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, varunit (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 = upper, 6 = lower)
380 lowercase e, lowe (on, off*)
382 Use lowercase e for E-notation (5e2 = 5 * 10^2).
383 lowercase numbers, lownum (on, off*)
385 Use lowercase letters for number bases > 10.
386 max decimals, maxdeci (-1 = off*, >= 0)
388 min decimals, mindeci (-1 = off*, >= 0)
390 rounding (0 = standard*, 1 = even, 2 = truncate)
392 Determines whether how approximate numbers are rounded (round
393 halfway numbers away from zero or towards the nearest even
394 digit, or round all numbers towards zero).
395 scientific notation, exp (0 = off, -1 = auto*, -3 = engineering, 1 =
397 pure, 3 = scientific, >= 0)
398 Determines how scientific notation is used (e.g. 5 543 000 =
399 5.543E6).
400 show ending zeroes, zeroes (on*, off)
402 If actived, zeroes are kept at the end of approximate numbers.
403 two's complement, twos (on*, off)
405 Enables two's complement representation for display of negative
406 binary numbers.
407 Parsing:
409 caret as xor, xor^ (on, off*)
411 Use ^ as bitwise exclusive OR operator.
412 decimal comma (locale*, off, on)
414 Determines the default decimal separator.
415 ignore comma (on, off*)
417 Allows use of ',' as thousands separator.
418 ignore dot (on, off*)
420 Allows use of '.' as thousands separator.
421 imaginary j, imgj (on, off*)
423 Use 'j' (instead of 'i') as default symbol for the imaginary
424 unit.
425 input base, inbase (-1114112 - 1114112, bin, oct, dec*, hex, roman)
427 limit implicit multiplication, limimpl (on, off*)
429 parsing mode, syntax (0* = adaptive, 1 = implicit first, 2 = conven‐
431 tional, 3 = chain, 4 = rpn)
432 See syntax section.
433 read precision, readprec (0* = off, 1 = always, 2 = when decimals)
435 If activated, numbers are interpreted as approximate with pre‐
436 cision equal to the number of significant digits (3.20 =
437 3.20+/-0.005).
438 Units:
440 all prefixes, allpref (on, off*)
442 Enables automatic use of hecto, deca, deci, and centi.
443 autoconversion, conv (0 = none, 1 = optimal*, 2 = base, 3 = optimalsi,
445 4 = mixed)
446 Controls automatic unit conversion of the result. 'optimalsi'
447 always converts non-SI units, while 'optimal' only converts to
448 more optimal unit expressions, with less units and exponents.
449 binary prefixes, binpref (on, off*)
451 If activated, binary prefixes are used by default for informa‐
452 tion units.
453 currency conversion, curconv (on*, off)
455 Enables automatic conversion to the local currency when optimal
456 unit conversion is enabled.
457 denominator prefixes, denpref (on*, off)
459 Enables automatic use of prefixes in the denominator of unit
460 expressions.
461 place units separately, unitsep (on*, off)
463 If activated, units are separated from variables at the end of
464 the result.
465 prefixes, pref (on*, off)
467 Enables automatic use of prefixes in the result.
468 show negative exponents, negexp (on, off*)
470 Use negative exponents instead of division for units in result
471 (m/s = m*s^-1).
472 sync units, sync (on*, off)
474 temperature units, temp (0 = hybrid*, 1 = absolute, 2 = relative)
476 Determines how expressions with temperature units are calcu‐
477 lated (hybrid acts as absolute if the expression contains dif‐
478 ferent temperature units, otherwise as relative).
479 update exchange rates, upxrates (-1 = ask*, 0 = never, > 0 = days)
481 Other:
483 clear history (yes, no*)
485 Do not save expression history on exit.
486 ignore locale (yes, no*)
488 Ignore system language and use English (requires restart).
489 rpn (on, off*)
491 Activates the Reverse Polish Notation stack.
492 save definitions (yes*, no)
494 Save functions, units, and variables on exit.
495 save mode (yes*, no)
497 Save settings on exit.
498 sigint action, sigint (0 = kill*, 1 = exit, 2 = interrupt)
500 Determines how the SIGINT signal (Ctrl+C) is handled.
501
503 Mathematical entities:
504 Numbers
506 These are the regular numbers composed by digits 0-9 and a deci‐
507 mal sign — a dot, or a comma if it is the default decimal point
508 in the locale/language used. If comma is used as decimal sign,
509 the dot is still kept as an alternative decimal sign, if not ex‐
510 plicitly deactivated. Numbers include integers, real numbers,
511 and complex numbers. The imaginary part of complex numbers are
512 written with as regular number followed by the special variable
513 "i" (can be changed to a "j"), which represents the square root
514 of -1. Spaces between digits are ignored ("5 5 = 55"). "E" (or
515 "e") can be considered as a shortcut for writing many zeroes and
516 is equivalent to multiplication by 10 raised to the power of the
517 right-hand value (e.g. "5E3 = 5000"). Sexagesimal numbers (and
518 time) can be entered directly using colons (e.g. "5:30 = 5.5").
519 A number immediately preceded "0b", "0o", "0d" or "0x" are in‐
520 terpreted as a number with base 2, 8, 12 or 16, respectively
521 (e.g. "0x3f = 63").
522 Intervals
524 A number interval can be entered using the interval() function,
525 the uncertainty() function, or using "±" or "+/-" (e.g. 5±1 =
526 uncertainty(5, 0.2) = interval(4, 6)). If the read precision op‐
527 tion is activated, decimal numbers are interpreted as an inter‐
528 val between the numbers that are normally rounded to the entered
529 number (e.g. 1.1 = 1.1±0.05). If interval calculation using
530 variance formula is activated (default), the interval represents
531 the standard uncertainty (deviation) of the value.
532 Vectors and Matrices
534 A matrix is a two-dimensional rectangular array of mathematical
535 objects. Vectors are matrices with only one row or column, and
536 thus one-dimensional sequences of objects. Vectors and matrices
537 are generated by various functions, or using syntax in the form
538 of [1 2 3 4] and [1 2; 3 4], with columns separated by space or
539 comma and rows separated by semi-colon, or (1, 2, 3, 4) and ((1,
540 2), (3, 4)).
541 Variables/Constants
543 See the list of variables in the GUI manual or using the command
544 .I list variables
545 Functions
547 See the list of functions in the GUI manual or using the command
548 .I list functions
549 Units and Prefixes
551 See the list of units and prefixes in the GUI manual or using
552 the command .I list units. Abbreviated, plural and singular
553 forms of unit names and prefixes are generally allowed. Prefixes
554 must be put immediately before the unit to be interpreted as
555 prefixes (eg. 5 mm = 0.005 m, but 5 m m = 5 m^2). For conve‐
556 nience units allow the power operator to be left out (e.g. 5 m2
557 = 5 m^2), with currencies excluded.
558 Unknowns
560 Unknowns are text strings without any associated value. These
561 are temporary unknown variables with default assumptions. Un‐
562 knowns can also be explicitly entered by placing a backslash (\)
563 before a single character (e.g. 5\a + 2\b) or using quotation
564 mark before and after a text string (e.g. 5 "apples" + 2 "ba‐
565 nanas"). If unknowns are activated characters without any asso‐
566 ciated variable, function or unit in an expression, will be re‐
567 garded as an unknown variable.
568 Date and Time
570 Date/time values are specified using quoted text string (quota‐
571 tion marks are not needed for function arguments), using stan‐
572 dard date and time format (YYYY-MM-DDTHH:MM:SS). Some local for‐
573 mats are also supported, but not recommended. The local time
574 zone are used, unless a time zone is specified at the end of the
575 time string (Z/UTC/GMT or +/-HH:MM). Date/time supports a small
576 subset of arithmetic operations. The time units represents cal‐
577 endar time, instead of average values, when added or subtracted
578 to a date.
579 Text
581 This category represent a number of different function argument
582 types, such as regular text and file names. They can, but do not
583 need to be put in quotes except when containing the argument
584 separator.
585 Comments
587 All text after a hashtag (e.g. (5*2)/2 #calculating triangle
588 area) is treated as a comment.
589 Operations and operators (word operators such as AND must be surrounded
591 by space):
592 Addition (+)
594 Subtraction (-)
596 Multiplication (*)
598 Division (/)
600 Remainder (%, rem) and modulo (%%, mod)
602 Returns the remainder after division.
603 Integer division (//, div)
605 Rounds the result of division towards zero.
606 Exponentiation (^, **)
608 Note that x^y^z equals x^(y^z), and not (x^y)^z. Note also that
609 for non-integer exponents with negative bases, the principal
610 root is returned and not the real root ((-8)^(1/3) equals 1 +
611 1.73i, and not -2). To calculate the real root for negative val‐
612 ues, use the cbrt() and root() functions.
613 10^x (E)
615 Parenthesis ((, ))
617 Parellel sum (∥, ||)
619 Returns the the reciprocal value of a sum of reciprocal values.
620 || is interpreted as parallel if units are used, otherwise as
621 logical OR.
622 Logical operators (!, NOT, ||, OR, &&, AND, XOR, NOR, NAND)
624 Bitwise operators (~, |, &, <<, >>, XOR)
626 Comparison operators (=, !=, <, <=, >, >=)
628 Returns 1 if expression is true and 0 if false. The x variable
629 is isolated if the expression does not evaluate as true or
630 false. Primarily used for equations and inequalities.
631 Dot product (.)
633 Element-wise operators (.*, ./, .^)
635 Save operator (:=, =)
637 Saves the expression to the right of the operator as a variable
638 or function (e.g. var1:=5, func1():=x+y, var1=ln(5)+2). If the
639 colon is omitted the expression is calculated before it is as‐
640 signed to the variable.
641 Evaluation priority order: parenthesis, 10^x, exponentiation, func‐
643 tions, bitwise NOT, logical NOT, multiplication/division/remainder,
644 parallel sum, addition/subtraction, bitwise NOT, bitwise shift, compar‐
645 isons, bitwise AND, bitwise XOR, bitwise OR, logical AND, logical OR.
646 The evaluation of short/implicit multiplication without any multiplica‐
648 tion sign (e.g. 5x, 5(2+3)), differs depending on the parsing mode. In
649 the conventional mode implicit multiplication does not differ from ex‐
650 plicit multiplication (12/2(1+2) = 12/2*3 = 18, 5x/5y = 5 * x/5 * y =
651 xy). In the parse implicit multiplication first mode, implicit multi‐
652 plication is parsed before explicit multiplication (12/2(1+2) = 12/(2 *
653 3) = 2, 5x/5y = (5 * x)/(5 * y) = x/y). The default adaptive mode works
654 as the parse implicit multiplication first mode, unless spaces are
655 found (1/5x = 1/(5 * x), but 1/5 x = (1/5) * x). In the adaptive mode
656 unit expressions are parsed separately (5 m/5 m/s = (5 * m)/(5 * (m/s))
657 = 1 s). Function arguments without parentheses are an exception, where
658 implicit multiplication in front of variables and units is parsed first
659 regardless of mode (sqrt 2x = sqrt(2x)).
660 In chain mode, expressions are calculated from left to right, ignoring
662 standard order of operations, like the immediate execution mode of a
663 traditional calculator (1+2*3 = (1+2)*3 = 9).
664 The "to"-operator is used for unit conversion and manipulation of how
666 the result is presented. Place " to " or a right arrow (e.g. "->") fol‐
667 lowed by one of expressions/commands the below, at the end of an ex‐
668 pression.
669 Unit conversion
671 - a unit or unit expression (e.g. meter or km/h)
672 prepend with ? to request the optimal prefix
673 prepend with b? to request the optimal binary prefix
674 prepend with + or - to force/disable use of mixed units
675 - a variable or physical constant (e.g. c)
676 - base (convert to base units)
677 - optimal (convert to optimal unit)
678 - mixed (convert to mixed units, e.g. hours + minutes)
679 Number base conversion
681 - bin, binary (show as binary number)
682 - bin# (show as binary number with specified number of bits)
683 - oct, octal (show as octal number)
684 - duo, duodecimal (show as duodecimal number)
685 - hex, hexadecimal (show as hexadecimal number)
686 - hex# (show as hexadecimal number with specified number of
687 bits)
688 - sex, sexa2, sexa3, sexagesimal (show as sexagesimal number;
689 sexa2 hides and sexa3 rounds arcseconds)
690 - latitude, latitude2, longitude, longitude2 (show as sexagesi‐
691 mal latitude/longitude; latitude2 and longitude2 hide arcsec‐
692 onds)
693 - bijective (shown in bijective base-26)
694 - fp16, fp32, fp64, fp80, fp128 (show in binary floating-point
695 format)
696 - bcd (show as binary-coded decimal)
697 - roman (show as roman numerals)
698 - time (show in time format)
699 - unicode
700 - base # (show in specified number base)
701 - bases (show as binary, octal, decimal and hexadecimal number)
702 Complex format
704 - rectangular, cartesian (show complex numbers in rectangular
705 form)
706 - exponential (show complex numbers in exponential form)
707 - polar (show complex numbers in polar form)
708 - cis (show complex numbers in cis form)
709 - angle, phasor (show complex numbers in angle/phasor notation)
710 Time and date conversion
712 - UTC (show date and time in UTC time zone)
713 - UTC+/-hh[:mm] (show date and time in specified time zone)
714 - calendars
715 Other conversion commands
717 - fraction (show result as mixed fraction)
718 - factors (factorize result)
719 Similarly where (or alternatively "/.") can be used at the end (but be‐
721 fore "to"), for variable assignments, function replacements, etc. (e.g.
722 "x+y where x=1 and y=2", "x^2=4 where x>0", and "sin(5) where
723 sin()=cos()").
724
726 Note that semicolon can be replaced with comma, if comma is not used as
727 decimal or thousands separator.
728 Basic functions and operators
730 sqrt 4 = sqrt(4)
732 = 4^(0.5)
733 = 4^(1/2)
734 = 2
735 sqrt(25; 16; 9; 4)
737 = [5 4 3 2]
738 sqrt(32)
740 = 4 * sqrt(2) (in exact mode)
741 cbrt(-27)
743 = root(-27; 3)
744 = -3 (real root)
745 (-27)^(1/3)
747 = 1.5 + 2.5980762i (principal root)
748 ln 25 = log(25; e)
750 = 3.2188758
751 log2(4)/log10(100)
753 = log(4; 2)/log(100; 10)
754 = 1
755 5! = 1 * 2 * 3 * 4 * 5
757 = 120
758 5\2 (integer division)
760 = 5//2
761 = trunc(5/2)
762 = 2
763 5 mod 3 = mod(5; 3)
765 = 2
766 52 to factors
768 = 2^2 * 13
769 25/4 * 3/5 to fraction
771 = 3 + 3/4
772 gcd(63; 27)
774 = 9
775 sin(pi/2) - cos(pi)
777 = sin(90 deg) - cos(180 deg)
778 = 2
779 sum(x; 1; 5)
781 = 1 + 2 + 3 + 4 + 5 = 15
782 sum(i^2+sin(i); 1; 5; i)
784 = 1^2 + sin(1) + 2^2 + sin(2) + ... = 55.176162
785 product(x; 1; 5)
787 = 1 * 2 * 3 * 4 * 5 = 120
788 var1:=5 store value 5 in variable var1
790 5^2 #this is a comment
792 = 25
793 sinh(0.5) where sinh()=cosh()
795 = cosh(0.5) = 1.1276260
796 plot(x^2; -5; 5)
798 plots the function y=x^2 from -5 to 5
799 Units
801 5 dm3 to L
803 = 25 dm^3 to L
804 = 5 L
805 20 miles / 2h to km/h
807 = 16.09344 km/h
808 1.74 to ft = 1.74 m to ft
810 = 5 ft + 8.5039370 in
811 1.74 m to -ft
813 = 5.7086614 ft
814 100 lbf * 60 mph to hp
816 = 16 hp
817 50 Ω * 2 A
819 = 100 V
820 50 Ω * 2 A to base
822 = 100 kg*m^2*s^-3*A^-1
823 10 N / 5 Pa
825 = (10 N)/(5 Pa) = 2 m^2
826 5 m/s to s/m
828 = 0.2 s/m
829 500 EUR - 20% to USD
831 = 451.04 USD
832 500 megabit/s * 2 h to b?byte
834 = 419.09516 gibibytes
835 Physical constants
837 k_e / G * a_0
839 = (coulombs_constant / newtonian_constant) * bohr_radius
840 = 7.126e9 kg*H*m^-1
841 planck ∕ (compton_wavelength * c)
843 = 9.1093837e-31 kg
844 5 ns * rydberg to c
846 = 6.0793194E-8c
847 atom(Hg; weight) + atom(C; weight) * 4 to g
849 = 4.129e-22 g
850 (G * planet(earth; mass) * planet(mars; mass))/(54.6e6 km)^2
852 = 8.58e16 N (gravitational attraction between earth and mars)
853 Uncertainty and interval arithmetic
855 result with interval arithmetic activated is shown in parenthesis
856 sin(5+/-0.2)^2/2+/-0.3
858 = 0.460±0.088 (0.46+/-0.12)
859 (2+/-0.02 J)/(523+/-5 W)
861 = 3.824+/-0.053 ms (3.82+/-±0.075 ms)
862 interval(-2; 5)^2
864 = intervall(-8.2500000; 12.750000) (intervall(0; 25))
865 Algebra
867 (5x^2 + 2)/(x - 3)
869 = 5x + 15 + 47/(x - 3)
870 (\a + \b)(\a - \b) = ("a" + "b")("a" - "b")
872 = 'a'^2 - 'b'^2
873 (x + 2)(x - 3)^3
875 = x^4 - 7x^3 + 9x^2 + 27x - 54
876 factorize x^4 - 7x^3 + 9x^2 + 27x - 54
878 = x^4 - 7x^3 + 9x^2 + 27x - 54 to factors
879 = (x + 2)(x - 3)^3
880 cos(x)+3y^2 where x=pi and y=2
882 = 11
883 gcd(25x; 5x^2)
885 = 5x
886 1/(x^2+2x-3) to partial fraction
888 = 1/(4x - 4) - 1/(4x + 12)
889 x+x^2+4 = 16
891 x = 3 or x = -4
892 x^2/(5 m) - hypot(x; 4 m) = 2 m where x > 0
894 x = 7.1340411 m
895 cylinder(20cm; x) = 20L
897 x = (1 / (2pi)) m
898 x = 16 cm (height of 20 L cylinder with radius 20 cm)
899 asin(sqrt(x)) = 0.2
901 x = sin(0.2)^2
902 x = 0.039469503
903 x^2 > 25x
905 = x > 25 or x < 0
906 solve(x = y+ln(y); y)
908 = lambertw(e^x)
909 solve2(5x=2y^2; sqrt(y)=2; x; y)
911 = 32/5
912 multisolve([5x=2y+32, y=2z, z=2x]; [x, y, z])
914 = [-32/3 -128/3 -64/3]
915 dsolve(diff(y; x) - 2y = 4x; 5)
917 = 6e^(2x) - 2x - 1
918 Calculus
920 diff(6x^2)
922 = 12x
923 diff(sinh(x^2)/(5x) + 3xy/sqrt(x))
925 = (2/5) * cosh(x^2) - sinh(x^2)/(5x^2) + (3y)/(2 * sqrt(x))
926 integrate(6x^2)
928 = 2x^3 + C
929 integrate(6x^2; 1; 5)
931 = 248
932 integrate(sinh(x^2)/(5x) + 3xy/sqrt(x))
934 = 2x * sqrt(x) * y + Shi(x^2) / 10 + C
935 integrate(sinh(x^2)/(5x) + 3xy/sqrt(x); 1; 2)
937 = 3.6568542y + 0.87600760
938 limit(ln(1 + 4x)/(3^x - 1); 0)
940 = 4 / ln(3)
941 Matrices and vectors
943 [1, 2, 3; 4, 5, 6]
945 = ((1; 2; 3); (4; 5; 6))
946 = [1 2 3; 4 5 6] (2x3 matrix)
947 (1; 2; 3) * 2 - 2
949 = [(1 * 2 - 2), (2 * 2 - 2), (3 * 2 - 2)]
950 = [0 2 4]
951 [1 2 3].[4 5 6]
953 = dot([1 2 3]; [4 5 6])
954 = 32 (dot product)
955 cross([1 2 3]; [4 5 6])
957 = [-3 6 -3] (cross product)
958 [1 2 3; 4 5 6].*[7 8 9; 10 11 12]
960 = hadamard([1 2 3; 4 5 6]; [7 8 9; 10 11 12])
961 = [7 16 27; 40 55 72] (hadamard product)
962 [1 2 3; 4 5 6] * [7 8; 9 10; 11 12]
964 = [58 64; 139 154] (matrix multiplication)
965 [1 2; 3 4]^-1
967 = inverse([1 2; 3 4])
968 = [-2 1; 1.5 -0.5]
969 Statistics
971 mean(5; 6; 4; 2; 3; 7)
973 = 4.5
974 stdev(5; 6; 4; 2; 3; 7)
976 = 1.87
977 quartile([5 6 4 2 3 7]; 1)
979 = percentile((5; 6; 4; 2; 3; 7); 25)
980 = 2.9166667
981 normdist(7; 5)
983 = 0.053990967
984 spearman(column(load(test.csv); 1); column(load(test.csv); 2))
986 = -0.33737388 (depends on the data in the CSV file)
987 Time and date
989 10:31 + 8:30 to time
991 = 19:01
992 10h 31min + 8h 30min to time
994 = 19:01
995 now to utc
997 = "2020-07-10T07:50:40Z"
998 "2020-07-10T07:50CET" to utc+8
1000 = "2020-07-10T14:50:00+08:00"
1001 "2020-05-20" + 523d
1003 = addDays(2020-05-20; 523)
1004 = "2021-10-25"
1005 today - 5 days
1007 = "2020-07-05"
1008 "2020-10-05" - today
1010 = days(today; 2020-10-05)
1011 = 87
1012 timestamp(2020-05-20)
1014 = 1 589 925 600
1015 stamptodate(1 589 925 600)
1017 = "2020-05-20T00:00:00"
1018 "2020-05-20" to calendars
1020 returns date in Hebrew, Islamic, Persian, Indian, Chinese, Ju‐
1021 lian, Coptic, and Ethiopian calendars
1022 Number bases
1024 52 to bin
1026 = 0011 0100
1027 52 to bin16
1029 = 0000 0000 0011 0100
1030 52 to oct
1032 = 064
1033 52 to hex
1035 = 0x34
1036 0x34 = hex(34)
1038 = base(34; 16)
1039 = 52
1040 523<<2&250 to bin
1042 = 0010 1000
1043 52.345 to float
1045 = 0100 0010 0101 0001 0110 0001 0100 1000
1046 float(01000010010100010110000101001000)
1048 = 1715241/32768
1049 = 52.345001
1050 floatError(52.345)
1052 = 1.2207031e-6
1053 52.34 to sexa
1055 = 52°20'24"
1056 1978 to roman
1058 = MCMLXXVIII
1059 52 to base 32
1061 = 1K
1062 sqrt(32) to base sqrt(2)
1064 = 100000
1065
1067 The manual of the graphical user interface at https://qalcu‐
1068 late.github.io/manual/index.html (includes more details about the syn‐
1069 tax and elements supported in mathematical expressions, and various op‐
1070 tions, and includes a complete list of functions, variables, and units)
1071
1073 Please report any bugs at https://github.com/Qalculate/libqalculate/is‐
1074 sues
1075
1077 Hanna Knutsson <hanna.knutsson@protonmail.com>.
1078 13 July 2020 QALC(1)