The Lab parser accepts Mathematica-style expressions like

2 + 3.54 cos[z]-3.1e+2 Sin[z]
2 pi+(3-2i)/(z^3+1)+exp[z-1]

The symbol * for multiplication is optional, functions are written with square brackets, and the parser is insensitive to case with regard to function names.

Functions supported by Lab include the following (for a complete list, see below):

• arithmetic operations: +, -, *, /, ^;
• exponential and logarithmic functions;
• trigonometric and hyperbolic functions and their inverses.
• elliptic theta functions, Weierstrass elliptic functions and Jacobi elliptic functions;

Arithmetic and related functions: unary plus, unary minus, addition, subtraction, multiplication, division, exponentiation:

operation	symbol	alternate	alternate
unitary plus	+x		pos[x]
unitary negation	-x		neg[x]
addition	x+y		add[x,y]
subtraction	x-y		sub[x,y]
multiplication	x*y	x y	mul[x,y]
division	x/y		div[x,y]
exponentiation	x^y	x**y	pow[x,y]

Other arithmetic functions:

operation	symbol	alternate
square	sqr[x]	x*x;
cube	cube[x]	x*x*x;
multiplicative inverse	inv[x]	1/x;
square root	sqrt[x]

Constants:

constant	symbol	value
imaginary unit	i
circle constant	pi	3.14159
base of natural logarithm	e	2.71828
Catalan's constant	cat	0.915966
Euler's constant	euler	0.577216
golden ratio	gold	1.61803

Real and imaginary parts, absolute value and norm:

function	symbol	alternate
real part	re[x]	real[x]
imaginary part	im[x]	imag[x]
square of absolute value	norm[x]
	abs[x]
conjugate	conj[x]

Exponential and logarithmic functions:

function	symbol
exp x	exp[x]
natural logarithm	log[x]
base 10 logarithm	log10[x]
base y logarithm	logb[x,y]

Trigonometric functions:

function	symbol
cos x	cos[x]
sin x	sin[x]
tan x	tan[x]
sec x	sec[x]
csc x	csc[x]
cot x	cot[x].

Inverse trigonometric functions:

function	symbol	alternate
arccos x	arccos[x]	acos[x]
arcsin x	arcsin[x]	asin[x]
arctan x	arctan[x]	atan[x]
arcsec x	arcsec[x]	asec[x]
arccsc x	arccsc[x]	acsc[x]
arccot x	arccot[x].	acot[x].

Hyperbolic functions:

function	symbol
cosh x	cosh[x]
sinh x	sinh[x]
tanh x	tanh[x]
sech x	sech[x]
csch x	csch[x]
coth x	coth[x].

Inverse hyperbolic functions:

function	symbol	alternate
arccosh x	arccosh[x]	acosh[x]
arcsinh x	arcsinh[x]	asinh[x]
arctanh x	arctanh[x]	atanh[x]
arcsech x	arcsech[x]	asech[x]
arccsch x	arccsch[x]	acsch[x]
arccoth x	arccoth[x]	acoth[x].

Elliptic theta functions:

function	symbol
	theta1[x,y]
	theta2[x,y]
	theta3[x,y]
	theta4[x,y]

Derivatives of elliptic theta functions. The number of appended p's is the order of the derivative with respect to the first argument.

function	symbol
	theta1_p[x,y]
	theta2_p[x,y]
	theta3_p[x,y]
	theta4_p[x,y]
	theta1_pp[x,y]
	theta1_ppp[x,y]

Weierstrass elliptic functions. The second argument is the the ratio of lattice generators (periods).

function	symbol
Weierstrass P function.	weierstrass_P[x,y]
first derivative of Weierstrass P function	weierstrass_P_p[x,y]
Weierstrass zeta function	weierstrass_zeta[x,y]
Weierstrass sigma function	weierstrass_sigma[x,y]

Functions related to the Weierstrass elliptic functions:

function	symbol
	weierstrass_e1[x]
	weierstrass_e2[x]
	weierstrass_e3[x]
	weierstrass_g2[x]
	weierstrass_g3[x]
	weierstrass_eta1[x]
	weierstrass_eta2[x]

Complete elliptic integrals:

function	symbol
	elliptic_K[x]

Jacobi Elliptic functions:

function	symbol
sn x	jacobi_sn[x,y]
cn x	jacobi_cn[x,y]
dn x	jacobi_dn[x,y]
ns x	jacobi_ns[x,y]
cs x	jacobi_cs[x,y]
ds x	jacobi_ds[x,y]
nc x	jacobi_nc[x,y]
sc x	jacobi_sc[x,y]
dc x	jacobi_dc[x,y]
nd x	jacobi_nd[x,y]
sd x	jacobi_sd[x,y]
cd x	jacobi_cd[x,y]

Functions related to the Jacobi Elliptic functions:

function	symbol
am x	jacobi_am[x,y].