ARITHMETIC/ALGEBRA 
Arithmetic 
BASE 
Convert an integer to the text representation of that number for a given radix (base).^{†} Available in XLeratorDB/math 2008 only 
BASE2DECIMAL 
Convert the text representation of a number in a given radix (base) to an integer.^{†} Available in XLeratorDB/math 2008 only 
COMBIN 
Calculate the number of combinations for a given number of items. 
COMBINA 
Calculate the number of combinations with repitition of n things taken r at a time.^{†} Available in XLeratorDB/math 2008 only 
DISTANCE 
Calculate the distance between 2 points on the globe, using the great circle formula. 
EGCD 
Calculate the greatest common divisor using Euclid's method. 
ELCM 
Calculate the least common multiple using Euclid's method. 
EVEN 
Calculate a number rounded up to the nearest even integer. 
FACT 
Calculate the factorial of a number. 
FACTDOUBLE 
Calculate the double factorial of a number. 
GCD 
Calculate a number rounded up to the nearest even integer. 
LCM 
Calculate the greatest common divisor of all the values, or only the DISTINCT values, in the expression. 
MAX 
Calculate the nth largest distinct value in a dataset. Available in XLeratorDB/math 2008 only 
MIN 
Calculate the nth smallest distinct value in a dataset. Available in XLeratorDB/math 2008 only 
MROUND 
Calculate a number rounded to the desired multiple. 
MULTINOMIAL 
Calculate the ratio of a sum of values to the product of the factorials of those values.^{†} 
MULTINOMIAL_q 
Calculate the ratio of a sum of values to the product of the factorials of those values.^{†} 
ODD 
Calculate a number rounded up to the nearest odd integer. 
POWER 
Calculate the value of the specified expression to the specified power. Available in XLeratorDB/math 2008 only 
PRODUCT 
Calculate the product of all the values, or only the DISTINCT values, in a dataset. 
PRODUCT38 
Calculate the product of 2 decimal(38,18) values as a decimal with precision 38 and scale 18. 
QUOTIENT 
Calculate integer portion of a division. 
QUOTIENT38 
Calculate the quotient of 2 decimal(38,18) values as a decimal with precision 38 and scale 18. 
SERIESSUM 
Calculate the sum of a power series.^{†} 
SERIESSUM_q 
Calculate the sum of a power series.^{†} 
SUMSQ 
Calculate the sum of the squares of all the values, or only the DISTINCT values, in the expression. 
WAVG 
Calculate the weighted average. Available in XLeratorDB/math 2008 only 

Equalities 
GREATEROF 
Calculate the greater of two values passed into the function. 
LESSEROF 
Calculate the lesser of two values passed into the function. 

Rounding 
CEILING 
Calculate a number rounded up, away from zero, to the nearest multiple of significance. 
FLOOR 
Calculate a number rounded down, towards zero, to the nearest multiple of significance. 
INT 
Calculate a number rounded down, towards zero, to the nearest integer. 
ROUNDDOWN 
Calculate a number rounded down, towards zero. 
ROUNDUP 
Calculate a number rounded up, away from zero. 
TRUNC 
Calculate a number truncated to an integer by removing the fractional part of the number. 

Formatting 
ROMAN 
Calculate an Arabic numeral converted to a Roman numeral, as text. 

TRIGONOMETRIC 
ACOSH 
Calculate the inverse hyperbolic cosine of a number. 
ACOT 
Calculate the arccotangent of a number.^{†} Available in XLeratorDB/math 2008 only 
ACOTH 
Calculate the hyperbolic arccotangent of a number.^{†} Available in XLeratorDB/math 2008 only 
ASINH 
Calculate the inverse hyperbolic sine of a number. 
ATANH 
Calculate the inverse hyperbolic tangent of a number. 
COSH 
Calculate the hyperbolic cosine of a number. 
COTH 
Calculate hyperbolic cotangent of a number.^{†} Available in XLeratorDB/math 2008 only 
CSC 
Calculate the cosecant of the given angle. 
CSCH 
Calculate the hyperbolic cosecant of the given angle.^{†} Available in XLeratorDB/math 2008 only 
SEC 
Calculate the secant of the given angle. 
SECH 
Calculate the hyperbolic secant of the given angle.^{†} Available in XLeratorDB/math 2008 only 
SINH 
Calculate the hyperbolic sine of a number. 
TANH 
Calculate the hyperbolic tangent of a number. 

NUMERICAL INTEGRATION 
QUAD 
Evaluate an infinite integral. 
QUADDE 
Evaluate an infinite integral. 
QUADGK 
Evaluate a finite integral. 
QUADOSC 
Evaluate an infinite integral. 
QUADTS 
Evaluate a finite integral. 

INTERPOLATION 
BILINEARINTERP 
Interpolate on a regular 2dimensional grid.^{†} 
INTERP 
Calculate the straightline interpolated value of y given x in the array (x, y). 
INTERP_q 
Calculate the straightline interpolated value of y given x in the array (x, y).^{†} 
INTERP2 
Interpolate on a 2dimensional grid in 3rd normal form. Available in XLeratorDB/math 2008 only 
LINEAR 
Calculate the straightline interpolated value of y given x in the array (x, y). 
MONOSPLINE 
Calculate the interpolated value of y given x in the array (x, y). Available in XLeratorDB/math 2008 only 
POLYCOEF 
Obtain a specific coefficient value from an approximating polynomial for a set of x and yvalues. Available in XLeratorDB/math 2008 only 
POLYFIT 
Calculate the coefficients of a polynomial p(x) of degree that fits the x and yvalues supplied to the function.^{†} (tablevalued function) 
POLYFIT_q 
Calculate the coefficients of a polynomial p(x) of degree n ;that fits the x and yvalues supplied to the function.^{†} (tablevalued function) 
POLYINTERP 
Calculate the interpolated value of y given x in the array (x, y). Available in XLeratorDB/math 2008 only 
POLYRSQ 
Calculate the goodness of fit for an approximating polynomial calculated from a series of x and yvalues for a specified number of degrees. Available in XLeratorDB/math 2008 only 
POLYVAL 
Calculate a new yvalue given a new xvalue using the coefficients of a polynomial p(x) of degree that fits the x and yvalues supplied to the function. Available in XLeratorDB/math 2008 only 
SPLINE 
Calculate the interpolated value of y given x in the array (x, y). 
SPLINE_q 
Calculate the interpolated value of y given x in the array (x, y).^{†} 

MATRIX FUNCTIONS 
Matrix Factorization 
LU 
Calculate the LU factorization of an N x N matrix using partial pivoting. 
LUdecomp 
Calculate the LU factorization of an N x N matrix using partial pivoting.^{†} 
LUdecomp_q 
Calculate the LU factorization of an N x N matrix using partial pivoting.^{†} 
LUdecompN 
Calculate the LU factorization of an N x N matrix using partial pivoting.^{†} 
LUdecompN_q 
Calculate the LU factorization of an N x N matrix using partial pivoting.^{†} 
MSYMMEIG 
Return the D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix.^{†} Available in XLeratorDB/math 2008 only (tablevalued function) 
QR 
Decompose a string representation of an N x N matrix into the product of an upper triangular matrix and an orthogonal matrix Q, such that A=QR. 
QRdecomp 
Decompose a denormalized N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q, such that A = QR.^{†} 
QRdecomp_q 
Decompose a denormalized N x N matrix into the product of an upper triangular matrix R and an orthogonal matrix Q, such that A = QR.^{†} 
SYMMEIG 
Return the D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix.^{†} Available in XLeratorDB/math 2008 only (tablevalued function) 

Matrix Math 
BKSUB 
Return a solution to the equation A*x=b, when A is an uppertriangular matrix. 
CORRM

Calculate a correlation matrix.^{†} (tablevalued function) 
COVM

Calculate a sample covariance matrix.^{†} (tablevalued function) 
CROSSPROD

Calculate the matrix crossproduct of 2 matrices. 
FWDSUB 
Return a solution to the equation A*x=b, when A is a lowertriangular matrix. 
MATADD 
Add a value to every element of a matrix or to add 2 matrices of the same dimensions together. 
MATINVERSE 
Calculate the matrix inverse of a square (N x N) matrix. 
MATMULT 
Calculate the product of two matrixes or to multiply a matrix by a constant. 
MATSUB 
Subtract a value from every element of a matrix or to calculate the difference between 2 matrices of the same dimensions. 
MCORR

Calculate a correlation matrix. 
MCOV

Calculate a sample covariance matrix. 
MCROSS

Calculate the matrix crossproduct of 2 matrices.^{†} (tablevalued function) 
MDETERM 
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.^{†} 
MDETERM_q 
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.^{†} 
MDETERMN 
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.^{†} 
MDETERMN_q 
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.^{†} 
MINVERSE 
Calculate the matrix inverse of a square (N x N) matrix.^{†} 
MINVERSE_q 
Calculate the matrix inverse of a square (N x N) matrix.^{†} 
MINVERSEN 
Calculate the matrix inverse of a square (N x N) matrix.^{†} 
MINVERSEN_q 
Calculate the matrix inverse of a square (N x N) matrix.^{†} 
MMULT 
Calculate the matrix product of two arrays.^{†} 
MMULT_q 
Calculate the matrix product of two arrays.^{†} 
MMULTN 
Calculate the matrix product of two arrays in thirdnormal form.^{†} 
MMULTN_q 
Calculate the matrix product of two arrays in thirdnormal form.^{†} 
MNORM 
Calculate the 1norm, 2norm, Infinitynorm, Frobenius norm, and maximum modulus of a matrix.^{†} Available in XLeratorDB/math 2008 only 
MRANK 
Calculate the rank of a matrix.^{†} Available in XLeratorDB/math 2008 only 
MTRACE 
Calculate the trace of a denormalized matrix.^{†} 
MTRACE_q 
Calculate the trace of a denormalized matrix.^{†} 
MTRACEN 
Calculate the trace of a matrix in thirdnormal form.^{†} 
MTRACEN_q 
Calculate the trace of a matrix in thirdnormal form.^{†} 
MTRIL 
Return the lower triangular part of the string representation of a matrix. 
MTRIU 
Return the upper triangular part of the string representation of a matrix. 
SPECRAD 
Calculate the spectral radius of a square matrix.^{†} Available in XLeratorDB/math 2008 only 
SUMPRODUCT 
Calculate the sum of the elementwise multiplication of 1 or more matrices.^{†} Available in XLeratorDB/math 2008 only 
SUMX2MY2 
Calculate the sum of the differences of the squares in the corresponding elements in 2 matrices.^{†} Available in XLeratorDB/math 2008 only 
SUMX2PY2 
Calculate the sum of the sum of the squares in the corresponding elements in 2 matrices.^{†} Available in XLeratorDB/math 2008 only 
SUMXMY2 
Calculate the sum of the sqaure of the differences in the corresponding elements in 2 matrices.^{†} Available in XLeratorDB/math 2008 only 
SVD

Calculate the economysized singular value decomposition of an mxn matrix A. 
SVdecomp

Calculate the economysized singular value decomposition of an mxn matrix A.^{†} (tablevalued function) 
TCROSSPROD

Calculate the matrix crossproduct of 2 matrices. 
TMCROSS

Calculate the matrix crossproduct of 2 matrices.^{†} (tablevalued function) 
TRANSPOSE 
Return the transposed matrix. 

Matrix Randomization 
MRAND 
Generate an mbyn matrix of pseudorandom numbers greater than or equal to zero and less than one. 
MRANDN 
Generate an mbyn matrix of pseudorandom numbers from the standard normal distribution. 
MRORTHO 
Generate an mbym random orthogonal matrix. Available in XLeratorDB/math 2008 only 

Matrix Helper Functions 
DIAG 
Return the vector of the diagonal of the string representation of a matrix. 
EYE 
Generate an mbyn identity matrix. 
MAPPEND 
Add columns or rows to an existing matrix variable.^{†} Available in XLeratorDB/math 2008 only 
MATRIX2STRING 
Turn table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semicolons.^{†} 
MATRIX2STRING_q 
Turn table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semicolons.^{†} 
MCOLS 
Find the number of columns in the string representation of a matrix. 
MCOLUMN 
Return a column from the string representation of a matrix. 
MINDEX 
Return the intersection of a row and a column from the string representation of a matrix. 
MROW 
Return a row from the string representation of a matrix. 
MROWS 
Find the number of rows in the string representation of a matrix. 
MUPDATE 
Change the values in the string representation of a matrix or to perform elementwise operations on a matrix or some portion of a matrix.^{†} Available in XLeratorDB/math 2008 only 
NMATRIX2STRING 
Turn thirdnormal form table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semicolons. Available in XLeratorDB/math 2008 only 
NMATRIX2STRING_q 
Turn thirdnormal form table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semicolons.^{†} 
ONES 
Generate an mbyn matrix of ones. 
VANDERMONDE 
Return the Vandermonde matrix. Available in XLeratorDB/math 2008 only 
ZERO 
Generate an mbyn matrix of zeroes. 

NUMBER/SERIES GENERATORS 
Random Number Functions 
RAND 
Calculate a random number greater than or equal to zero and less than one. 
RANDBETWEEN 
Calculate a random integer number between the numbers you specify. 
RANDNORM 
Calculate a pseudorandom number based on a normal distribution for the given mean and standard deviation. 

Random Number Generators 
RANDBETA 
Generate q sequence of random numbers from the beta distribution with two positive shape parameters alpha and beta. (tablevalued function) 
RANDBINOM 
Generate a sequence of random integers from the binomial distribution for a given probability of success and a given number of trials. (tablevalued function) 
RANDCAUCHY 
Generate a sequence of random numbers from a Cauchy distribution for a given location parameter and scale. (tablevalued function) 
RANDCHISQ 
Generate a sequence of random numbers from a chisquared distribution for a specified degrees of freedom. (tablevalued function) 
RANDEXP 
Generate a sequence of random numbers from an exponential distribution with rate lambda. (tablevalued function) 
RANDFDIST 
Generate a sequence of random numbers from an Fdistribution with the degree of freedom parameters df1 and df2. (tablevalued function) 
RANDGAMMA 
Generate a sequence of random numbers from a gamma distribution for the supplied shape and scale parameters. (tablevalued function) 
RANDLAPLACE 
Generate a sequence of random numbers from a LaPlace distribution with supplied location and scales parameters. (tablevalued function) 
RANDLOGISTIC 
Generate a sequence of random numbers from a logistic distribution of the supplied location and scale parameters. (tablevalued function) 
RANDNORMAL 
Generate a sequence of random numbers from the normal distribution with mean μ and standard deviation σ. (tablevalued function) 
RANDPOISSON 
Generate a sequence of random integers from the Poisson distribution for a given λ. (tablevalued function) 
RANDSNORMAL 
Generate a sequence of random numbers from the standard normal distribution. (tablevalued function) 
RANDTDIST 
Generate a sequence of random numbers from Student's t distribution with for the supplied degrees of freedom. (tablevalued function) 
RANDWEIBULL 
Generate a sequence of random numbers from w Weibull distribution with parameters shape (λ) and scale (κ). (tablevalued function) 

Series Generators 
SeriesInt 
Generate a range of integer values. (tablevalued function) 
SeriesFloat 
Generate a range of floating point values. (tablevalued function) 
SeriesDate 
Generate a range of date values. (tablevalued function) 

Optimization 
BFGS *!* 
Find the minimum of a function using the BroydenFletcherGoldfarbShanno (BFGS) method.^{†} Available in XLeratorDB/math 2008 only 
BRENT *!* 
Find the root of a continuous function of one variable.^{†} Available in XLeratorDB/math 2008 only 
FDERIV *!* 
Numerical function differentiation for orders n = 1 to 4 using finite difference approximations.^{†} Available in XLeratorDB/math 2008 only 
GRAD *!* 
Numerically compute the gradient.^{†} Available in XLeratorDB/math 2008 only 
HESSIAN *!* 
Numerically computer the Hessian matrix.^{†} Available in XLeratorDB/math 2008 only 
JACOBIAN *!* 
Numerically compute the Jacobian matrix.^{†} Available in XLeratorDB/math 2008 only 
NEWTON *!* 
Find the root of a univariate function.^{†} Available in XLeratorDB/math 2008 only 
NLMIN *!* 
NelderMead Minimization.^{†} Available in XLeratorDB/math 2008 only (tablevalued function) 
SECANT *!* 
Find the root of singlevariable continuous function.^{†} Available in XLeratorDB/math 2008 only 

MISC FUNCTIONS 

XLDB_MATH_VERSION 
Display version information for the XLeratorDB/math module. 