1QALC(1) General Commands Manual QALC(1)
2
6 qalc - Powerful and easy to use command line calculator
7
9 qalc [options] [expression]
10
12 Qalculate! is a multi-purpose cross-platform desktop calculator. It is
13 simple to use but provides power and versatility normally reserved for
14 complicated math packages, as well as useful tools for everyday needs
15 (such as currency conversion and percent calculation). Features include
16 a large library of customizable functions, unit calculations and con‐
17 version, physical constants, symbolic calculations (including integrals
18 and equations), arbitrary precision, uncertainty propagation, interval
19 arithmetic, plotting, and a user-friendly interface. qalc is the com‐
20 mand line interface of Qalculate!.
21
23 -b, --base base
24 set the number base for results and, optionally, expressions
25 -c, --color
27 use colors to highlight different elements of expressions and
28 results
29 --defaults
31 load default settings
32 -e, --exrates
34 update exchange rates
35 -f, --file file
37 execute commands from a file first
38 -h, --help
40 display this help and exits
41 -i, --interactive
43 start in interactive mode
44 -l, --list [search term]
46 displays a list of all user-defined or matching variables,
47 functions, units, and prefixes.
48 --list-functions [search term]
50 displays a list of all or matching functions.
51 --list-prefixes [search term]
53 displays a list of all or matching prefixes.
54 --list-units [search term]
56 displays a list of all or matching units.
57 --list-variables [search term]
59 displays a list of all or matching variables.
60 -m, --time milliseconds
62 terminate calculation and display of result after specified
63 amount of time
64 -n, --nodefs
66 do not load any functions, units, or variables from file
67 --nocurrencies
69 do not load any global currencies from file
70 --nodatasets
72 do not load any global data sets from file
73 --nofunctions
75 do not load any global functions from file
76 --nounits
78 do not load any global units from file
79 --novariables
81 do not load any global variables from file
82 -p [base]
84 start in programming mode (same as -b "base base" -s "xor^",
85 with base conversion)
86 -s, --set "option value"
88 as set command in interactive program session (ex. --set "base
89 16")
90 -t, --terse
92 reduce output to just the result of the input expression
93 -/+u8 switch unicode support on/off
95 -v, --version
97 show application version and exit
98 The program will start in interactive mode if no expression and no file
100 is specified (or interactive mode is explicitly selected).
101
103 approximate
104 Equivalent to set approximation try exact.
105 assume assumptions
107 Set default assumptions for unknown variables (unknown, non-
108 zero, positive, negative, non-positive, non-negative + number,
109 real, rational, integer, boolean).
110 base base
112 Sets the result number base (equivalent to set base).
113 clear Clears the screen
115 clear history
117 Clears the expression history
118 delete name
120 Removes the user-defined variable or function with the speci‐
121 fied name.
122 Example: delete var1.
123 exact Equivalent to set approximation exact.
125 expand Expands the current result.
127 exrates Downloads current exchange rates from the Internet.
129 factor Factorizes the current result.
131 find, list [name]
133 Displays a list of variables, functions and units. Enter with
134 argument 'currencies', 'functions', 'variables', 'units', or
135 'prefixes' to show a list of all currencies, functions, vari‐
136 ables, units, or prefixes. Enter a search term to find matching
137 variables, functions, units, and/or prefixes. If command is
138 called with no argument all user-definied objects are listed.
139 Example: list functions.
140 Example: find dinar.
141 Example: find variables planck.
142 function name expression
144 Creates a function with the specified name and expression. Use
145 '\x', '\y', '\z', '\a', etc. for arguments in the expression.
146 Example: function func1 5*\x.
147 help [command]
149 info Displays information about a function, variable, unit, or pre‐
151 fix.
152 Example: info sin.
153 MC/MS/M+/M-
155 Memory operations (memory clear, memory store, memory plus,
156 memory minus). Recall the memory using the MR/MRC variable.
157 mode Displays the current mode.
159 partial fraction
161 Applies partial fraction decomposition to the current result.
162 save, store name [category] [title]
164 Saves the current result in a variable with the specified name.
165 You may optionally also provide a category (default "Tempo‐
166 rary") and a title. If name equals "mode" or "definitions",
167 the current mode and definitions, respectively, will be saved.
168 Example: store var1.
169 save definitions
171 save mode
173 set option value
175 to, convert, -> unit/"to"-command
177 Converts the previous result. Equivalent to using "to" at the
178 end of an expression. Example: to m/s
179 Example: to bin
180 variable name expression
182 Create a variable with the specified name and expression.
183 Example: variable var1 pi / 2.
184 quit/exit
186 Terminates the program.
187 Commands for RPN mode:
189 rpn state
191 (De)activates the Reverse Polish Notation stack and syntax.
192 "syntax" activates only the RPN syntax and "stack" enables the
193 RPN stack.
194 stack Displays the RPN stack.
196 clear stack
198 Clears the entire RPN stack.
199 copy [index]
201 Duplicates a value on the RPN stack to the top of the stack. If
202 no index is specified, the top of the stack is duplicated. In‐
203 dex 1 is the top of stack and negative index values count from
204 the bottom of the stack.
205 move index 1 index 2
207 Changes the position of a value on the RPN stack. Index 1 is
208 the top of stack and negative index values count from the bot‐
209 tom of the stack.
210 Example: move 2 4
211 pop [index]
213 Removes the top of the RPN stack or the value at the specified
214 index. Index 1 is the top of stack and negative index values
215 count from the bottom of the stack.
216 rotate [direction]
218 Rotates the RPN stack up (default) or down.
219 swap [index 1] [index 2]
221 Swaps position of values on the RPN stack. If no index is spec‐
222 ified, the values on the top of the stack (index 1 and index 2)
223 will be swapped and if only one index is specified, the value
224 at this index will be swapped with the top value. Index 1 is
225 the top of stack and negative index values count from the bot‐
226 tom of the stack.
227 Example: swap 2 4
228 When a line begins with '/', the text that follows is always inter‐
230 preted as a command.
231
233 Tab shows a list of functions, variables, and units that matches
234 the last object in the current expression
235 Ctrl+D terminates the program
237 Ctrl+E switches between approximation modes (exact, try exact, auto)
239 Ctrl+F switches between fraction modes (simple, decimal, auto)
241 Ctrl+A saves the current result in a temporary variable
243 Ctrl+L clears the screen
245
247 These settings are changed using the set command (e.g. set base 16) or
248 the -s, --set command line option (e.g. qalc -s "base 16"). Possible
249 values are shown in parenthesis. 1 and 0 can be used instead of on and
250 off, yes and no. If the value is left out, a value of 1 is generally
251 assumed. The default value is marked with '*'.
252 Algebraic mode:
254 algebra mode, alg (1* = expand, 2 = factorize)
256 Determines if the expression is factorized or not after calcu‐
257 lation.
258 assume nonzero denominators, nzd (on*, off)
260 Determines if unknown values will be assumed non-zero (x/x=1).
261 warn nonzero denominators, warnnzd (on*, off)
263 Display a message after a value has been assumed non-zero.
264 assumptions, asm (unknown*, non-zero, positive, negative, non-positive,
266 non-negative + number, real*, rational, integer, boolean)
267 Default assumptions for unknown variables.
268 Calculation:
270 angle unit, angle (0 = none, 1* = radians, 2 = degrees, 3 = gradians)
272 Default angle unit for trigonometric functions.
273 approximation, appr (-1* = auto, 0 = exact, 1 = try exact, 2 = approxi‐
275 mate, 3 = dual)
276 How approximate variables and calculations are handled. In ex‐
277 act mode approximate values will not be calculated.
278 interval arithmetic, ia (on*, off)
280 If activated, interval arithmetic determines the final preci‐
281 sion of calculations (avoids wrong results after loss of sig‐
282 nificance) with approximate functions and/or irrational num‐
283 bers.
284 interval calculation, ic (1* = variance formula, 2 = interval arith‐
286 metic)
287 Determines the method used for interval calculation / uncer‐
288 tainty propagation.
289 precision, prec (> 0) 10*
291 Specifies the default number of significant digits displayed
292 and determines the precision used for approximate calculations.
293 Enabled objects:
295 calculate functions, calcfunc (on*, off)
297 calculate variables, calcvar (on*, off)
299 complex numbers, cplx (on*, off)
301 functions, func (on*, off)
303 infinite numbers, inf (on*, off)
305 units (on*, off)
307 unknowns (on, off*)
309 Interpret undefined symbols in expressions as unknown vari‐
310 ables.
311 variables, var (on*, off)
313 variable units, varunits (on*, off)
315 If activated physical constants include units (e.g. c =
316 299 792 458 m∕s).
317 Generic display options:
319 abbreviations, abbr (on*, off)
321 Use abbreviated names for units and variables.
322 color (0 = off, 1* = default, 2 = light)
324 Use colors to highlight different elements of expressions and
325 results.
326 division sign, divsign (0* = /, 1 = division slash, 2 = division sign)
328 excessive parentheses, expar (on, off*)
330 minus last, minlast (on, off*)
332 Always place negative values last.
333 multiplication sign, mulsign (0 = *, 1 = multiplication dot, 2* = mul‐
335 tiplication x, 3 = middle dot)
336 short multiplication, shortmul (on*, off)
338 spacious, space (on*, off)
340 Add extra space around operators.
341 spell out logical, spellout (on*, off)
343 unicode, uni (on*, off)
345 Display Unicode characters.
346 vertical space, vspace (on*, off)
348 Add empty lines before and after result.
349 Numerical display:
351 base (-1114112 - 1114112, bin, oct, dec*, hex, sexa, time, roman)
353 base display, basedisp (0 = none, 1* = normal, 2 = alternative)
355 complex form, cplxform (0* = rectangular, 1 = exponential, 2 = polar, 3
357 = cis, 4 = angle)
358 decimal comma (locale*, off, on)
360 Determines the default decimal separator.
361 digit grouping, group (0* = off, 1 = standard, 2 = locale)
363 fractions, fr (-1* = auto, 0 = off, 1 = exact, 2 = on, 3 = mixed, 4 =
365 long, 5 = dual)
366 Determines how rational numbers are displayed (e.g. 5/4 = 1 +
367 1/4 = 1.25). 'long' removes limits on the size of the numerator
368 and denonimator.
369 hexadecimal two's, hextwos (on, off*)
371 Enables two's complement representation for display of negative
372 hexadecimal numbers.
373 imaginary j, imgj (on, off*)
375 Use 'j' (instead of 'i') as default symbol for the imaginary
376 unit.
377 interval display, ivdisp (0* = adaptive, 1 = significant, 2 = interval,
379 3 = plusminus, 4 = midpoint, 5 = lower, 6 = upper, 7 = concise, 8 =
380 relative)
381 lowercase e, lowe (on, off*)
383 Use lowercase e for E-notation (5e2 = 5 * 10^2).
384 lowercase numbers, lownum (on, off*)
386 Use lowercase letters for number bases > 10.
387 max decimals, maxdeci (-1 = off*, >= 0)
389 min decimals, mindeci (-1 = off*, >= 0)
391 rounding (0 = standard*, 1 = even, 2 = truncate)
393 Determines whether how approximate numbers are rounded (round
394 halfway numbers away from zero or towards the nearest even
395 digit, or round all numbers towards zero).
396 scientific notation, exp (0 = off, -1 = auto*, -3 = engineering, 1 =
398 pure, 3 = scientific, >= 0)
399 Determines how scientific notation is used (e.g. 5 543 000 =
400 5.543E6).
401 show ending zeroes, zeroes (on*, off)
403 If actived, zeroes are kept at the end of approximate numbers.
404 two's complement, twos (on*, off)
406 Enables two's complement representation for display of negative
407 binary numbers.
408 duodecimal symbols, duosyms (on, off*)
410 Use special symbols for digits 10 and 11 in numbers with base
411 12.
412 Parsing:
414 caret as xor, xor^ (on, off*)
416 Use ^ as bitwise exclusive OR operator.
417 concise uncertainty, concise (on, off*)
419 Allow input of uncertainty using concise notation.
420 decimal comma (locale*, off, on)
422 Determines the default decimal separator.
423 ignore comma (on, off*)
425 Allows use of ',' as thousands separator.
426 ignore dot (on, off*)
428 Allows use of '.' as thousands separator.
429 imaginary j, imgj (on, off*)
431 Use 'j' (instead of 'i') as default symbol for the imaginary
432 unit.
433 input base, inbase (-1114112 - 1114112, bin, oct, dec*, hex, roman)
435 limit implicit multiplication, limimpl (on, off*)
437 parsing mode, syntax (0* = adaptive, 1 = implicit first, 2 = conven‐
439 tional, 3 = chain, 4 = rpn)
440 See syntax section.
441 read precision, readprec (0* = off, 1 = always, 2 = when decimals)
443 If activated, numbers are interpreted as approximate with pre‐
444 cision equal to the number of significant digits (3.20 =
445 3.20+/-0.005).
446 Units:
448 all prefixes, allpref (on, off*)
450 Enables automatic use of hecto, deca, deci, and centi.
451 autoconversion, conv (0 = none, 1 = optimal*, 2 = base, 3 = optimalsi,
453 4 = mixed)
454 Controls automatic unit conversion of the result. 'optimalsi'
455 always converts non-SI units, while 'optimal' only converts to
456 more optimal unit expressions, with less units and exponents.
457 binary prefixes, binpref (on, off*)
459 If activated, binary prefixes are used by default for informa‐
460 tion units.
461 currency conversion, curconv (on*, off)
463 Enables automatic conversion to the local currency when optimal
464 unit conversion is enabled.
465 denominator prefixes, denpref (on*, off)
467 Enables automatic use of prefixes in the denominator of unit
468 expressions.
469 place units separately, unitsep (on*, off)
471 If activated, units are separated from variables at the end of
472 the result.
473 prefixes, pref (on*, off)
475 Enables automatic use of prefixes in the result.
476 show negative exponents, negexp (on, off*)
478 Use negative exponents instead of division for units in result
479 (m/s = m*s^-1).
480 sync units, sync (on*, off)
482 temperature units, temp (0 = hybrid*, 1 = absolute, 2 = relative)
484 Determines how expressions with temperature units are calcu‐
485 lated (hybrid acts as absolute if the expression contains dif‐
486 ferent temperature units, otherwise as relative).
487 update exchange rates, upxrates (-1 = ask*, 0 = never, > 0 = days)
489 Other:
491 clear history (yes, no*)
493 Do not save expression history on exit.
494 ignore locale (yes, no*)
496 Ignore system language and use English (requires restart).
497 rpn (on, off*)
499 Activates the Reverse Polish Notation stack.
500 save definitions (yes*, no)
502 Save functions, units, and variables on exit.
503 save mode (yes*, no)
505 Save settings on exit.
506 sigint action, sigint (0 = kill*, 1 = exit, 2 = interrupt)
508 Determines how the SIGINT signal (Ctrl+C) is handled.
509
511 Mathematical entities:
512 Numbers
514 These are the regular numbers composed by digits 0-9 and a deci‐
515 mal sign — a dot, or a comma if it is the default decimal point
516 in the locale/language used. If comma is used as decimal sign,
517 the dot is still kept as an alternative decimal sign, if not ex‐
518 plicitly deactivated. Numbers include integers, real numbers,
519 and complex numbers. The imaginary part of complex numbers are
520 written with as regular number followed by the special variable
521 "i" (can be changed to a "j"), which represents the square root
522 of -1. Spaces between digits are ignored ("5 5 = 55"). "E" (or
523 "e") can be considered as a shortcut for writing many zeroes and
524 is equivalent to multiplication by 10 raised to the power of the
525 right-hand value (e.g. "5E3 = 5000"). Sexagesimal numbers (and
526 time) can be entered directly using colons (e.g. "5:30 = 5.5").
527 A number immediately preceded "0b", "0o", "0d" or "0x" are in‐
528 terpreted as a number with base 2, 8, 12 or 16, respectively
529 (e.g. "0x3f = 63").
530 Intervals
532 A number interval can be entered using the interval() function,
533 the uncertainty() function, or using "±" or "+/-" (e.g. 5±1 =
534 uncertainty(5, 0.2) = interval(4, 6)). If the read precision op‐
535 tion is activated, decimal numbers are interpreted as an inter‐
536 val between the numbers that are normally rounded to the entered
537 number (e.g. 1.1 = 1.1±0.05). If interval calculation using
538 variance formula is activated (default), the interval represents
539 the standard uncertainty (deviation) of the value.
540 Vectors and Matrices
542 A matrix is a two-dimensional rectangular array of mathematical
543 objects. Vectors are matrices with only one row or column, and
544 thus one-dimensional sequences of objects. Vectors and matrices
545 are generated by various functions, or using syntax in the form
546 of [1 2 3 4] and [1 2; 3 4], with columns separated by space or
547 comma and rows separated by semi-colon, or (1, 2, 3, 4) and ((1,
548 2), (3, 4)).
549 Variables/Constants
551 See the list of variables in the GUI manual or using the command
552 .I list variables
553 Functions
555 See the list of functions in the GUI manual or using the command
556 .I list functions
557 Units and Prefixes
559 See the list of units and prefixes in the GUI manual or using
560 the command .I list units. Abbreviated, plural and singular
561 forms of unit names and prefixes are generally allowed. Prefixes
562 must be put immediately before the unit to be interpreted as
563 prefixes (eg. 5 mm = 0.005 m, but 5 m m = 5 m^2). For conve‐
564 nience units allow the power operator to be left out (e.g. 5 m2
565 = 5 m^2), with currencies excluded.
566 Unknowns
568 Unknowns are text strings without any associated value. These
569 are temporary unknown variables with default assumptions. Un‐
570 knowns can also be explicitly entered by placing a backslash (\)
571 before a single character (e.g. 5\a + 2\b) or using quotation
572 mark before and after a text string (e.g. 5 "apples" + 2 "ba‐
573 nanas"). If unknowns are activated characters without any asso‐
574 ciated variable, function or unit in an expression, will be re‐
575 garded as an unknown variable.
576 Date and Time
578 Date/time values are specified using quoted text string (quota‐
579 tion marks are not needed for function arguments), using stan‐
580 dard date and time format (YYYY-MM-DDTHH:MM:SS). Some local for‐
581 mats are also supported, but not recommended. The local time
582 zone are used, unless a time zone is specified at the end of the
583 time string (Z/UTC/GMT or +/-HH:MM). Date/time supports a small
584 subset of arithmetic operations. The time units represents cal‐
585 endar time, instead of average values, when added or subtracted
586 to a date.
587 Text
589 This category represent a number of different function argument
590 types, such as regular text and file names. They can, but do not
591 need to be put in quotes except when containing the argument
592 separator.
593 Comments
595 All text after a hashtag (e.g. (5*2)/2 #calculating triangle
596 area) is treated as a comment.
597 Operations and operators (word operators such as AND must be surrounded
599 by space):
600 Addition (+)
602 Subtraction (-)
604 Multiplication (*)
606 Division (/)
608 Remainder (%, rem) and modulo (%%, mod)
610 Returns the remainder after division.
611 Integer division (//, div)
613 Rounds the result of division towards zero.
614 Exponentiation (^, **)
616 Note that x^y^z equals x^(y^z), and not (x^y)^z. Note also that
617 for non-integer exponents with negative bases, the principal
618 root is returned and not the real root ((-8)^(1/3) equals 1 +
619 1.73i, and not -2). To calculate the real root for negative val‐
620 ues, use the cbrt() and root() functions.
621 10^x (E)
623 Parenthesis ((, ))
625 Parellel sum (∥, ||)
627 Returns the the reciprocal value of a sum of reciprocal values.
628 || is interpreted as parallel if units are used, otherwise as
629 logical OR.
630 Logical operators (!, NOT, ||, OR, &&, AND, XOR, NOR, NAND)
632 Bitwise operators (~, |, &, <<, >>, XOR)
634 Comparison operators (=, !=, <, <=, >, >=)
636 Returns 1 if expression is true and 0 if false. The x variable
637 is isolated if the expression does not evaluate as true or
638 false. Primarily used for equations and inequalities.
639 Dot product (.)
641 Element-wise operators (.*, ./, .^)
643 Save operator (:=, =)
645 Saves the expression to the right of the operator as a variable
646 or function (e.g. var1:=5, func1():=x+y, var1=ln(5)+2). If the
647 colon is omitted the expression is calculated before it is as‐
648 signed to the variable.
649 Evaluation priority order: parenthesis, 10^x, exponentiation, func‐
651 tions, bitwise NOT, logical NOT, multiplication/division/remainder,
652 parallel sum, addition/subtraction, bitwise NOT, bitwise shift, compar‐
653 isons, bitwise AND, bitwise XOR, bitwise OR, logical AND, logical OR.
654 The evaluation of short/implicit multiplication without any multiplica‐
656 tion sign (e.g. 5x, 5(2+3)), differs depending on the parsing mode. In
657 the conventional mode implicit multiplication does not differ from ex‐
658 plicit multiplication (12/2(1+2) = 12/2*3 = 18, 5x/5y = 5 * x/5 * y =
659 xy). In the parse implicit multiplication first mode, implicit multi‐
660 plication is parsed before explicit multiplication (12/2(1+2) = 12/(2 *
661 3) = 2, 5x/5y = (5 * x)/(5 * y) = x/y). The default adaptive mode works
662 as the parse implicit multiplication first mode, unless spaces are
663 found (1/5x = 1/(5 * x), but 1/5 x = (1/5) * x). In the adaptive mode
664 unit expressions are parsed separately (5 m/5 m/s = (5 * m)/(5 * (m/s))
665 = 1 s). Function arguments without parentheses are an exception, where
666 implicit multiplication in front of variables and units is parsed first
667 regardless of mode (sqrt 2x = sqrt(2x)).
668 In chain mode, expressions are calculated from left to right, ignoring
670 standard order of operations, like the immediate execution mode of a
671 traditional calculator (1+2*3 = (1+2)*3 = 9).
672 The "to"-operator is used for unit conversion and manipulation of how
674 the result is presented. Place " to " or a right arrow (e.g. "->") fol‐
675 lowed by one of expressions/commands listed below, at the end of an ex‐
676 pression.
677 Unit conversion
679 - a unit or unit expression (e.g. meter or km/h)
680 prepend with ? to request the optimal prefix
681 prepend with b? to request the optimal binary prefix
682 prepend with + or - to force/disable use of mixed units
683 - a variable or physical constant (e.g. c)
684 - base (convert to base units)
685 - optimal (convert to optimal unit)
686 - mixed (convert to mixed units, e.g. hours + minutes)
687 Number base conversion
689 - bin, binary (show as binary number)
690 - bin# (show as binary number with specified number of bits)
691 - oct, octal (show as octal number)
692 - duo, duodecimal (show as duodecimal number)
693 - hex, hexadecimal (show as hexadecimal number)
694 - hex# (show as hexadecimal number with specified number of
695 bits)
696 - sex, sexa2, sexa3, sexagesimal (show as sexagesimal number;
697 sexa2 hides and sexa3 rounds arcseconds)
698 - latitude, latitude2, longitude, longitude2 (show as sexagesi‐
699 mal latitude/longitude; latitude2 and longitude2 hide arcsec‐
700 onds)
701 - bijective (shown in bijective base-26)
702 - fp16, fp32, fp64, fp80, fp128 (show in binary floating-point
703 format)
704 - bcd (show as binary-coded decimal)
705 - roman (show as roman numerals)
706 - time (show in time format)
707 - unicode
708 - base # (show in specified number base)
709 - bases (show as binary, octal, decimal and hexadecimal number)
710 Complex format
712 - rectangular, cartesian (show complex numbers in rectangular
713 form)
714 - exponential (show complex numbers in exponential form)
715 - polar (show complex numbers in polar form)
716 - cis (show complex numbers in cis form)
717 - angle, phasor (show complex numbers in angle/phasor notation)
718 Time and date conversion
720 - UTC (show date and time in UTC time zone)
721 - UTC+/-hh[:mm] (show date and time in specified time zone)
722 - calendars
723 Other conversion commands
725 - fraction (show result as mixed fraction)
726 - factors (factorize result)
727 Similarly where (or alternatively "/.") can be used at the end (but be‐
729 fore "to"), for variable assignments, function replacements, etc. (e.g.
730 "x+y where x=1 and y=2", "x^2=4 where x>0", and "sin(5) where
731 sin()=cos()").
732 Note that to and where can only be applied to the whole expression. Ev‐
734 erything before the operator is always treated as the expression to
735 convert (or apply replacement to), and everything after as the conver‐
736 sion/replacement expression, regardless of any parentheses.
737
739 Note that semicolon can be replaced with comma, if comma is not used as
740 decimal or thousands separator.
741 Basic functions and operators
743 sqrt 4 = sqrt(4)
745 = 4^(0.5)
746 = 4^(1/2)
747 = 2
748 sqrt(25; 16; 9; 4)
750 = [5 4 3 2]
751 sqrt(32)
753 = 4 * sqrt(2) (in exact mode)
754 cbrt(-27)
756 = root(-27; 3)
757 = -3 (real root)
758 (-27)^(1/3)
760 = 1.5 + 2.5980762i (principal root)
761 ln 25 = log(25; e)
763 = 3.2188758
764 log2(4)/log10(100)
766 = log(4; 2)/log(100; 10)
767 = 1
768 5! = 1 * 2 * 3 * 4 * 5
770 = 120
771 5\2 (integer division)
773 = 5//2
774 = trunc(5/2)
775 = 2
776 5 mod 3 = mod(5; 3)
778 = 2
779 52 to factors
781 = 2^2 * 13
782 25/4 * 3/5 to fraction
784 = 3 + 3/4
785 gcd(63; 27)
787 = 9
788 sin(pi/2) - cos(pi)
790 = sin(90 deg) - cos(180 deg)
791 = 2
792 sum(x; 1; 5)
794 = 1 + 2 + 3 + 4 + 5 = 15
795 sum(i^2+sin(i); 1; 5; i)
797 = 1^2 + sin(1) + 2^2 + sin(2) + ... = 55.176162
798 product(x; 1; 5)
800 = 1 * 2 * 3 * 4 * 5 = 120
801 var1:=5 store value 5 in variable var1
803 5^2 #this is a comment
805 = 25
806 sinh(0.5) where sinh()=cosh()
808 = cosh(0.5) = 1.1276260
809 plot(x^2; -5; 5)
811 plots the function y=x^2 from -5 to 5
812 Units
814 5 dm3 to L
816 = 25 dm^3 to L
817 = 5 L
818 20 miles / 2h to km/h
820 = 16.09344 km/h
821 1.74 to ft = 1.74 m to ft
823 = 5 ft + 8.5039370 in
824 1.74 m to -ft
826 = 5.7086614 ft
827 100 lbf * 60 mph to hp
829 = 16 hp
830 50 Ω * 2 A
832 = 100 V
833 50 Ω * 2 A to base
835 = 100 kg*m^2*s^-3*A^-1
836 10 N / 5 Pa
838 = (10 N)/(5 Pa) = 2 m^2
839 5 m/s to s/m
841 = 0.2 s/m
842 500 EUR - 20% to USD
844 = 451.04 USD
845 500 megabit/s * 2 h to b?byte
847 = 419.09516 gibibytes
848 Physical constants
850 k_e / G * a_0
852 = (coulombs_constant / newtonian_constant) * bohr_radius
853 = 7.126e9 kg*H*m^-1
854 planck ∕ (compton_wavelength * c)
856 = 9.1093837e-31 kg
857 5 ns * rydberg to c
859 = 6.0793194E-8c
860 atom(Hg; weight) + atom(C; weight) * 4 to g
862 = 4.129e-22 g
863 (G * planet(earth; mass) * planet(mars; mass))/(54.6e6 km)^2
865 = 8.58e16 N (gravitational attraction between earth and mars)
866 Uncertainty and interval arithmetic
868 result with interval arithmetic activated is shown in parenthesis
869 sin(5+/-0.2)^2/2+/-0.3
871 = 0.460±0.088 (0.46+/-0.12)
872 (2+/-0.02 J)/(523+/-5 W)
874 = 3.824+/-0.053 ms (3.82+/-±0.075 ms)
875 interval(-2; 5)^2
877 = intervall(-8.2500000; 12.750000) (intervall(0; 25))
878 Algebra
880 (5x^2 + 2)/(x - 3)
882 = 5x + 15 + 47/(x - 3)
883 (\a + \b)(\a - \b) = ("a" + "b")("a" - "b")
885 = 'a'^2 - 'b'^2
886 (x + 2)(x - 3)^3
888 = x^4 - 7x^3 + 9x^2 + 27x - 54
889 factorize x^4 - 7x^3 + 9x^2 + 27x - 54
891 = x^4 - 7x^3 + 9x^2 + 27x - 54 to factors
892 = (x + 2)(x - 3)^3
893 cos(x)+3y^2 where x=pi and y=2
895 = 11
896 gcd(25x; 5x^2)
898 = 5x
899 1/(x^2+2x-3) to partial fraction
901 = 1/(4x - 4) - 1/(4x + 12)
902 x+x^2+4 = 16
904 x = 3 or x = -4
905 x^2/(5 m) - hypot(x; 4 m) = 2 m where x > 0
907 x = 7.1340411 m
908 cylinder(20cm; x) = 20L
910 x = (1 / (2pi)) m
911 x = 16 cm (height of 20 L cylinder with radius 20 cm)
912 asin(sqrt(x)) = 0.2
914 x = sin(0.2)^2
915 x = 0.039469503
916 x^2 > 25x
918 = x > 25 or x < 0
919 solve(x = y+ln(y); y)
921 = lambertw(e^x)
922 solve2(5x=2y^2; sqrt(y)=2; x; y)
924 = 32/5
925 multisolve([5x=2y+32, y=2z, z=2x]; [x, y, z])
927 = [-32/3 -128/3 -64/3]
928 dsolve(diff(y; x) - 2y = 4x; 5)
930 = 6e^(2x) - 2x - 1
931 Calculus
933 diff(6x^2)
935 = 12x
936 diff(sinh(x^2)/(5x) + 3xy/sqrt(x))
938 = (2/5) * cosh(x^2) - sinh(x^2)/(5x^2) + (3y)/(2 * sqrt(x))
939 integrate(6x^2)
941 = 2x^3 + C
942 integrate(6x^2; 1; 5)
944 = 248
945 integrate(sinh(x^2)/(5x) + 3xy/sqrt(x))
947 = 2x * sqrt(x) * y + Shi(x^2) / 10 + C
948 integrate(sinh(x^2)/(5x) + 3xy/sqrt(x); 1; 2)
950 = 3.6568542y + 0.87600760
951 limit(ln(1 + 4x)/(3^x - 1); 0)
953 = 4 / ln(3)
954 Matrices and vectors
956 [1, 2, 3; 4, 5, 6]
958 = ((1; 2; 3); (4; 5; 6))
959 = [1 2 3; 4 5 6] (2x3 matrix)
960 (1; 2; 3) * 2 - 2
962 = [(1 * 2 - 2), (2 * 2 - 2), (3 * 2 - 2)]
963 = [0 2 4]
964 [1 2 3].[4 5 6]
966 = dot([1 2 3]; [4 5 6])
967 = 32 (dot product)
968 cross([1 2 3]; [4 5 6])
970 = [-3 6 -3] (cross product)
971 [1 2 3; 4 5 6].*[7 8 9; 10 11 12]
973 = hadamard([1 2 3; 4 5 6]; [7 8 9; 10 11 12])
974 = [7 16 27; 40 55 72] (hadamard product)
975 [1 2 3; 4 5 6] * [7 8; 9 10; 11 12]
977 = [58 64; 139 154] (matrix multiplication)
978 [1 2; 3 4]^-1
980 = inverse([1 2; 3 4])
981 = [-2 1; 1.5 -0.5]
982 Statistics
984 mean(5; 6; 4; 2; 3; 7)
986 = 4.5
987 stdev(5; 6; 4; 2; 3; 7)
989 = 1.87
990 quartile([5 6 4 2 3 7]; 1)
992 = percentile((5; 6; 4; 2; 3; 7); 25)
993 = 2.9166667
994 normdist(7; 5)
996 = 0.053990967
997 spearman(column(load(test.csv); 1); column(load(test.csv); 2))
999 = -0.33737388 (depends on the data in the CSV file)
1000 Time and date
1002 10:31 + 8:30 to time
1004 = 19:01
1005 10h 31min + 8h 30min to time
1007 = 19:01
1008 now to utc
1010 = "2020-07-10T07:50:40Z"
1011 "2020-07-10T07:50CET" to utc+8
1013 = "2020-07-10T14:50:00+08:00"
1014 "2020-05-20" + 523d
1016 = addDays(2020-05-20; 523)
1017 = "2021-10-25"
1018 today - 5 days
1020 = "2020-07-05"
1021 "2020-10-05" - today
1023 = days(today; 2020-10-05)
1024 = 87
1025 timestamp(2020-05-20)
1027 = 1 589 925 600
1028 stamptodate(1 589 925 600)
1030 = "2020-05-20T00:00:00"
1031 "2020-05-20" to calendars
1033 returns date in Hebrew, Islamic, Persian, Indian, Chinese, Ju‐
1034 lian, Coptic, and Ethiopian calendars
1035 Number bases
1037 52 to bin
1039 = 0011 0100
1040 52 to bin16
1042 = 0000 0000 0011 0100
1043 52 to oct
1045 = 064
1046 52 to hex
1048 = 0x34
1049 0x34 = hex(34)
1051 = base(34; 16)
1052 = 52
1053 523<<2&250 to bin
1055 = 0010 1000
1056 52.345 to float
1058 = 0100 0010 0101 0001 0110 0001 0100 1000
1059 float(01000010010100010110000101001000)
1061 = 1715241/32768
1062 = 52.345001
1063 floatError(52.345)
1065 = 1.2207031e-6
1066 52.34 to sexa
1068 = 52°20'24"
1069 1978 to roman
1071 = MCMLXXVIII
1072 52 to base 32
1074 = 1K
1075 sqrt(32) to base sqrt(2)
1077 = 100000
1078
1080 The manual of the graphical user interface at https://qalcu‐
1081 late.github.io/manual/index.html (includes more details about the syn‐
1082 tax and elements supported in mathematical expressions, and various op‐
1083 tions, and includes a complete list of functions, variables, and units)
1084
1086 Please report any bugs at https://github.com/Qalculate/libqalculate/is‐
1087 sues
1088
1090 Hanna Knutsson <hanna.knutsson@protonmail.com>.
1091 13 July 2020 QALC(1)