Expressions

General mathematical expressions can be used in several contexts, such as expressing constraints in least squares fitting, and Custom Population Functions or Custom Transition Functions. Each context has some specific variables introduced, but the same logic is otherwise used for all expressions:

Parameter names can be used to include parameter values in expressions. To find the name of a parameter, right click on it in the constants window and select "Show Full Name". The name is also copied to the clipboard. Depending on the context, parts of the parameter name can be omitted if no ambiguity is introduced as to the parameter concerned. Quotes might be needed around the parameter name if it contains special characters, as in "NH3.NH3.s.<0-|J+-^6|0->.Value".
Any unrecognised names are typically created as variables.
The standard mathematical operators are available: + - * /, with power expressible as ^ or **.
The standard functions sqrt, sqr, abs,sin, cos, tan, acos, asin, atan, arccos, arcsin, arctan, exp, ln, log10, ceil, floor, round,factorial are available. See also the special functions below.
The comparison operators =, <>, !=, >, <, >= and <= evaluate to 1 for true, 0 for false. To express a conditional combine these with multiply and add, so for example (a>b)*a+(a<=b)*b would give the maximum of a and b.
All arithmetic is done in double precision.
Comments are # or // to end of line, or enclosed in {...} or /* ... */
A simple test calculator is available from "View, Calculator".

The following special functions and operators are also available:

`int(a)`	Integer part of `a`; number is closer to zero than `a` (or equal to `a`).
`frac(a)`	`a` `- int(a)`
`%`	modulus operator: `a % b = frac(a/b)*b`
`mod(a,b)`	`a % b` except if `a < 0` in which case `b-frac(\|a\|/b)*b` is used.
`pi`	3.14159...
`min(a,b,c...)`	The minimum value of all the arguments
`max(a,b,c...)`	The maximum value of all the arguments
`poly(x,a0,a1,a2...)`	a₀+a₁.x+a₂.x²+...
`lor(x,l)`	Lorenztian function with FWHM `l`.
`gau(x,g)`	Gaussian function with FWHM `g`.
`voigt(x,l,g)`	Voigt profile at offset `x` from the line centre. `l` is the FWHM of the Lorenztian component, `g` of the Gaussian.
`air(s)`	Air wavelength/nm given vacuum wavenumber `s`/cm^-1. The refractive index is taken from from B Edlen, Metrologia, 2, 71 (1966).
`vac(l)`	Vacuum wavenumber/cm^-1 given air wavelength in nm.
`atan2(x,y)`	atan(x/y), but with a -π...π result range.
`threej(j1,m1,j2,m2,j3,m3)`	Wigner 3-j function
`cg(j1,m1,j2,m2,j3,m3)`	Clebsch-Gordan coefficient = (-1)^j1-j2+m3(2j₃+1)^½threej(j1,m1,j2,m2,j3,-m3)
`sixj(j1,j2,j3,j4,j5,j6)`	Wigner 6-j function
`ninej(j11,j12,j13,j21,j22,j23,j31,j32,j33)`	Wigner 9-j function

Selected fundamental constants (in SI units) are available in many contexts, though not all to avoid confusion:

`a0`	Bohr radius/m
`c`	Speed of light
`ee`	Charge on the electron
`ep`	Permittivity of a vacuum
`ge`	g value for an electron
`gg`	Gravitational Constant
`f`	Faraday Constant
`k`	Boltzmann Constant
`l`	Avagadro's Number
`r`	Gas Constant
`h`	Planck constant
`hc`	h/2π
`me`	mass of electron
`mn`	mass of neutron
`mp`	mass of proton
`mub`	Bohr magneton
`mun`	nuclear magneton
`rydberg`	Rydberg constant/m^-1
`u`	Atomic mass unit/kg

Debugging

A nDebug flag is available in each object that uses an expression. If non zero, that the values of all the variables and the value of the function on each evaluation will be written to the log window. The value specifies the number of times this is done; use View, Clear Cache to reset the count if necessary. Negative values have special interpretation:

-1 outputs every evaluation, which can produce a lot of output.
-2 only prints evaluations with a non-zero result
-3 only prints evaluations where the result differs from the standard result.