calc.org

calc examples

1 Version information

(princ (concat (format "Emacs version: %s\n" (emacs-version))
               (format "org version: %s\n" (org-version))))

Emacs version: GNU Emacs 24.5.1 (x86_64-unknown-linux-gnu, GTK+ Version 3.10.8)
 of 2015-05-04 on dflt1w
org version: 8.3.2

2 General

• refer to the Calc info pages
• Note that, unlike in usual computer notation, multiplication binds more strongly than division: `a*b/c*d’ is equivalent to `(a*b)/(c*d)’

3 babel calc

Not too useful, yet. Embedded calc certainly is better for inlining math in documents. Using Elisp to directly interacting with calc also is more powerful.

24
3
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• solving an equation

  fsolve(x*2+x=4,x)
      

  x = 1.33333333333
      

• solving a linear system of equations

  fsolve([x + y = a, x - y = b],[x,y])
      

4 calc usage in tables

4.1 Unit conversions

• from http://article.gmane.org/gmane.emacs.orgmode/93489

Displaying all calc units in a buffer can be obtained by executing

Calc preserves units and variables in table operations.

distance	time	speed
3 km	2.5 hr	1.2 km / hr

speed	simplified speed
40km / 2.5hr	16. km / hr

We can also decide to use calc via its elisp api. To understand the following lisp formula that involves calc internal functions q.v. the Calc from lisp section.

km	ft
2.5km	8202.10

Defining a new calc function for unit conversion with defmath

(defmath uconv (expr target-units &optional pure)
  (math-convert-units expr target-units pure))

km	ft
2.5 km	8202.0997 ft

Using the units from the table header:

km	ft
2.5	8202.0997

The same without a user’s defmath:

km	ft
2.5	8202.0997

Unit	Definition
km	#ERROR

5 Calc from lisp

• Emacs Info Manual: Calling Calc from your programs
• nice blog post on RSA cryptography using emacs Calc by Chris Wellons on his nullprogram blog. Contains examples on calc-eval usage.

5.1 basic use of calc-eval

The variables in formulas are replaced by the additional arguments. Arguments can be given as string or number.

(print (calc-eval "2^$1 - 1" nil 128))
(print (calc-eval "$1 < $2" 'pred "4000" "5000"))
(print (calc-eval "nextprime($1)" nil "100000000000000000"))

;; radix can be chosen by separating radix by # from number
(print (calc-eval "16#deadbeef"))
(print (calc-eval "2#1111"))

The second argument serves as a separator if the input string parses to a list of expressions. By default the list is printed comma-separated.

(print (calc-eval "10+5,7*3,5/2"))
(print (calc-eval "10+5,7*3,5/2" ";"))
(print (calc-eval "10+5,7*3,5/2" "___"))

5.2 Stack operations: push, pop and top

• push pushes the element onto the stack
• pop deletes as many elements from the stack as the preceding integer argument indicates
  • 0 pop is convenient for finding out the size of the stack
• top retrieves the value at the indicated position of the stack

(princ (format "Size of the stack: %s\n" (calc-eval 0 'pop)))
(calc-eval "10 ft" 'push)
(calc-eval "20 ft" 'push)
(calc-eval "30 ft" 'push)
(princ (format "After 3*push: Size of the stack: %s (top element: %s)\n"
               (calc-eval 0 'pop)
               (calc-eval 1 'top)))
(princ (format "element on second level of stack: %s\n" (calc-eval 2 'top)))
(calc-eval 2 'pop)
(princ (format "After 3*push: Size of the stack: %s (top element: %s)\n"
               (calc-eval 0 'pop)
               (calc-eval 1 'top)))
(calc-eval 1 'pop)

Size of the stack: 5
After 3*push: Size of the stack: 8 (top element: 30 ft)
element on second level of stack: 20 ft
After 3*push: Size of the stack: 6 (top element: 10 ft)

5.3 executing functions on the stack

(calc-eval "10 ft" 'push)
(calc-base-units)
;; retrieve the value from the stack as a string. Note that it still stays on the stack!
(print (calc-eval 1 'top))
;; clean the value from the stack
(calc-eval 1 'pop)

"3.048 m"

It is also possible to execute Calc keyboard macros, i.e. the string is interpreted as interactive keyboard strokes in calc mode.

(calc-eval "10 ft" 'push)
;; calc keys for base unit conversion
(calc-eval "ub" 'macro)
(print (calc-eval 1 'top))
;; pop one item from stack
(calc-eval "\C-d" 'macro)

"3.048 m"

5.4 raw calc objects as input to functions

calc internal functions deal with raw calc objects. These can also be obtained through calc-eval by passing the raw as the second argument.

(calc-eval (math-convert-units (calc-eval "10 m" 'raw)
                               (calc-eval "ft" 'raw)))

6 A sample of functions that can be used in formulas

• info:calc#Formulas
• factorial: $6! => 720 $ also fact(6) can be used in writing
• find: $ find([5, 6, 7, 8], 6) => 2 $
• power: $pow(2, 3) => 8 $ $2^3 => 8 $
• modulo: $mod(10, 3) => 1$ $10 % 3 => 1 $
• binomial coefficient: $choose(3, 2) => 3$
• random numbers: $random(10) => 7$
• binomial distribution: the result (`utpb(x,n,p)’) is the probability that an event will occur X or more times out of N trials, if its probability of occurring in any given trial is P: $utpb(2, 6, 1/6) => 0.263224451304$
• gaussian distribution with mean m and stdev s. Probability that a normal distributed random variable will exceed x: uttn(x,m,s): $utpn(0.2b, 0, 0.5) => 0.34457825839$
  • http://www-zeuthen.desy.de/~kolanosk/smd_ss02/skripte/

    $now(0) => <11:03:18pm Sun Aug 11, 2013>$ $unixtime(now(0)) => 1376262280$