+  -  *  /
^  **  #
==  !=  <>
>  <  >=  <=
&  |  ->
!  !!
<<  >>  >>>
,  \ 
°

A
abs
acos
acosh
acot
acotg
acotgh
acoth
acsc
acsch
and
angle
ans
arccos
arccot
arccotg
arcsin
arctan
arctg
arg
argcosh
argcotgh
argcoth
argsinh
argtanh
argtgh
asec
asech
asin
asinh
atan
atanh
atg
atgh
ave
aveq
avex
avexq
avey
aveyq

B
base
bin
biteqv
bitimp
bitnand
bitnor

C
ceil
combin
complex
conjg
cos
cosec
cosh
cot
cotg
cotgh
coth
count
csc
csch
ctof

D
dec
deg
degtograd
degtorad
det
div
divisor
dms

E
elim
eqv
exp

F
fact
ffact
fibon
floor
for
foreach
frac
ftoc

G
gcd
geom
goto
gotor
grad
gradtodeg
gradtorad

H
harmon
height
hex
hypot

I
if
imag
imp
int
integral
invert
isprime
L
lcm
listfor
listforeach
ln
log
logn
lra
lrb
lrr
lrx
lry
lsh

M
matrix
max
maxfor
maxforeach
mean
meanq
meanx
meanxq
meany
meanyq
med
min
minfor
minforeach
mod
mode

N
nand
ncr
nor
not
npr

O
oct
or

P
permut
pi
polar
polynom
prime
print
product
productfor
productforeach

R
rad
radtodeg
radtograd
rand
random
rank
real
return
reverse
round
rowsfor
rowsforeach
rsh
rshi

S
sec
sech
sign
sin
sinh
solve
sort
sortd
sqrt
stdev
stdeva
stdevx
stdevxa
stdevy
stdevya
sum
sumfor
sumforeach
sumq
sumx
sumxq
sumxy
sumy
sumyq
swap

T
tan
tanh
tg
tgh
todeg
todms
tograd
torad
transp
trunc

V
var
vara
varx
varxa
vary
varya
vert

W
width

X
xor

+addition
-subtraction
*multiplication
/division
divx div y= trunc(x/y)
modremainder, x mod y= x-y*(x div y)
hypothypotenuse, hypot(a,b)=sqrt(a^2+b^2)
angleangle(a,b)=atan(a/b)
randrandom number, 0<=rand<1
randomrandom(n)=trunc(rand*n)
ctofconverts °Celsius to °Fahrenheit
ftocconverts °Fahrenheit to °Celsius
baseNnext number is in base N, 2<=N<=36, there is no space before N
decbase10
hexbase16
binbase2
octbase8
pi3.14159...
ansresult of previous expression
powers and logarithms
^, **power
#root, y#x= x^(1/y)
sqrtsquare root, sqrt(x)= 2#x = x^0.5
expexponential function, exp(x)=e^x, e=2.718...
lnnatural logarithm, inverse function to exp
lognlogarithm, logn(n,x)=ln(x)/ln(n)
loglog(x)=logn(10,x)
complex numbers
realreal part, real(a+bi)=a
imagimaginary part, imag(a+bi)=b
conjgconjugate, conjg(a+bi)=a-bi
absabsolute value, abs x=hypot(real x,imag x)
argphase angle, arg x=angle(imag x,real x)
signsign x=x/abs x
polarpolar(r,a)=r*cos a + i*r*sin a
complexcomplex(a,b)= a + b i
conditions and commands
==1 if operands are equal, 0 otherwise
!=, <>not equal
>greater
<less
>=greater or equal
<=less or equal
if(p,a,b)b if p is zero, or a if p is not zero
returnstops computation
return xstops computation and displays result x
goto njump to a label or to the n-th semicolon, goto0 jumps to the beginning
gotor nrelative jump, gotor -1 jumps to the previous command, gotor1 jump to next command, gotor0 will freeze the calculator
print x,”t”prints number x and then text t
swap(a,b)exchange variables a,b
rounding
roundround to the nearest integer
int, floorround down
ceilround up
truncinteger part
fracfractional part, frac x=x-trunc x
bitwise functions
and, &bitwise and
or, |bitwise or
xorbitwise exclusive or
notthe one's complement of the integer part
bitnandx bitnand y=not(x and y)
nandx nand y=(x==0 or y==0)
bitnorx bitnor y=not(x or y)
norx nor y=(x==0 and y==0)
bitimpx bitimp y=y or not x
imp, ->x imp y=(x==0 or y<>0)
biteqvx biteqv y= not(x xor y)
eqvx eqv y=((x==0)==(y==0))
lsh, <<shift left, x<<y=x*2^y
rsh, >>shift right, x>>y=x<<-y
rshi, >>>x>>>y=trunc(x>>y)
integer functions
!, factfactorial, n!=fact(n)= productfor(i,1,n,i)
!!, ffactn!!=ffact(n)= productfor(i,0,n/2-1,n-2*i)
combin, nCrcombination, n nCr k = n!/(n-k)!/k!
permut, nPrvariation, n nPr k = n!/(n-k)!
gcdthe greatest common divisor
lcmthe least common multiple, lcm(a,b)=a*b/gcd(a,b)
divisorthe least prime divisor of an operand
primeprime that is greater then an operand
isprimeisprime(n)=(divisor(n)==n)
fibonFibonacci, fibon(n)=fibon(n-1)+fibon(n-2)
angle conversions
radtodegconverts radians to degrees, radtodeg x= x/pi*180
degtoradconverts degrees to radians
radtogradconverts radians to gradients, radtograd x= x/pi*200
gradtoradconverts gradients to radians
degtogradconverts degrees to gradients, degtograd x= x*10/9
gradtodegconverts gradients to degrees
deg , °converts degrees to the current units
radconverts radians to the current units
gradconverts gradients to the current units
todegconverts the current units to degrees
toradconverts the current units to radians
togradconverts the current units to gradients
dmsconverts degrees, minutes and seconds to degrees, the integer part is degrees, two digits after a decimal point are minutes, next two digits are seconds, next digits are tenth of a second, hundredth of a second, ...
todmsinverse function to dms
trigonometric functions
sinsine, (opposite side / hypotenuse)
coscosine, (adjacent side / hypotenuse)
tan, tgtangent, (opposite side / adjacent side)
cosec, csccosecant, (hypotenuse / opposite side)
secsecant, (hypotenuse / adjacent side)
cot, cotgcotangent, (adjacent side / opposite side)
inverse trigonometric functions
asin, arcsinasin(x)=-ln(x i+sqrt(1-x^2)) i
acos, arccosacos(x)=-ln(x+sqrt(1-x^2) i) i
atan, atg, arctan, arctgatan(x)=(ln(1+x i)-ln(1-x i))/2i
acscacsc(x)=asin(1/x)
asecasec(x)=acos(1/x)
acot, acotg, arccot, arccotgacot(x)=atan(1/x)
hyperbolic functions
sinhsinh(x)=(exp(x)-exp(-x))/2
coshcosh(x)=(exp(x)+exp(-x))/2
tanh, tghtanh(x)=sinh(x)/cosh(x)
cschcsch(x)=1/sinh(x)
sechsech(x)=1/cosh(x)
coth, cotghcoth(x)=cosh(x)/sinh(x)
inverse hyperbolic functions
asinh, argsinhasinh(x)=ln(x+sqrt(x^2+1))
acosh, argcoshacosh(x)=ln(x+sqrt(x+1)*sqrt(x-1))
atanh, atgh, argtanh, argtghatanh(x)=(ln(1+x)-ln(1-x))/2
acschacsch(x)=asinh(1/x)
asechasech(x)=acosh(1/x)
acoth, acotgh, argcoth, argcotghacoth(x)=atanh(1/x)
matrices
+, -, ==, <>, and, or, xor, lsh, rsh, real, imag, conjg, round, trunc, floor, ceil, frac
widthnumber of columns
heightnumber of rows
matrix(r,c)zero matrix which has r rows and c columns
countcount A= width A * height A
,concatenation alongside, operands must have the same number of rows
\concatenation below, operands must have the same number of columns
*matrix multiplication or scalar multiplication
vertvector product, A vert B=(A[1]*B[2]-A[2]*B[1], A[2]*B[0]-A[0]*B[2], A[0]*B[1]-A[1]*B[0])
/A/B= A*invert B
^A^n= productfor(i,1,n,A); A^(-n)=1/(A^n)
invertinverted matrix, invert A= 1/A= A^(-1)
detdeterminant
rankcount of linearly independend rows
transp, ‘diagonal symmetry
elimelimination method that makes elementary transformations with rows
solvesimultaneous linear equations, every row represents one equation, last column is the right side of equations, (number of columns) = 1 + (number of variables), number of rows is not restricted, but it is usually same as number of variables
absvector length, matrix norm, abs A= sqrt sumq A
angleangle between two vectors, angle(A,B)=acos(A*B/abs(A)/abs(B))
polynompolynom(x,A)=sumfor(i,0,count A-1, A[i]*x^i)
sortsort items from lesser to greater
sortdsort items from greater to lesser
reversechange order of items from last to the first
loops
for(x,a,b,f(x))values from a to b are assigned to variable x and command f is executed, result is 0, f can modify variables, f can contain command if, return, ...
foreach(x,A,f(x))this function is similar to for except that every element of matrix A is assigned to variable x
sumfor(x,a,b,f(x))S=0; for(x,a,b,S=S+f(x)); S
productfor(x,a,b,f(x))S=1; for(x,a,b,S=S*f(x)); S
listfor(x,a,b,f(x))row vector which contains values f(x) where x is from a to b. If f(x) returns column vectors, then listfor returns matrix. If a>b then listfor returns 0.
rowsfor(x,a,b,f(x))column vector which contains values f(x) where x is from a to b. If f(x) returns row vectors, then rowsfor returns matrix. If a>b then rowsfor returns 0.
minfor(x,a,b,f(x))min(listfor(x,a,b,f(x)))
maxfor(x,a,b,f(x))max(listfor(x,a,b,f(x)))
sumforeach, productforeach, listforeach, rowsforeach, minforeach, maxforeach - these functions are similar to the foregoing functions, but the x values are taken from matrix A
integral(x,a,b,n,f(x))integral from a to b from function f(x), n is precision (number of correct decimal digits, other digits are wrong !), if n>=100 then n is duration in milliseconds
statistical functions
minminimal value
maxmaximal value
medmedian, middle value
modemost frequent value
sumtotal sum
sumqsum of squared values
productproduct
ave, meanmean, ave=sum/count
aveq, meanqmean of squared values, aveq=sumq/count
geomgeometric mean, geom=count#product
harmonharmonic mean, harmon(A)=count(A)/sumforeach(x,A,1/x)
varvariance, var=(sumq-sum^2/count)/(count-1)
varavariance of population, vara=aveq-ave^2
stdevstandard deviation, stdev=sqrt(var)
stdevastandard deviation of population, stdeva=sqrt(vara)
linear regression
Points in a plane are represented by a matrix which has two columns. The first column contains x coordinates, the second column contains y coordinates. Functions lra and lrb get coeficients of line y=a+b*x which goes through the points. If all points are exactly on the line, then function lrr returns 1 or -1.
lralra=(sumy-b*sumx)/n
lrblrb=(n*sumxy-sumx*sumy)/(n*sumxq-sumx^2)
lrrcorrelation coeficient, lrr=(n*sumxy-sumx*sumy)/sqrt((n*sumxq-sumx^2)*(n*sumyq-sumy^2))
lrxlrx(D,y)=(y-lra D)/lrb D
lrylry(D,x)=lra D + x*lrb D
sumxsumx D= sum D[][0]
sumysumy D= sum D[][1]
sumxysumxy D= sumfor(i,0, height data-1, data[i][0]*data[i][1])
sumxq, sumyq, avex, avey, avexq, aveyq, varx, vary, varxa, varya, stdevx, stdevy, stdevxa, stdevya