 12]
= [58 64; 139 154] (matrixmultiplication)
[1 2; 3 4]^-1
= inverse([1 2; 3 4])
= [-2 1; 1.5 -0.5]
Statistics
mean(5; 6; 4; 2; 3; 7)
= 4.5
stdev(5; 6; 4; 2; 3; 7)
= 1.87
quartile([5 6 4 2 3 7]; 1)
= percentile((5; 6; 4; 2; 3; 7); 25)
= 2.9166667
normdist(7; 5)
= 0.053990967
spearman(column(load(test.csv); 1); column(load(test.csv); 2))
= -0.33737388 (dependsonthedataintheCSVfile)Timeanddate
10:31 + 8:30 to time
= 19:01
10h 31min + 8h 30min to time
= 19:01
now to utc
= "2020-07-10T07:50:40Z"
"2020-07-10T07:50CET" to utc+8
= "2020-07-10T14:50:00+08:00"
"2020-05-20" + 523d
= addDays(2020-05-20; 523)
= "2021-10-25"
today - 5 days
= "2020-07-05"
"2020-10-05" - today
= days(today; 2020-10-05)
= 87
timestamp(2020-05-20)
= 1 589 925 600
stamptodate(1 589 925 600)
= "2020-05-20T00:00:00"
"2020-05-20" to calendars
returns date in Hebrew, Islamic, Persian, Indian, Chinese, Julian, Coptic, and Ethiopian
calendars
Numberbases
52 to bin
= 0011 0100
52 to bin16
= 0000 0000 0011 0100
52 to oct
= 064
52 to hex
= 0x34
0x34 = hex(34)
= base(34; 16)
= 52
523<<2&250 to bin
= 0010 1000
52.345 to float
= 0100 0010 0101 0001 0110 0001 0100 1000
float(01000010010100010110000101001000)
= 1715241/32768
= 52.345001
floatError(52.345)
= 1.2207031e-6
52.34 to sexa
= 52°20'24"
1978 to roman
= MCMLXXVIII
52 to base 32
= 1K
sqrt(32) to base sqrt(2)
= 100000
Keybindings
Tab(Ctrl+I)
shows a list of functions, variables, and units that matches the last object in the current
expression, or, if cursor is at beginning of line or after operator, inserts the previous result
(either with text of value, or as a temporary variable for approximate or long values)
Ctrl+A saves the current result in a temporary variable
Ctrl+D terminates the program
Ctrl+E switches between approximation modes (exact, try exact, auto)
Ctrl+F switches between fraction modes (simple, decimal, auto)
Ctrl+L clears the screen
Name
qalc - Powerful and easy to use command line calculator
Options
-b,--basebase
set the number base for results and, optionally, expressions
-c,--color
use colors to highlight different elements of expressions and results
--defaults
load default settings
-e,--exrates
update exchange rates
-f,--filefile
execute commands from a file first
-h,--help
display a list of command line options and exit
-i,--interactive
start in interactive mode
-l,--list[searchterm]
display a list of all user-defined or matching variables, functions, units, and prefixes, and
exit
--list-functions[searchterm]
display a list of all or matching functions and exit
--list-prefixes[searchterm]
display a list of all or matching prefixes and exit
--list-units[searchterm]
display a list of all or matching units and exit
--list-variables[searchterm]
display a list of all or matching variables and exit
-m,--timemilliseconds
terminate calculation and display of result after specified amount of time
-n,--nodefs
do not load any functions, units, or variables from file
--nocurrencies
do not load any global currencies from file
--nodatasets
do not load any global data sets from file
--nofunctions
do not load any global functions from file
--nounits
do not load any global units from file
--novariables
do not load any global variables from file
-p[base]
start in programming mode (same as -b "base base" -s "xor^", with base conversion)
-s,--set"optionvalue"
as set command in interactive program session (ex. --set "base 16")
-t,--terse
reduce output to just the result of the input expression
-/+u8 switch unicode support on/off
-v,--version
show application version and exit
The program will start in interactive mode if no expression and no file is specified (or interactive mode
is explicitly selected).
See Also
The manual of the graphical user interface at https://qalculate.github.io/manual/index.html (includes
more details about the syntax and elements supported in mathematical expressions, and various options,
and includes a complete list of functions, variables, and units)
Settings
These settings are changed using the set command (e.g. set base 16) or the -s,--set command line option
(e.g. qalc -s "base 16"). Possible values are shown in parenthesis. 1 and 0 can be used instead of on and
off, yes and no. If the value is left out, a value of 1 is generally assumed. The default value is marked
with '*'.
Algebraic mode:
algebramode,alg(1*=expand,2=factorize)
Determines if the expression is factorized or not after calculation.
assumenonzerodenominators,nzd(on*,off)
Determines if unknown values will be assumed non-zero (x/x=1).
warnnonzerodenominators,warnnzd(on*,off)
Display a message after a value has been assumed non-zero.
assumptions,asm(unknown*,non-zero,positive,negative,non-positive,non-negative+number,real*,rational,integer,boolean)
Default assumptions for unknown variables.
Calculation:
angleunit,angle(0=none,1*=radians,2=degrees,3=gradians,4=custom)
Default angle unit for trigonometric functions.
approximation,appr(-1*=auto,0=exact,1=tryexact,2=approximate,3=dual)
How approximate variables and calculations are handled. In exact mode approximate values will not
be calculated.
intervalarithmetic,ia(on*,off)
If activated, interval arithmetic determines the final precision of calculations (avoids wrong
results after loss of significance) with approximate functions and/or irrational numbers.
intervalcalculation,ic(1*=varianceformula,2=intervalarithmetic)
Determines the method used for interval calculation / uncertainty propagation.
precision,prec(>0)10*
Specifies the default number of significant digits displayed and determines the precision used
for approximate calculations.
Enabled objects:
calculatefunctions,calcfunc(on*,off)calculatevariables,calcvar(on*,off)complexnumbers,cplx(on*,off)functions,func(on*,off)infinitenumbers,inf(on*,off)units(on*,off)unknowns(on,off*)
Interpret undefined symbols in expressions as unknown variables.
variables,var(on*,off)variableunits,varunits(on*,off)
If activated physical constants include units (e.g. c = 299 792 458 m∕s).
Generic display options:
abbreviations,abbr(on*,off)
Use abbreviated names for units and variables.
color(0=off,1*=default,2=light)
Use colors to highlight different elements of expressions and results.
divisionsign,divsign(0*=/,1=divisionslash,2=divisionsign)excessiveparentheses,expar(on,off*)minuslast,minlast(on*,off)
Always place negative values last.
multiplicationsign,mulsign(0=*,1=multiplicationdot,2*=multiplicationx,3=middledot)shortmultiplication,shortmul(on*,off)spacious,space(on*,off)
Add extra space around operators.
spelloutlogical,spellout(on*,off)unicode,uni(on*,off)
Display Unicode characters.
unicodeexponents,uniexp(0=off,1*=on,2=units)
Display exponents 0-9 using Unicode superscript characters.
verticalspace,vspace(on*,off)
Add empty lines before and after result.
Numerical display:
base(-1114112-1114112,bin,oct,dec*,hex,sexa,time,roman)basedisplay,basedisp(0=none,1*=normal,2=alternative)binarybits,bits(0*=auto,>=2)complexform,cplxform(0*=rectangular,1=exponential,2=polar,3=cis,4=angle)decimalcomma(locale*,off,on)
Determines the default decimal separator.
digitgrouping,group(0*=off,1=standard,2=locale)digits(-1*=auto,>=2)
Specifies the number of displayed significant digits (by default determined by precision).
expdisplay,edisp(E*,e,10)
Determines how scientific notation are displayed (e.g. 3E6, 3e6, or 3 * 10^6).
fractions,fr(-1*=auto,0=off,1=exact,2=on,3=mixed,4=long,5=dual,1/n)
Determines how rational numbers are displayed (e.g. 5/4 = 1 + 1/4 = 1.25). 'long' removes limits
on the size of the numerator and denonimator.
hexadecimaltwo's,hextwos(on,off*)
Enables two's complement representation for display of negative hexadecimal numbers.
imaginaryj,imgj(on,off*)
Use 'j' (instead of 'i') as default symbol for the imaginary unit.
intervaldisplay,ivdisp(0*=adaptive,1=significant,2=interval,3=plusminus,4=midpoint,5=lower,6=upper,7=concise,8=relative)lowercasenumbers,lownum(on,off*)
Use lowercase letters for number bases > 10.
maxdecimals,maxdeci(-1*=off,>=0)mindecimals,mindeci(-1*=off,>=0)repeatingdecimals,repdeci(on,off*)
If activated, 1/6 is displayed as '0.1 666...', otherwise as '0.166667'.
rounding(0*=halfawayfromzero,1=halftoeven,2=towardzero,3=halftoodd,4=halftowardzero,5=halfup,6=halfdown,7=halfrandom,8=awayfromzero,9=up,10=down)
Determines how approximate numbers are rounded.
scientificnotation,exp(0=off,-1*=auto,-3=engineering,1=pure,3=scientific,>=0,<=-2)
Determines how scientific notation is used (e.g. 5 543 000 = 5.543E6). A value >= 0 specifies the
minimum exponent used. A value <= -2 specifies the multiplier used for the exponent.
showendingzeroes,zeroes(on*,off)
If actived, zeroes are kept at the end of approximate numbers.
two'scomplement,twos(on*,off)
Enables two's complement representation for display of negative binary numbers.
duodecimalsymbols,duosyms(on,off*)
Use special symbols for digits 10 and 11 in numbers with base 12.
Parsing:
caretasxor,xor^(on,off*)
Use ^ as bitwise exclusive OR operator.
conciseuncertainty,concise(on,off*)
Allow input of uncertainty using concise notation.
decimalcomma(locale*,off,on)
Determines the default decimal separator.
hexadecimaltwo'sinput,hextwosin(on,off*)
Enables two's complement representation for input of negative hexadecimal numbers. All
hexadecimal numbers starting with 8 or higher are negative, unless binary bits is set.
ignorecomma(on,off*)
Allows use of ',' as thousands separator.
ignoredot(on,off*)
Allows use of '.' as thousands separator.
imaginaryj,imgj(on,off*)
Use 'j' (instead of 'i') as default symbol for the imaginary unit.
inputbase,inbase(-1114112-1114112,bin,oct,dec*,hex,roman)limitimplicitmultiplication,limimpl(on,off*)parsingmode,syntax(0*=adaptive,1=implicitfirst,2=conventional,3=chain,4=rpn)
See syntax section.
readprecision,readprec(0*=off,1=always,2=whendecimals)
If activated, numbers are interpreted as approximate with precision equal to the number of
significant digits (3.20 = 3.20+/-0.005).
simplifiedpercentage,percent(on*,off)
Interpret addition/subtraction of percentage as percentage increase/decrease of the first term
(100 + 10% = 110).
two'sinput,twosin(on,off*)
Enables two's complement representation for input of negative binary numbers. All binary numbers
starting with 1 are negative, unless binary bits is set.
Units:
allprefixes,allpref(on,off*)
Enables automatic use of hecto, deca, deci, and centi.
autoconversion,conv(0=none,1*=optimal,2=base,3=optimalsi,4=mixed)
Controls automatic unit conversion of the result. 'optimalsi' always converts non-SI units, while
'optimal' only converts to more optimal unit expressions, with less units and exponents.
binaryprefixes,binpref(on,off*)
If activated, binary prefixes are used by default for information units.
currencyconversion,curconv(on*,off)
Enables automatic conversion to the local currency when optimal unit conversion is enabled.
denominatorprefixes,denpref(on*,off)
Enables automatic use of prefixes in the denominator of unit expressions.
placeunitsseparately,unitsep(on*,off)
If activated, units are separated from variables at the end of the result.
prefixes,pref(on*,off)
Enables automatic use of prefixes in the result.
shownegativeexponents,negexp(on,off*)
Use negative exponents instead of division for units in result (m/s = m*s^-1).
syncunits,sync(on*,off)temperaturecalculation,temp(0*=hybrid,1=absolute,2=relative)
Determines how expressions with temperature units are calculated (hybrid acts as absolute if the
expression contains different temperature units, otherwise as relative).
updateexchangerates,upxrates(-1*=ask,0=never,>0=days)
Other:
calculateasyoutype,autocalc(on,off*)
Activates continuous calculation of the currently edited expression.
clearhistory(yes,no*)
Do not save expression history on exit.
ignorelocale(yes,no*)
Ignore system language and use English (requires restart).
rpn(on,off*)
Activates the Reverse Polish Notation stack.
savedefinitions(yes*,no)
Save functions, units, and variables on exit.
savemode(yes*,no)
Save settings on exit.
sigintaction,sigint(0=kill,1*=exit,2=interrupt)
Determines how the SIGINT signal (Ctrl+C) is handled.
Synopsis
qalc [options] [expression]
Syntax
Mathematical entities:
Numbers
These are the regular numbers composed by digits 0-9 and a decimal sign — a dot, or a comma if it
is the default decimal point in the locale/language used. If comma is used as decimal sign, the
dot is still kept as an alternative decimal sign, if not explicitly deactivated. Numbers include
integers, real numbers, and complex numbers. The imaginary part of complex numbers are written
with as regular number followed by the special variable "i" (can be changed to a "j"), which
represents the square root of -1. Spaces between digits are ignored ("5 5 = 55"). "E" (or "e")
can be considered as a shortcut for writing many zeroes and is equivalent to multiplication by 10
raised to the power of the right-hand value (e.g. "5E3 = 5000"). Sexagesimal numbers (and time)
can be entered directly using colons (e.g. "5:30 = 5.5"). A number immediately preceded "0b",
"0o", "0d" or "0x" are interpreted as a number with base 2, 8, 12 or 16, respectively (e.g. "0x3f
= 63").
Intervals
A number interval can be entered using the interval() function, the uncertainty() function, or
using "±" or "+/-" (e.g. 5±1 = uncertainty(5, 0.2) = interval(4, 6)). If the read precision option
is activated, decimal numbers are interpreted as an interval between the numbers that are normally
rounded to the entered number (e.g. 1.1 = 1.1±0.05). If interval calculation using variance
formula is activated (default), the interval represents the standard uncertainty (deviation) of
the value.
VectorsandMatrices
A matrix is a two-dimensional rectangular array of mathematical objects. Vectors are matrices with
only one row or column, and thus one-dimensional sequences of objects. Vectors and matrices are
generated by various functions, or using syntax in the form of [1 2 3 4] and [1 2; 3 4], with
columns separated by space or comma and rows separated by semi-colon, or (1, 2, 3, 4) and ((1, 2),
(3, 4)). A vector with sequence of numbers can be created using "..." (e.g. "1...4"), or colon
(e.g. "[1:4]", or "[1:1:4]" where the second value specifies the increment). A single element of a
vector can be selected by placing the index (first index is 1) in parenthesis after a variable or
function (e.g. "v(1)" or "f[1]").
Variables/Constants
See the list of variables in the GUI manual or using the command .I list variables
Functions
See the list of functions in the GUI manual or using the command .I list functions
UnitsandPrefixes
See the list of units and prefixes in the GUI manual or using the command .I list units.
Abbreviated, plural and singular forms of unit names and prefixes are generally allowed. Prefixes
must be put immediately before the unit to be interpreted as prefixes (eg. 5 mm = 0.005 m, but 5 m
m = 5 m^2). For convenience units allow the power operator to be left out (e.g. 5 m2 = 5 m^2),
with currencies excluded.
Unknowns
Unknowns are text strings without any associated value. These are temporary unknown variables with
default assumptions. Unknowns can also be explicitly entered by placing a backslash (\) before a
single character (e.g. 5\a + 2\b) or using quotation mark before and after a text string (e.g. 5
"apples" + 2 "bananas"). If unknowns are activated characters without any associated variable,
function or unit in an expression, will be regarded as an unknown variable.
DateandTime
Date/time values are specified using quoted text string (quotation marks are not needed for
function arguments), using standard date and time format (YYYY-MM-DDTHH:MM:SS). Some local formats
are also supported, but not recommended. The local time zone are used, unless a time zone is
specified at the end of the time string (Z/UTC/GMT or +/-HH:MM). Date/time supports a small subset
of arithmetic operations. The time units represents calendar time, instead of average values, when
added or subtracted to a date.
Text
This category represent a number of different function argument types, such as regular text and
file names. They can, but do not need to be put in quotes except when containing the argument
separator.
Comments
All text after a hashtag (e.g. (5*2)/2 #calculating triangle area) is treated as a comment.
Operations and operators (word operators such as AND must be surrounded by space):
Addition(+)Subtraction(-)Multiplication(*)Division(/)Remainder(%,rem)andmodulo(%%,mod)
Returns the remainder after division.
Integerdivision(//,div)
Rounds the result of division towards zero.
Exponentiation(^,**)
Note that x^y^z equals x^(y^z), and not (x^y)^z. Note also that for non-integer exponents with
negative bases, the principal root is returned and not the real root ((-8)^(1/3) equals 1 + 1.73i,
and not -2). To calculate the real root for negative values, use the cbrt() and root() functions.
10^x(E)Parenthesis((,))Parellelsum(∥,||)
Returns the reciprocal value of a sum of reciprocal values. || is interpreted as parallel if units
are used, otherwise as logical OR.
Logicaloperators(!,NOT,||,OR,&&,AND,XOR,NOR,NAND)Bitwiseoperators(~,|,&,<<,>>,XOR)Comparisonoperators(=,!=,<,<=,>,>=)
Returns 1 if expression is true and 0 if false. The x variable is isolated if the expression does
not evaluate as true or false. Primarily used for equations and inequalities.
Dotproduct(.)Element-wiseoperators(.*,./,.^)Saveoperator(:=,=)
Saves the expression to the right of the operator as a variable or function (e.g. var1:=5,
func1():=x+y, var1=ln(5)+2). If the colon is omitted the expression is calculated before it is
assigned to the variable.
Evaluationpriorityorder: parenthesis, 10^x, exponentiation, functions, bitwise NOT, logical NOT,
multiplication/division/remainder, parallel sum, addition/subtraction, bitwise NOT, bitwise shift,
comparisons, bitwise AND, bitwise XOR, bitwise OR, logical AND, logical OR.
The evaluation of short/implicitmultiplication without any multiplication sign (e.g. 5x, 5(2+3)),
differs depending on the parsing mode. In the conventionalmode implicit multiplication does not differ
from explicit multiplication (12/2(1+2) = 12/2*3 = 18, 5x/5y = 5 * x/5 * y = xy). In the parse implicitmultiplicationfirst mode, implicit multiplication is parsed before explicit multiplication (12/2(1+2) =
12/(2 * 3) = 2, 5x/5y = (5 * x)/(5 * y) = x/y). The default adaptivemode works as the parse implicit
multiplication first mode, unless spaces are found (1/5x = 1/(5 * x), but 1/5 x = (1/5) * x). In the
adaptive mode unit expressions are parsed separately (5 m/5 m/s = (5 * m)/(5 * (m/s)) = 1 s). Function
arguments without parentheses are an exception, where implicit multiplication in front of variables and
units is parsed first regardless of mode (sqrt 2x = sqrt(2x)).
In chainmode, expressions are calculated from left to right, ignoring standard order of operations, like
the immediate execution mode of a traditional calculator (1+2*3 = (1+2)*3 = 9).
The "to"-operator is used for unit conversion and manipulation of how the result is presented. Place " to
" or a right arrow (e.g. "->") followed by one of expressions/commands listed below, at the end of an
expression.
Unitconversion
- a unit or unit expression (e.g. meter or km/h)
prepend with ? to request the optimal prefix
prepend with b? to request the optimal binary prefix
prepend with + or - to force/disable use of mixed units
- a variable or physical constant (e.g. c)
- base (convert to base units)
- optimal (convert to optimal unit)
- prefix (convert to optimal prefix)
- mixed (convert to mixed units, e.g. hours + minutes)
Numberbaseconversion
- bin, binary (show as binary number)
- bin# (show as binary number with specified number of bits)
- oct, octal (show as octal number)
- duo, duodecimal (show as duodecimal number)
- hex, hexadecimal (show as hexadecimal number)
- hex# (show as hexadecimal number with specified number of bits)
- sexa, sexa2, sexa3, sexagesimal (show as sexagesimal number; sexa2 hides and sexa3 rounds
arcseconds)
- latitude, latitude2, longitude, longitude2 (show as sexagesimal latitude/longitude; latitude2
and longitude2 hide arcseconds)
- bijective (shown in bijective base-26)
- fp16, fp32, fp64, fp80, fp128 (show in binary floating-point format)
- bcd (show as binary-coded decimal)
- roman (show as roman numerals)
- time (show in time format)
- unicode
- base # (show in specified number base)
- bases (show as binary, octal, decimal and hexadecimal number)
Complexformat
- rectangular, cartesian (show complex numbers in rectangular form)
- exponential (show complex numbers in exponential form)
- polar (show complex numbers in polar form)
- cis (show complex numbers in cis form)
- angle, phasor (show complex numbers in angle/phasor notation)
Timeanddateconversion
- UTC (show date and time in UTC time zone)
- UTC+/-hh[:mm] (show date and time in specified time zone)
- calendars
Fractions
- fraction (show result as mixed fraction)
- decimals (show result as decimal fraction)
- 1/# (show as mixed fraction with specified denominator)
prepend with - to show as simple fraction
Otherconversioncommands
- factors (factorize result)
Similarly where (or alternatively "/.") can be used at the end (but before "to"), for variable
assignments, function replacements, etc. (e.g. "x+y where x=1 and y=2", "x^2=4 where x>0", and "sin(5)
where sin()=cos()"). Variables assignments can also be placed before the expression, separated by comma,
e.g. <quote>x=1, y=2, x+y</quote>, but this syntax is more strict.
Note that to and where can only be applied to the whole expression. Everything before the operator is
always treated as the expression to convert (or apply replacement to), and everything after as the
conversion/replacement expression, regardless of any parentheses.
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