+  -  *  / ^  **  # ==  !=  <> >  <  >=  <= &  |  -> !  !! <<  >>  >>> ,  \  ‘ ° A abs acos acosh acot acotg acotgh acoth acsc acsch agm 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 filterfor filterforeach 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
div	x div y= trunc(x/y)
mod	remainder, x mod y= x-y*(x div y)
hypot	hypotenuse, hypot(a,b)=sqrt(a^2+b^2)
angle	angle(a,b)=atan(a/b)
rand	random number, 0<=rand<1
random	random(n)=trunc(rand*n)
ctof	converts °Celsius to °Fahrenheit
ftoc	converts °Fahrenheit to °Celsius
baseN	next number is in base N, 2<=N<=36, there is no space before N
dec	base10
hex	base16
bin	base2
oct	base8
pi	3.14159...
ans	result of previous expression

powers and logarithms
^, **	power
#	root, y#x= x^(1/y)
sqrt	square root, sqrt(x)= 2#x = x^0.5
exp	exponential function, exp(x)=e^x, e=2.718...
ln	natural logarithm, inverse function to exp
logn	logarithm, logn(n,x)=ln(x)/ln(n)
log	log(x)=logn(10,x)

complex numbers
real	real part, real(a+bi)=a
imag	imaginary part, imag(a+bi)=b
conjg	conjugate, conjg(a+bi)=a-bi
abs	absolute value, abs x=hypot(real x,imag x)
arg	phase angle, arg x=angle(imag x,real x)
sign	sign x=x/abs x
polar	polar(r,a)=r*cos a + i*r*sin a
complex	complex(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
return	stops computation
return x	stops computation and displays result x
goto n	jump to a label or to the n-th semicolon, goto0 jumps to the beginning
gotor n	relative 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
round	round to the nearest integer
int, floor	round down
ceil	round up
trunc	integer part
frac	fractional part, frac x=x-trunc x

bitwise functions
and, &	bitwise and
or, |	bitwise or
xor	bitwise exclusive or
not	the one's complement of the integer part
bitnand	x bitnand y=not(x and y)
nand	x nand y=(x==0 or y==0)
bitnor	x bitnor y=not(x or y)
nor	x nor y=(x==0 and y==0)
bitimp	x bitimp y=y or not x
imp, ->	x imp y=(x==0 or y<>0)
biteqv	x biteqv y= not(x xor y)
eqv	x 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
!, fact	factorial, n!=fact(n)= productfor(i,1,n,i)
!!, ffact	n!!=ffact(n)= productfor(i,0,n/2-1,n-2*i)
combin, nCr	combination, n nCr k = n!/(n-k)!/k!
permut, nPr	variation, n nPr k = n!/(n-k)!
gcd	the greatest common divisor
lcm	the least common multiple, lcm(a,b)=a*b/gcd(a,b)
divisor	the least prime divisor of an operand
prime	prime that is greater then an operand
isprime	isprime(n)=(divisor(n)==n)
fibon	Fibonacci, fibon(n)=fibon(n-1)+fibon(n-2)

angle conversions
radtodeg	converts radians to degrees, radtodeg x= x/pi*180
degtorad	converts degrees to radians
radtograd	converts radians to gradients, radtograd x= x/pi*200
gradtorad	converts gradients to radians
degtograd	converts degrees to gradients, degtograd x= x*10/9
gradtodeg	converts gradients to degrees
deg , °	converts degrees to the current units
rad	converts radians to the current units
grad	converts gradients to the current units
todeg	converts the current units to degrees
torad	converts the current units to radians
tograd	converts the current units to gradients
dms	converts 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, ...
todms	inverse function to dms

trigonometric functions
sin	sine, (opposite side / hypotenuse)
cos	cosine, (adjacent side / hypotenuse)
tan, tg	tangent, (opposite side / adjacent side)
cosec, csc	cosecant, (hypotenuse / opposite side)
sec	secant, (hypotenuse / adjacent side)
cot, cotg	cotangent, (adjacent side / opposite side)

inverse trigonometric functions
asin, arcsin	asin(x)=-ln(x i+sqrt(1-x^2)) i
acos, arccos	acos(x)=-ln(x+sqrt(1-x^2) i) i
atan, atg, arctan, arctg	atan(x)=(ln(1+x i)-ln(1-x i))/2i
acsc	acsc(x)=asin(1/x)
asec	asec(x)=acos(1/x)
acot, acotg, arccot, arccotg	acot(x)=atan(1/x)

hyperbolic functions
sinh	sinh(x)=(exp(x)-exp(-x))/2
cosh	cosh(x)=(exp(x)+exp(-x))/2
tanh, tgh	tanh(x)=sinh(x)/cosh(x)
csch	csch(x)=1/sinh(x)
sech	sech(x)=1/cosh(x)
coth, cotgh	coth(x)=cosh(x)/sinh(x)

inverse hyperbolic functions
asinh, argsinh	asinh(x)=ln(x+sqrt(x^2+1))
acosh, argcosh	acosh(x)=ln(x+sqrt(x+1)*sqrt(x-1))
atanh, atgh, argtanh, argtgh	atanh(x)=(ln(1+x)-ln(1-x))/2
acsch	acsch(x)=asinh(1/x)
asech	asech(x)=acosh(1/x)
acoth, acotgh, argcoth, argcotgh	acoth(x)=atanh(1/x)

matrices
+, -, ==, <>, and, or, xor, lsh, rsh, real, imag, conjg, round, trunc, floor, ceil, frac
width	number of columns
height	number of rows
matrix(r,c)	zero matrix which has r rows and c columns
count	count 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
vert	vector 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)
invert	inverted matrix, invert A= 1/A= A^(-1)
det	determinant
rank	count of linearly independend rows
transp, ‘	diagonal symmetry
elim	elimination method that makes elementary transformations with rows
solve	simultaneous 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
abs	vector length, matrix norm, abs A= sqrt sumq A
angle	angle between two vectors, angle(A,B)=acos(A*B/abs(A)/abs(B))
polynom	polynom(x,A)=sumfor(i,0,count A-1, A[i]*x^i)
sort	sort items from lesser to greater
sortd	sort items from greater to lesser
reverse	change 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)))
filterfor(x,a,b,f(x))	row vector of x values from a to b for which f(x) is nonzero
sumforeach, productforeach, listforeach, rowsforeach, minforeach, maxforeach, filterforeach - 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
min	minimal value
max	maximal value
med	median, middle value
mode	most frequent value
sum	total sum
sumq	sum of squared values
product	product
ave, mean	mean, ave=sum/count
aveq, meanq	mean of squared values, aveq=sumq/count
geom	geometric mean, geom=count#product
agm	arithmetic–geometric mean
harmon	harmonic mean, harmon(A)=count(A)/sumforeach(x,A,1/x)
var	variance, var=(sumq-sum^2/count)/(count-1)
vara	variance of population, vara=aveq-ave^2
stdev	standard deviation, stdev=sqrt(var)
stdeva	standard 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.
lra	lra=(sumy-b*sumx)/n
lrb	lrb=(n*sumxy-sumx*sumy)/(n*sumxq-sumx^2)
lrr	correlation coeficient, lrr=(n*sumxy-sumx*sumy)/sqrt((n*sumxq-sumx^2)*(n*sumyq-sumy^2))
lrx	lrx(D,y)=(y-lra D)/lrb D
lry	lry(D,x)=lra D + x*lrb D
sumx	sumx D= sum D[][0]
sumy	sumy D= sum D[][1]
sumxy	sumxy 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