; LN is the principal natural logarithm, base 2.71828...
LN 1

; Logarithms of nonnegative arguments are usually collected
LN 6 - LN 2

; Logarithms of perfect powers are simplified
LN 16 / LN 8

; Logarithms can take complex arguments
LN (1 + #i)

; There are various simplifications for nonnumeric logarithms
LN(x^2)/LN(x^(-2))

; LOG (x, b) is the logarithm of x to the base b
LOG (10^3, 10)

; If omitted, the second argument defaults to #e
LOG x

; EXP is the inverse of LN
EXP LN x

; For real x, LN is also the inverse of EXP
LN EXP x

; Inversion can be applied to only part of an argument
LN (2 x^3 EXP y)

; e-hat exactly represents 2.71828... .  EXP x simplifies to e-hat ^ x
EXP x

; You can enter e-hat as #e
#e^(3 x LN y)

; Cancellations can be dramatic
#e^(2x(y+1)+y) - #e^(2 x y+2x+y)

; Other nonnumeric powers are also simplified
4 (2^z)^2 - 4^(z+1)

; The base can also be a variable
a^(x+1) - a a^x

; Exponentials of complex numbers are transformed to rectangular form
#e^(1 + pi/4 #i)

; Hyperbolic functions transform into exponentials
COSH x

; Arc-hyperbolic functions transform into logarithms
ASINH x

; For real or complex z, SIGN z is defined as z/ABS z
SIGN 5

SIGN -3

SIGN (3 + 4 #i)

; SIGN 0 represents an arbitrary point on the unit circle
SIGN 0

; There are various simplifications for nonnumeric arguments
SIGN SIGN z

; Some simplifications are applicable only to real arguments
SIGN ATAN x

SIGN LN (1 + COS x)

; Absolute values also simplify for nonnumeric arguments
ABS z SIGN z

; Some simplifications are applicable only to real arguments
ABS (x^2)

(ABS x)^2

COS ABS x

ABS (x ATAN x)

ABS (1 + COS x)

ABS x / SIGN x

; The gamma function is transformed into a factorial
GAMMA (x+1)

; Factorials are defined even for fractional arguments
(1/2) !

; Factorials are also defined for negative arguments
(- 1/2) !

; There are factorial simplifications even for nonnumeric arguments
(n+2)!/(n-1)!

; PERM (m, n) is the number of permutations of m things taken n at a time
PERM (m, n)

; COMB (m, n) is the number of combinations of m things taken n at a time
COMB (m, n)

; AVERAGE (z1, z2, ..., zn) is the arithmetic mean of its arguments
AVERAGE (x, y, z)

; RMS (z1, z2, ..., zn) is the root mean-square of its arguments
RMS (x, y, z)

; VAR (z1, z2, ..., zn) is the variance of its arguments
VAR (x, y)

; STDEV (z1, z2, ..., zn) is the standard deviation of its arguments
STDEV (x, y)

; Approx this for the monthly payment on a $12,000, 4 year loan at 10% interest
PMT (10%/12, 4 12, 12000)
