Calc

• i manual
• h help
  • h all keybindings
  • s summary appendix
  • i manual
• ? rotate through the brief help

• <, > scroll to the right/left
• {, } scroll up/down

Edit

• U undo, D redo
• <TAB> rotate the top two
  • rotate the top N elements downward while wrapping if positive
  • move the entire stack N step downward if negative.
  • <M-...> rotate upwards
• <DEL> remove the top
  • remove the top N elements if positive
  • Delete the entire stack if 0
  • N th element form the top is removed if negative
  • <M-...> remove from the bottom

Input

• <RET> duplicate the top element
• <M-RET> push the last arguments
  • recover the deleted elements by a function
• [2-32]#NN input number in a given radix
• NNeNN scientific notation
• _ negative sign
• : enters the fraction
• [ .. , .. ; .. ] vector and matrix, [ .. ] [ .. ) interval, representing all number between the bounds
  • [ ( pushes the incomplete object and complete it later.
  • { .. , .. } can also be used. comma is required
• ( .. , .. ) ( .. ; .. ) complex number (in polar),
• NN@ NN' NN" hms time
• " string
• Operation can be put right after number
• $ can be used in place of the top stack element, the output will be replace the top
  • $$, $$$ repeatedly using dollar sign access N th element from the top
• ' algebraic input
  • Insert an expression containing symbols, equations, and various others
  • <RET> evaluate and the expression and insert
    • <M-RET> evaluate with the variables resolved, and insert
    • <C-j> or <LFD> (Line Feed) does not evaluate it, = to evaluate it later.
  • / has lower precedence than *.
  • a mod b modulo arithmetic
  • +/- to include the uncertainty
• < , : > inline function
  • The arguments are given in a vector.
  • It cannot be used on its own. It needs to be evaluated by another function, such as, call(f, a, b), v A, apply(f, v)

• They take the elements from the stack and perform certain operations
• Number prefix can be given
  • The binary operation is going to be reduce the top N elements if positive, or operate on each N next-to-top element by the top element if negative.
• +, -, *, /, ^
• \ integer division, % modulo
• : fraction
• ~ can be used to use the top element as the prefix number
• K keep the arguments in the stack by prefixing this
• Evaluation
  • = evaluate and substitute the stored variables
  • N expand the irrational values
  • a v evaluate algebra
• Simplification
  • a s algebraic simplification
  • u s unit simplification
    • Automatically applied when in UnitSymp mode

• p, pack(a, ...) pack first few top element into another object depending on the mode specified by numeric prefix N, or the value of the top element.
  • Vector of length N if N is nonnegative
  • -1 complex number
  • -2 polar complex number
  • -3 HMS form
  • -4 error form
  • -5 modulo form
  • -6 closed interval, -7 upper half-open interval, -8 lower half-open interval, -9 open interval
  • -10 fraction
  • -11 mantissa and exponent into floating point number
• u, unpack(a, ...) unpack the top element
  • negative number specifies the mode
  • It can unpack any formula as well, including equations
    • It unpack the structure given by the underlying lisp representation.
• (Without the prefix) |, vconcat(a,b) concatenate top two element into a vector, I | in reverse order, H | not recursively.
• E convert an interval into a vector of integers
• : vector into an interval
• i push an identity matrix
• d diagonal matrix out of the top
• x push the index vector
• r, c, mrow(m, i), mcol(m, i) extract the row/column of a matrix at the index of the top element or numeric prefix. s, subvec(m, i1, i2) extract a subvector from the first index up to the second index excluding it.
  • The index is counted from 1
    • A row/column is removed if negative number
  • m_i, subscr can be used for the algebraic case.
• f search for an element in a vector
• a arrange a vector or a matrix into a matrix of a given number of column
• v reverse the vector
• h, head(v) take the head, the first element of a vector.

• v evaluate the algebra, " expand into the definition
• s simplify
  • x expand: divide fractions, distribute multiplication
  • f factor a polynomial
    • H a f return the list of factors with its multiplicity.
  • c, collect express the polynomial in a given variable.
  • n, nrat(a) normalize rational (symbolic fractions into a one rational expression), a partial fraction
  • \ polynomial division, % polynomial remainder, g polynomial gcd
  • I a s trigonometric function simplification
  • H a s hyperbolic function simplification
  • a e extended (unsafe) simplification
• d derivative, i (integ(f), integ(f(x), x, a, b)) integrate
  • I (ninteg) numerical integration
• M map equation
  • Map both side of the equation
• P find the root of polynomial
• S solve the equations
  • It can also take a vector of equations and a vector of variables.
• R root finding
  • A formula or an equation is solved numerically, starting from the top element
  • It can also take a vector of equations, and a vector of initial values, a vector of variables.
  • Assigned variable can be used, _ dose not constitute a variable.
  • The formulas have to be differentiable
• F curve fitting
  • It act on a list of list containing each variables consecutively.
  • The number specify the detail
  • 1 linear, 2 - 9 multilinear
  • e, x, E, X polynomial, l, L logarithmic
  • q quadratic
  • g Gaussian function
  • s Logistic
  • …
• + sum over a given range
• * product over a given range

• Inverse modifier I, and hyperbolic modifier H are often used
• Q, sqrt(a)
• F, floor(a), I F, ceil(a)
• R, round(a), I R, trunc(a)
• J, conj(a) complex conjugate, G, arg(z) argument
• L, ln(z), E, exp(z), H L, log10(z), B, log(b x)
• S, sin(z), C, cos(z), T, tan(z), H ...
• ! factorial
• f
  • h, hypot(a,b) hypotenuse
  • Q, isqrt(a) integer square root, square root rounded down
  • n, min(m, n)
  • x, max(m, n)
  • r, re(z) real part, i, im(z) imaginary part
  • g, gamma(z) Gamma function
  • b, beta(a,b) Beta function
  • e, erf(z) Error function
  • j, besJ(n,x), y, besY(n,x) Bessel function
• k Combinatorial/Statistical
  • g, gcd(a,x) Greatest common divisor
  • l, lcm(a,x) Least Common Multiple
  • c, choose(n,m) , H ... permutation
  • b, bern(n) Bernoulli numbers
  • e, euler(n) Euler numbers, H ... Euler polynomial
  • s, stir1(n) of the first kind, H ... stir2(n) of second kind
  • p test if prime
    • For a large integer, probabilistic method in The Art of Computer Programming-volume 2-section 4.5.4-algorithm P is used.
  • f, prfac(n) prime factorization
  • n, nextprime(n), I ..., prevprime(n)
  • t, totient(n) Euler's totient function
  • m, mobius(n)
  • Probability Distributions
    • The nomenclature is X utpx, H ... ltpx for cumulative
    • The random variable is the top element
    • B, utpb(x,n,p) Binomial distribution
    • C, utpc(x,v) Chi-squared distribution
    • F, utpf(F,v1,v2) F-distribution
    • N, utpn(x,m,s) Normal distribution
    • T, utpt(t,v) t-distribution

• r random()
  • It generate a random integer between 0 and the numeric prefix, or the top element
    • a generate a number reusing the recent value
    • h shuffle
  • It shuffles the top vector, may be truncated to a desired length

• Units are just unassigned variables that are in the unit table
• Number with unit can be entered as a algebraic expression. Most common units and constants are predefined
  • eps0 ɛ0, mu0 μ0, c, G, h, hbar, e ech, k, …
• s simplify for the unit expression, a autorange unit prefix the unit with appropriate one.
• c unit convert, n convert if exact, b convert to base unit, equivalent to s base
• d, u define/undefine unit, r remove unit, u p make it permanent in the calc.el
• g get unit definition, v show unit table
• s Store
• inf, e, pi, phi, gamma, uinf, nan are preassigned variables
  • These are only evaluated by N, not =

• If the variable name is a number N it is stored in special variable qN. The quick variables can be directly specified without s
• If the top element is an assign statement: =, :=, it will perform it
• r recall, push the value
• u unstore
• t store into, pop the top element and store
• x exchange with the top of the stack
• c copy to another variable
• +, - , … perform the operation and assign, equivalent to +=
• = evaluate to, enter the evaluation statement of the top element
  • => The expression on the left is untact, the value on the right is recomputed by = (evaluate) whenever something changes.
• d declare the type of a variable or a function
• l temporarily store the top element and evaluate the second-top element with it.
• i (calc-insert-variables) insert all variables in current calc to a buffer.
  • variable can be defined any other buffer than calc
  • literal string is interpreted automatically by calc
• p (calc-permanent-variable) specify variable to store into the calc-settings-file (.emacs.d/calc.el by default)
  • edit the file directly when deleting variable

• Select within a entry and perform operation on them
• s, u select/unselect
• a add, b break selection, m l select more/less, 1, …, 9 select =N=th part
• n, p select next/previous
• d highlight selected part within the whole formula
• c clear all selection
• e enable/disable selection. the * marker disappears and the operation works on the entire formula anyway. It is enables by default.
• ' replace selection through minibuffer input
• ` edit selection through a temporary buffer
• R, L commute right/left, C commute within a selection
• D, M distribute/merge a level
• J jump equals, move a term on the other side of the equation
• +, -, *, /, … Operate on both side of a equation, or numerator and denominator of a fraction.

• f convert fraction to float, F float to fraction
• p between polar and rectangular complex numbers
• d, r, h degree, radian, hms

• t Truncate. It cuts the stack at the cursor, and stashes the ones "above" it.
• r change the radix
• c, i, j, complex number format
• Language
  • N normal, B big (pretty print), U unformatted(raw Lisp), C, L LaTeX, T TeX
  • The complex number format does not apply in B and C

• The current mode is displayed in the mode line
  • a partly algebraic mode, ( and [ also starts algebraic input.
  • t full algebraic mode, <ESC> to not use algebraic input.
• S ignore cases, the prefix key becomes case insensitive.
  • d degree, r radian
    • The default unit of the output of functions that produce angles
  • p polar mode, prefer complex number
  • f fraction mode, prefer fraction
    • c f can be used to evaluate the fractions
  • i infinite mode, 1/0 produce inf
  • s symbolic mode, the irrational result will be left symbolic
    • N can be used evaluate into numeric result
  • v matrix mode, every object is assumed to be matrices unless it cannot be
  • C toggle automatic recomputation, =>
  • Simplification
    • I basic simplification
    • U unit simplification
    • A algebraic simplification (Default)
    • N number simplification, only number operations are simplified
    • E extended simplification
    • O no simplification
  • m save modes, including display/language/precision/definition/calculation
  • g get modes, push the mode numbers
  • R record mode change directly into the file

• d toggle trail
• i, o focus into/outof trail
• n, p, [, ] move the trail marker > (to the start/end), y push trail marker to the stack
• s, r search (in reverse)

• N push current datetime
• D date into a number measured since Jan 1, 1 AD
• J convert date into Julian day count
• U convert date into unix time value
• C convert time zone of date

• It stores the values in a temporary buffer and let the Gnuplot plot it.
• f Fast plot. graph the top two element using . top element is the \(y\).
  • \(x\), \(y\) can be a vector of same length
  • \(x\) can be an interval, then \(y\) needs to be an algebraic expression in one unassigned variable
  • The top element can be a formula of the form xy(x(t), y(t)).
• p plot
• a, d, c add/delete/clear the plot
• g, b, k… grid, border, key
• N select the number of datapoints
• q quit the plot

• Z D bind the function to a key

• C-x ( , C-x ) the global kmacro can include the following calc specific functionalities.

  • Branch
    • <COND> Z [ start if, Z | else if, Z : else, Z ] end if

  • Loop

    • <repeat count> Z < <BODY> Z > repeats a command in between, the top value times.
      • <repeat count> is the top element
        • <init> <final> Z ( <BODY> <step> Z ) for loop, repeat with

    counter

    • <init>, <final> are the top two elements of the stack
    • <step> is a number
      • <COND> Z / break out of macro loop
    • Breaks when the top element <COND> evaluates to true.
      • Z {, Z } loop forever
    • Scope
      • Z `
      • Z '
    • Z K set macro name for the last recorded macro, which can

  be executed by z

  • Z E edit macro
  • <C-x> e or X execute macro
    • <C-x> e create a undo history for each command, X create a single undo history
• Z I define user invocation
  • m m saves this
• Z F define a formula
  • The formula at the top element is stored into specified key, command and function.
  • The anonymous function can also be used.
  • Z G push the formula to the stack
• Z P define a command permanently in the calc.el
• Z U undefine
• z is prefixed to use the user defined keys and functions
• Lisp
  • defmath can be used
  • (interactive NUM TAG)
    • Takes NUM arguments from the stack.
  • (calc-eval "expr") is available

• s copy the region as calc stack to register
• i insert calc stack, or parse the string and insert