Functions

The built-in functions, by group:

And all of them from A to Z:

Function	What it does
`abs`	The absolute value of x, or the magnitude of a complex number. Also written \|x\|.
`acos`	The angle whose cosine is x, between 0 and π.
`acosh`	The inverse hyperbolic cosine of x, for x of 1 or more.
`acot`	The angle whose cotangent is x, between 0 and π.
`acoth`	The inverse hyperbolic cotangent of x, for x beyond −1 and 1.
`acsc`	The angle whose cosecant is x.
`arg`	The angle of z in the complex plane, between −π and π.
`asec`	The angle whose secant is x.
`asin`	The angle whose sine is x, between −π/2 and π/2.
`asinh`	The inverse hyperbolic sine of x.
`atan`	The angle whose tangent is x, between −π/2 and π/2.
`atan2`	The angle of the point (x, y) from the x axis, between −π and π; x and y may have units, the same.
`atanh`	The inverse hyperbolic tangent of x, for x between −1 and 1.
`augment`	The matrices side by side; they need the same number of rows.
`Ceil`	The smallest multiple of y not below x.
`ceil`	The smallest integer not below x.
`cells`	A range of a named table’s grid, written as in a spreadsheet, the header being row 1.
`CFFT`	As cfft, scaled by 1/n and with the opposite sign in the exponent.
`cfft`	The Fourier transform of a complex vector or matrix of any size, scaled by 1/√n.
`cnorm`	The probability that a standard normal variable is below x.
`cols`	The number of columns of A.
`concat`	The strings joined.
`conj`	The complex conjugate of z, element by element in an array.
`corr`	The correlation coefficient of the two vectors.
`cos`	The cosine of x.
`cosh`	The hyperbolic cosine of x.
`cot`	The cotangent of x, 1/tan(x).
`coth`	The hyperbolic cotangent of x, 1/tanh(x).
`cross`	The cross product of the three-element vectors u and v.
`csc`	The cosecant of x, 1/sin(x).
`csch`	The hyperbolic cosecant of x, 1/sinh(x).
`csort`	The rows of A sorted by column j.
`cspline`	A cubic spline through the points, with cubic ends, for interp.
`diff`	The derivative of f with respect to x (the nth derivative, up to 5) at x’s current value.
`dnorm`	The probability density of the normal distribution at x.
`eigenvals`	The eigenvalues of the square matrix M, as a column.
`eigenvec`	The eigenvector of M for the eigenvalue λ, of length 1.
`eigenvecs`	The eigenvectors of M, one per column, in the order of eigenvals(M), each of length 1.
`erf`	The error function.
`erfc`	The complementary error function, 1 − erf(x).
`error`	Stops with the message s: in a program, for a value that can’t be used.
`exp`	e to the power x.
`FFT`	As fft, scaled by 1/n and with the opposite sign in the exponent.
`fft`	The Fourier transform of the real vector v (2ⁿ elements), its first half and the middle, scaled by 1/√n.
`find`	Below `given`, the values of the unknowns that satisfy its constraints, starting from their current values.
`Floor`	The largest multiple of y not above x; x and y may have units, the same.
`floor`	The largest integer not above x.
`gamma`	The gamma function, as Γ(x).
`hist`	How many of the data fall in each interval: intervals is a vector of their ends, or the number of equal intervals.
`histogram`	As hist, beside the middle of each interval: a column of middles, then one of counts.
`hlookup`	The elements of row i of A in the columns whose first element is z.
`ICFFT`	The inverse of CFFT.
`icfft`	The inverse of cfft.
`identity`	The n×n identity matrix.
`if`	a if c is true (not zero), otherwise b; only the one chosen is evaluated.
`IFFT`	The inverse of FFT.
`ifft`	The inverse of fft: the real vector whose transform is c.
`Im`	The imaginary part of z.
`int`	The definite integral of f over x from a to b; either limit may be ∞.
`intercept`	Where the least-squares straight line crosses x = 0.
`interp`	The value at x of a spline from cspline, pspline or lspline, or of a polynomial from regress.
`IsArray`	1 if x is an array, 0 if not.
`IsScalar`	1 if x is a number, 0 if not.
`IsString`	1 if x is a string, 0 if not.
`last`	The index of the last element of v, counting from ORIGIN.
`length`	The number of elements of the vector v.
`linfit`	The least-squares coefficients of a sum of terms: F(x) returns a vector of the terms.
`linspace`	n values evenly spaced from a to b, as a column.
`linterp`	The value at x of the straight lines between the points (vx, vy); beyond the ends, the end line carries on.
`ln`	The natural logarithm of x.
`lnΓ`	The natural logarithm of the gamma function, for large x.
`log`	The logarithm of x to base 10, or to base b.
`logspace`	n values from a to b, evenly spaced on a log scale.
`lookup`	The elements of B in the places where A holds z.
`lspline`	A cubic spline with straight ends (the natural spline), for interp.
`match`	The positions in A of the value z, or with mode “near”, “lt”, “gt”, “leq” or “geq” of the nearest value, the one just below or just above.
`matrix`	An m×n matrix whose element (i, j) is f(i, j), i and j counting from 0.
`max`	The largest of the numbers given, arrays included element by element.
`Maximize`	The values of the variables where f(x, y, …) is greatest.
`mean`	The mean of all the numbers given.
`median`	The median of all the numbers given.
`min`	The smallest of the numbers given.
`minerr`	Below `given`, the values that come closest to satisfying its constraints, when they can’t all hold.
`Minimize`	The values of the variables, from their current values, where f(x, y, …) is least; below `given`, within its constraints.
`mod`	The remainder of x divided by y, with the sign of x.
`nthroot`	The real nth root of x; an odd root of a negative number is negative.
`num2str`	The number x as a string.
`Odesolve`	Below `given`, the solution of its differential equation and initial conditions as a function of t, up to b.
`pause`	Returns x, for compatibility with imported sheets.
`pnorm`	The probability that a normal variable is below x.
`polyroots`	The roots of the polynomial v₀ + v₁x + v₂x² + …, as a column, complex where they are.
`prod`	The product of the elements of v, or of f over i. Also written with Π.
`pspline`	A cubic spline with parabolic ends, for interp.
`qnorm`	The x below which a normal variable falls with probability p.
`Re`	The real part of z.
`READCSV`	A comma-separated file as a matrix, numbers and text kept apart.
`READEXCEL`	The cells of an Excel workbook (.xlsx or .xls), all of its first sheet or a range; in the desktop app.
`READFILE`	A data file, type being “delimited” (spaces, tabs or commas) or “csv”.
`READPRN`	The numbers in a text file, in columns separated by spaces, tabs or commas; lines that aren’t numbers are skipped.
`regress`	The least-squares polynomial of degree k through the points, for interp.
`reverse`	The elements of v in reverse order (the rows of a matrix).
`Rkadapt`	As rkfixed, at the same n points, with adaptive steps between them for accuracy.
`rkadapt`	The same as Rkadapt.
`rkfixed`	The solution of y’ = D(x, y) from x1 to x2 in n equal steps (fourth-order Runge–Kutta): a column of x, then one per element of y.
`rnd`	A random number between 0 and x, the same at every recalculation.
`rnorm`	m random numbers from the normal distribution, as a column.
`root`	A value of x where f is zero: from x’s current value as a guess, or between a and b where f changes sign.
`Round`	x rounded to the nearest multiple of y.
`round`	x rounded to n decimal places, or to an integer.
`rows`	The number of rows of A (0 for a number).
`rsort`	The columns of A sorted by row i.
`runif`	m random numbers between a and b, as a column.
`search`	The position of t in s, looking from position m, or −1 if it isn’t there.
`sec`	The secant of x, 1/cos(x).
`sech`	The hyperbolic secant of x, 1/cosh(x).
`sign`	−1, 0 or 1, as x is negative, zero or positive.
`signum`	z divided by its magnitude, or 0 when z is 0.
`sin`	The sine of x, an angle in radians, or with a unit such as deg.
`sinh`	The hyperbolic sine of x.
`SIUnitsOf`	One of x’s unit in SI, so that x/SIUnitsOf(x) is the plain number.
`slope`	The slope of the least-squares straight line through the points.
`sort`	The elements of v in ascending order.
`sqrt`	The square root of x, with its units halved.
`stack`	The matrices one above the other; they need the same number of columns.
`Stdev`	The standard deviation of a sample.
`stdev`	The standard deviation of a whole population.
`str2num`	The number written in the string s.
`strlen`	The number of characters in s.
`submatrix`	The part of A from row ir to jr and column ic to jc, counting from ORIGIN.
`substr`	n characters of s from position m (counting from 0).
`sum`	The sum of the elements of v, or of f over the range variable i, or over i from a to b. Also written with Σ.
`tan`	The tangent of x.
`tanh`	The hyperbolic tangent of x.
`time`	The time now in seconds (z is not used), for timing a long calculation.
`tr`	The trace of the square matrix M, the sum of its diagonal.
`trace`	Returns x, for compatibility with imported sheets.
`Trunc`	The multiple of y nearest x towards zero.
`trunc`	The integer part of x, towards zero.
`UnitsOf`	The same as SIUnitsOf.
`use`	The functions of a Python file, as a module: `bt := use "beam.py"`, then `bt.f(x)`; in the desktop app.
`Var`	The variance of the numbers as a sample (dividing by n − 1).
`var`	The variance of the numbers as a whole population (dividing by n).
`vec`	The expression evaluated element by element over its arrays (the vectorize arrow).
`vlookup`	The elements of column j of A in the rows whose first element is z.
`Γ`	The gamma function: Γ(n) is (n − 1)! for a whole number n.