Active Operators in CalcLib Build 2023.0505
Operator	A simple description of the actions of each operator
!	Unary conventional factorial operator
!!	Unary parity factorial operator
#	Array indexing operation implemented as a binary operator
##	Binomial coefficient operator (n ## k)
#$#	Bells Triangle operator (n #$# m)
#%#	Euler numbers operator (n #%# m)
#*^	Evaluate an Euler polynomial defined by a specified order
#/	Binary Factorial falling operator
#/#	Arithmetic division operator (expressed as fraction)
$#	Mark function call for Trapezoidal integral approximation
$$	Stirling numbers (first) operator (n $$ k)
$$$	Stirling numbers (second) operator (n $$$ k)
$%	Mark function call for adjustment for brute force approximation
$@	Mark function call for Clenshaw-Curtis integral approximation
$|	Mark function call for Tanh-Sinh integral approximation
%	Binary conventional remainder operator n%m; integer only
&	Logical AND
'	Mark function call for first derivative approximation
''	Mark function call for second derivative approximation
*	Arithmetic multiplication operator
*%*	Cross product of two arrays; lengths of arrays must match
**	Binary conventional exponentiation operator x**y
*@*	Dot product of two arrays; lengths of arrays must match
*\	Binary root operator (left [times root of] right)
*^#	Evaluate an exponential ( a * exp (b * x) ) defined by an array containing (a : b)
*^*	Compute tensor product of two matrices
+	Arithmetic addition operator
+!*	Complex value (left + i * right) as a binary operator
+#*	Evaluate a harmonic series defined by an array of coefficients ( c0 + c1*cos(x) + c2*cos(2x) + ... )
+*^	Evaluate a polynomial defined by an array of coefficients ( c0 + c1*x + c2*x^2 + ... )
+*^'	Evaluate a polynomial derivative defined by an array of coefficients ( c0 + c1*x + c2*x^2 + ... )
+*^''	Evaluate a polynomial second derivative defined by an array of coefficients ( c0 + c1*x + c2*x^2 + ... )
+|-	Plus or Minus operator
-	Arithmetic (binary) subtraction or (unary) negate operator
-!*	Complex value (left - i * right) as a binary operator
-#	Matrix indexing operation selecting row vector
->	Lambda anonymous function declarative expression
-|+	Minus or Plus operator
.	Dot product of two arrays; lengths of arrays must match
..	Array range operation implemented as a binary operator
/	Arithmetic division operator
/#	Binary Factorial rising operator
/#+	Pochhammer rising operator
:	Choice based on condition code
<	Less than
<*>	Integral delta marker for presentation
<<	Left shift operator
<<=	Logical implied by
<=	Less than or equal to
<>	Derivative approximation evaluated at left parameter using delta value in right parameter
<||	Less than absolute value of
==	Equal to
=>>	Logical implies
>	Greater than
>=	Greater than or equal to
>>	Right shift operator
>||	Greater than absolute value of
?	Logical condition code set
@!#	Complex value (left * CIS right) as a binary (polar) operator
@#	Evaluate function defined by array at X
@*^	Evaluate a Chebyshev polynomial using Clenshaw's special case defined by an array of coefficients ( c0 + c1*T[1](x) + c2*T[2](x) + ... )
@*^'	Evaluate a Chebyshev polynomial derivative using Clenshaw's special case defined by an array of coefficients,ClenshawPrime
@*^''	Evaluate a Chebyshev polynomial second derivative using Clenshaw's special case defined by an array of coefficients
@|	Pointer dereference
ADJ	Compute adjugate of matrix
APPEND	Append a series of arrays into one long array
ARRAY	Collect values into array
ARRAYDER	Compute derivative of function described by array
ARRAYINT	Compute integral of function described by array
AUGMENTED	Construct augmented matrix from source matrix and additional column
BERNOULLI	Bernoulli function B(m) for second (n=1) Bernoulli numbers
CHARACTERISTIC	Compute characteristic polynomial for matrix
CHEBDER	Compute derivative of Chebyshev T polynomial
CHEBDOM	Compute domain across given number of Chebyshev points
CHEBINTERP	Generate Chebyshev interpolation polynomial for function described by array
CHEBPTS	Compute given number of Chebyshev points
CHEBYSHEV	Apply Vandermonde matrix to solve for Chebyshev interpolation polynomial as curve of best fit
CLENQUAD	Compute integral of function described by Chebyshev polynomial
COFACTOR	Compute cofactor matrix from source
COL	Read column vector from matrix
COMATRIX	Compute comatrix matrix from source
CONCAT	Append a series of arrays into one long array
CONV	Compute product of polynomials
DECOMPOSE	Decompose a matrix using a linear algebra library instance
DECONV	Compute quotient of polynomials
DET	Compute determinant of matrix
DOT	Dot product of two arrays; lengths of arrays must match
DYADIC	Compute dyadic product of 2 arrays
EIG	Compute Von Mises dominant eigen-pair
EVALSPLINE	Evaluate a VC31 spline function at specified parameter
EVD	Eigensystem decomposition returning vectors and values
FALSE	Logical FALSE
FITEXP	Apply non-linear (logarithmic) regression to find curve of best fit
FITHARMONIC	Apply harmonic series regression to find curve of best fit
FITLINE	Apply least squares regression to find line of best fit
FITPOLY	Apply Vandermonde matrix to solve for polynomial coefficients to find curve of best fit
GAMMA	Lanczos Gamma function approximation
GAUSSIAN	Solve linear equations with Gaussian elimination
GAUSSQUAD	Apply Gauss Quadrature to build an integral of an interpolated Lagrange polynomial
GENKNOT	Construct a zero knot for odd or even functions
GET	Get a component of a structure
Gamma	Gamma function
HARMONIC	Harmonic function
HYPOT	Distance in multi-dimensional space; SQRT of sum of squares of array elements
IDENTITY	Compute identity matrix with specified size
INFINITY	Approximation to use for infinity
INTEGRAL	Sum of items of an array constructed based on delta terms; using traditional integral notation
INTEGRALC	Sum of items of an array constructed based on delta terms; using traditional contour integral notation
INTEGRALS	Sum of items of an array constructed based on delta terms; using traditional surface integral notation
INTEGRALV	Sum of items of an array constructed based on delta terms; using traditional volume integral notation
INTERPOLATE	Generate Lagrange interpolation polynomial for function described by array
INTERVAL	Select sub-list of elements for interval lo-hi
INV	Compute inverse of matrix
Im	Imaginary part of complex value
In	Bessel In
In3	Bessel I function -1/3
Ip	Bessel Ip
Ip3	Bessel I function 1/3
J2	Bessel J function
Jp	Bessel Jp
K3	Bessel K function
Ka	Bessel Ka
LAGRANGE	Apply Lagrange series to derive interpolation polynomial as curve of best fit
LENGTH	Length of an array treated as a unary function
LOAD	Load a stored value
LUD	Decompose specified matrix using LU algorithm
LUDDET	Compute matrix determinant using LUD
LUDINV	Compute matrix inverse using LUD
LUXB	matrix,Solve LUx=b general case from assignment array=LUXB(L;U;b)
Li1	Jonquiere polylog function
MATADD	Compute sum of two matrices
MATMUL	Compute product of two matrices
MATRIX	Construct matrix from array with dimensions
MAX	Maximum value found in array
MIN	Minimum value found in array
MINOR	Compute minor of matrix
MINUS	Arithmetic binary subtraction operator
NEGATE	Arithmetic unary negation operator
PEARSON	Compute Pearson regression coefficient for X/Y data set pair
PI	Product of items of an array; traditional capital PI notation
PIVOT	Reorder a vector to a specified pattern
POLYADD	Compute sum of two polynomials
POLYDER	Compute derivative of polynomial
POLYHG	Compute coefficients of hyper geometric polynomial
POLYINT	Compute integral of polynomial
POLYMUL	Compute product of two polynomials
QRD	Decompose specified matrix using QR algorithm
QRS	Compute solution to system given requested vector and QR decomposed matrix
ROOTS	Compute roots of polynomial
ROW	Read row vector from matrix
Re	Real part of complex value
SIGMA	Sum of items of an array; traditional capital SIGMA notation
SOE	Solve a system of equations using a linear algebra library instance
SOLVE	Solve linear equations with column substitution
STACK	Append a series of arrays as rows into a matrix
STORE	Store a portable value
SUMMATION	Sum of items of an array; summation functionality using SIGMA notation
TR	Compute trace of matrix
TRANSPOSE	Compute transpose of matrix
TRIL	Compute lower triangular matrix from source
TRIU	Compute upper triangular matrix from source
TRUE	Logical TRUE
VANCHE	Construct Vandermonde matrix for a Chebyshev interpolation
VC31	Solve LUx=b using VC31LU to produce Chebyshev spline for function values
VERSION	software development version
\	Binary root operator (left [root of] right)
\#	Matrix indexing operation selecting diag vector
^	Binary conventional exponentiation operator x^n; intended for small integer exponents
abs	Absolute value (distance from origin) of parameter
acos	Complex ARC COS function
acot	ARC Cotangent Operator
acsc	ARC Cosecant Operator
arcosh	Complex ARC COSH function
arcoth	ARC Hyperbolic Cotangent Operator
arcsch	ARC Hyperbolic Cosecant Operator
arg	Phase angle of a complex value
arsech	ARC Hyperbolic Secant Operator
arsinh	Complex ARC SINH function
artanh	ARC Hyperbolic Tangent Operator
asec	ARC Secant Operator
asin	Complex ARC SIN function
atan	Complex ARC Tan function
ceil	Ceiling function
cis	Complex CIS (cos x + i * sin x) function operator
conj	Complex conjugate operator
cos	Complex cos function of parameter
cosCb	Cosine Cubed Operator
cosSq	Complex cos (squared) function of parameter
cosh	Complex cosh function of parameter
cot	Cotangent Operator
cotCb	Cotangent Cubed Operator
cotSq	Cotangent Squared Operator
coth	Hyperbolic Cotangent Operator
csc	Cosecant Operator
cscCb	Cosecant Cubed Operator
cscSq	Cosecant Squared Operator
csch	Hyperbolic Cosecant Operator
cschSq	Hyperbolic Cosecant Squared Operator
curl	Curl operator
digamma	Digamma
div	Divergence operator
e	Epsilon base of natural log
ep	Euler Product function
eta	Dedekind Eta modular form
exp	Euler exponential function
floor	Floor function
floordiv	Floor function for quotient
gammainc	Incomplete Gamma function
grad	Gradient operator
i	Imaginary root of -1
ln	Natural log function of complex value
loggamma	Loggamma function
modSq	Modulus (distance from origin) squared of parameter
omega	Lambert Omega function
omega0	Lambert W (omega) function
pi	Symbol for the irrational value of pi
polygamma	Polygamma function
polylog	Jonquiere polylog function
psi0	Digamma (psi0) function
psi1	Trigamma (psi1) function
sec	Secant Operator
secCb	Secant Cubed Operator
secSq	Secant Squared Operator
sech	Hyperbolic Secant Operator
sechSq	Hyperbolic Secant Squared Operator
sgn	Sign SGN function value of parameter
sin	Complex sin function of parameter
sinCb	Sine Cubed Operator
sinSq	Complex sin (squared) function of parameter
sinh	Complex sinh function of parameter
sqrt	Unary square root operator
tan	Complex tan function of parameter
tanCb	Tangent Cubed Operator
tanSq	Complex tan (squared) function of parameter
tanh	Hyperbolic Tangent Operator
trigamma	Trigamma
watten	Watten Zeta function
zeta	Riemann Zeta function
|	Logical OR
|#	Matrix indexing operation selecting column vector
||	Mark function call for interval evaluation
|~	Logical XOR
~	Logical NOT
~&	Logical NAND
~<<=	Logical NOT implied by
~=	Not equal to
~=>>	Logical NOT implies
~|	Logical NOR
~|~	Logical NOT XOR