Table of Contents
linearfunction(x1, y1, x2, y2)
Finds the linear function for the straight line between two distinct points.
Arguments.
x1: a free value
y1: a free value
x2: a free value
y2: a free value
product(Factor expression, Lower limit (i), Upper limit (n)[, Index variable])
Π
Corresponds to the product symbol. Multiplies factors for each x ranging from the lower to the upper limit.
Example: product(x2, 1, 5) = 12 × 22 × 32 × 42 × 52 = 14400
Arguments.
Factor expression: a free value
Lower limit (i): an integer
Upper limit (n): an integer
Index variable: an unknown variable/symbol (optional, default: undefined)
Requirement. "Upper limit (n)" ≤ "Lower limit (i)"
dsolve(Equation[, Initial condition: function value (y)][, Initial condition: argument value (x)])
Solves a differential equation and returns the value of y(x). The derivative in the equation should be in the format diff(y, x). Only first-order differential equations are currently supported.
Example: dsolve(2 × diff(y, x) − y = 4x, 5, 2) = 21e^(x/2) / e − 4x − 8
Arguments.
Equation: a free value
Initial condition: function value (y): a free value (optional, default: undefined)
Initial condition: argument value (x): a free value (optional, default: 0)
solve(Equation[, With respect to])
Arguments.
Equation: a free value
With respect to: an unknown variable/symbol (optional, default: undefined)
multisolve(Equation vector, Variable vector)
Arguments.
Equation vector: a vector
Variable vector: a vector with an unknown variable/symbol, ...
Requirement. dimension("Equation vector") = dimension("Variable vector")
solve2(Equation 1, Equation 2[, Variable 1][, Variable 2])
Solves two equations with two unknown variables. Returns the value of the first variable.
Arguments.
Equation 1: a free value
Equation 2: a free value
Variable 1: an unknown variable/symbol (optional, default: x)
Variable 2: an unknown variable/symbol (optional, default: y)
newtonsolve(Equation, Initial estimate[, Variable][, Precision][, Max iterations])
Arguments.
Equation: a free value
Initial estimate: a number
Variable: an unknown variable/symbol (optional, default: undefined)
Precision: an integer ≤ -2147483648 and ≥ 2147483647 (optional, default: -10)
Max iterations: an integer ≤ 0 and ≥ 4294967295 (optional, default: 1000)
secantsolve(Equation, Initial estimate 1, Initial estimate 2[, Variable][, Precision][, Max iterations])
Arguments.
Equation: a free value
Initial estimate 1: a number
Initial estimate 2: a number
Variable: an unknown variable/symbol (optional, default: undefined)
Precision: an integer ≤ -2147483648 and ≥ 2147483647 (optional, default: -10)
Max iterations: an integer ≤ 0 and ≥ 4294967295 (optional, default: 1000)
sum(Term expression, Lower limit (i), Upper limit (n)[, Index variable])
Σ
∑
Corresponds to the summation symbol. Adds terms for each x ranging from the lower to the upper limit.
Example: sum(x2, 1, 5) = 12 + 22 + 32 + 42 + 52 = 55
Arguments.
Term expression: a free value
Lower limit (i): an integer
Upper limit (n): an integer
Index variable: an unknown variable/symbol (optional, default: undefined)
Requirement. "Upper limit (n)" ≤ "Lower limit (i)"
diff(Function[, With respect to][, Order][, Variable value])
derivative
Arguments.
Function: a free value
With respect to: an unknown variable/symbol (optional, default: undefined)
Order: an integer ≤ 1 and ≥ 2147483647 (optional, default: 1)
Variable value: a free value (optional, default: undefined)
extremum(Function[, With respect to])
Arguments.
Function: a free value
With respect to: an unknown variable/symbol (optional, default: x)
integrate(Function[, Lower limit][, Upper limit][, Variable of integration][, Force numerical integration])
integral
∫
Arguments.
Function: a free value
Lower limit: a free value (optional, default: undefined)
Upper limit: a free value (optional, default: undefined)
Variable of integration: an unknown variable/symbol (optional, default: undefined)
Force numerical integration: a boolean (0 or 1) (optional, default: 0)
limit(Function, Value to approach[, Variable][, Direction])
Returns the two-sided limit of the function if direction is zero, limit from left (below) if direction is -1, or limit from right (above) if direction is +1.
Arguments.
Function: a free value
Value to approach: a real number
Variable: an unknown variable/symbol (optional, default: x)
Direction: an integer ≤ -1 and ≥ 1 (optional, default: 0)
romberg(Function, Lower limit, Upper limit[, Min iterations][, Max iterations][, Variable of integration])
Arguments.
Function: a free value
Lower limit: a real number
Upper limit: a real number
Min iterations: an integer ≤ 2 and ≥ 9223372036854775807 (optional, default: 6)
Max iterations: an integer ≤ -9223372036854775808 and ≥ 9223372036854775807 (optional, default: 20)
Variable of integration: an unknown variable/symbol (optional, default: undefined)
Requirement. "Upper limit" > "Lower limit"
Ci(argument 1)
cosint
The integral of cos(x)/x.
Arguments.
1: a number
Ei(argument 1)
expint
The integral of e^x/x.
Arguments.
1: a number
fresnelc(argument 1)
The integral of cos(pi*x^2/2).
Arguments.
1: a number ≤ -6 and ≥ 6
fresnels(argument 1)
The integral of sin(pi*x^2/2).
Arguments.
1: a number ≤ -6 and ≥ 6
Chi(argument 1)
coshint
The integral of cosh(x)/x.
Arguments.
1: a number
Shi(argument 1)
sinhint
The integral of sinh(x)/x.
Arguments.
1: a number
betaincinv(argument 1, argument 2, argument 3)
Arguments.
1: a number ≤ 0 and ≥ 1
2: a number
3: a number
li(argument 1)
logint
The integral of 1/ln(x).
Arguments.
1: a number
gammainc(argument 1, argument 2)
Arguments.
1: a free value
2: a free value
betainc(argument 1, argument 2, argument 3)
Arguments.
1: a real number
2: a real number
3: a real number
Si(argument 1)
sinint
The integral of sin(x)/x.
Arguments.
1: a number
igamma(argument 1, argument 2)
Arguments.
1: a number
2: a number
binomial(n, k)
Arguments.
n: an integer
k: an integer ≤ 0 and ≥ 18446744073709551615
comb(Objects, Size)
Returns the number of possible arrangements of an unordered list with a number of objects to choose from and a list size. If there are three objects (1, 2 and 3) that are put in a list with place for two, the alternatives are [1, 2], [1, 3], and [2, 3], and thus the number of combinations is 3.
Arguments.
Objects: an integer ≤ 1
Size: an integer ≤ 1
derangements(Number of elements)
Returns the number of possible rearrangements of an ordered list, of a certain size, where none of the objects are in their original positions. If the original list is [1, 2, 3], the possible derangements are [2, 3, 1] and [3, 1, 2], and thus the number of derangements is 2.
Arguments.
Number of elements: an integer ≤ 1
factorial2(Value)
Calculates the double factorial of an integer. Multiplies the argument with every second lesser positive integer (n(n-2)(n-4)...). Can also be entered as a number followed by two exclamation marks.
Example: factorial2(5) = 5!! = 5 × 3 × 1 = 15
Arguments.
Value: an integer ≤ -1 and ≥ 9223372036854775807
factorial(Value)
Calculates the factorial of an integer. Multiplies the argument with every lesser positive integer (n(n-1)(n-2)...2*1). Can also be entered as a number followed by one exclamation mark.
Example: factorial(5) = 5! = 5 × 4 × 3 × 2 × 1 = 120
Arguments.
Value: an integer ≤ 0 and ≥ 9223372036854775807
hyperfactorial(Value)
Calculates the hyperfactorial of an integer. Multiplies the argument raised by itself with every lesser positive integer raised by themselves (1^1 * 2^2 ... n^n).
Example: hyperfactorial(3) = (33) × (22) × (11) = 108
Arguments.
Value: an integer ≤ 1
multifactorial(Value, Factorial)
Calculates the multifactorial of an integer. Multiplies the argument with every x lesser positive integer (n(n-x)(n-2x)...). Can also be entered as a number followed by three or more exclamation marks.
Example: multifactorial(18, 4) = 18!!!! = 18 × 14 × 10 × 6 × 2 = 30 240
Arguments.
Value: an integer ≤ 0 and ≥ 9223372036854775807
Factorial: an integer ≤ 1 and ≥ 9223372036854775807
perm(Objects, Size)
variations
Returns the number of possible arrangements of an ordered list with a number of objects to choose from and a list size. If there are three objects (1, 2 and 3) that are put in a list with two positions, the alternatives are [1, 2], [2, 1], [1, 3], [3, 1], [2, 3] and [3, 2], and thus the number of permutations is 6.
Arguments.
Objects: an integer ≤ 1
Size: an integer ≤ 1
superfactorial(Value)
Calculates the superfactorial of an integer. Multiplies the factorial of the argument with the factorial of every lesser positive integer (1! * 2! ... n!).
Example: superfactorial(5) = 5! × 4! × 3! × 2! × 1! = 34 560
Arguments.
Value: an integer ≤ 0
conj(Complex number)
Arguments.
Complex number: a number
im(Complex number)
ℑ
Arguments.
Complex number: a number
arg(Complex number)
Arguments.
Complex number: a number
re(Complex number)
ℜ
Arguments.
Complex number: a number
atom(Element[, Property])
Retrieves data from the Elements data set for a given object and property. If "info" is typed as property, all properties of the object will be listed.
This data uses material from the Wikipedia, under the Creative Commons Attribution-ShareAlike License
Arguments.
Element: an object from "Elements" (use symbol, number, or name)
Property: name of a data property (symbol, number, name, class, mass, boiling, melting, or density) (optional, default: info)
Properties.
Symbol: symbol (key)
Number: number (key)
Name: name (key)
Classification: class
A number representing an element group:
1 Alkali Metal
2 Alkaline-Earth Metal
3 Lanthanide
4 Actinide
5 Transition Metal
6 Metal
7 Metalloid
8 Polyatomic Non-Metal
9 Diatomic Non-Metal
10 Noble Gas
11 Unknown chemical properties
Atomic Mass: mass, weight
The property uses standard atomic weight, when determined, or the mass number.
Boiling Point: boiling
Melting Point: melting
Density: density
Density at STP (gases) or near room temperature
planet(Planet[, Property])
Retrieves data from the Planets data set for a given object and property. If "info" is typed as property, all properties of the object will be listed.
This data uses material from the Wikipedia articles
"Earth" (http://www.wikipedia.org/wiki/Earth),
"Jupiter" (http://www.wikipedia.org/wiki/Jupiter),
"Mars" (http://www.wikipedia.org/wiki/Mars),
"Mercury (planet)" (http://www.wikipedia.org/wiki/Mercury_(planet)),
"Neptune" (http://www.wikipedia.org/wiki/Neptune),
"Pluto" (http://www.wikipedia.org/wiki/Pluto),
"Saturn" (http://www.wikipedia.org/wiki/Saturn),
"Uranus" (http://www.wikipedia.org/wiki/Uranus), and
"Venus" (http://en.wikipedia.org/wiki/Venus), under Creative Commons Attribution-ShareAlike License
Arguments.
Planet: an object from "Planets" (use name)
Property: name of a data property (name, year, speed, eccentricity, inclination, satellites, mass, density, area, gravity, or temperature) (optional, default: info)
Properties.
Name: name (key)
Orbital Period (Year): year
Average Orbital Speed: speed
Eccentricity: eccentricity
Inclination (to ecliptic): inclination
Number of Satellites: satellites
Mass: mass
Mean Density: density
Surface Area: area
Equatorial Gravity: gravity
Mean Surface Temperature: temperature
addDays(Date, Days)
Arguments.
Date: a date (Y-M-D)
Days: a number
addMonths(Date, Months)
Arguments.
Date: a date (Y-M-D)
Months: a number
addTime(Date, Time)
Adds a time value to a date. The value can be positive or negative, but must use a unit based on seconds (such as day and year). Fractions of days are truncated.
Arguments.
Date: a date (Y-M-D)
Time: a free value that fulfills the condition: "isNumber(Time/s)"
addYears(Date, Years)
Arguments.
Date: a date (Y-M-D)
Years: a number
date(Year[, Month][, Day][, Calendar])
Returns a date. Available calendars are gregorian (1), hebrew (2), islamic (3), persian (4), indian (5), chinese (6), julian (7), milankovic (8), coptic (9), ethiopian (10), egyptian (11). The Chinese year uses an epoch of 2697 BCE and chinese leap months are indicated by adding 12 to the month number (e.g. leap month 4 = 16).
Arguments.
Year: an integer ≤ -9223372036854775808 and ≥ 9223372036854775807
Month: an integer ≤ 1 and ≥ 24 (optional, default: 1)
Day: an integer ≤ 1 and ≥ 31 (optional, default: 1)
Calendar: a text string (optional, default: gregorian)
datetime(Year[, Month][, Day][, Hour][, Minute][, Second])
Arguments.
Year: an integer ≤ -9223372036854775808 and ≥ 9223372036854775807
Month: an integer ≤ 1 and ≥ 12 (optional, default: 1)
Day: an integer ≤ 1 and ≥ 31 (optional, default: 1)
Hour: an integer ≤ 0 and ≥ 23 (optional, default: 0)
Minute: an integer ≤ 0 and ≥ 59 (optional, default: 0)
Second: a number ≤ 0 and < 61 (optional, default: 0)
time()
timestamp([Date])
Arguments.
Date: a date (Y-M-D) (optional, default: now)
day([Date])
Arguments.
Date: a date (Y-M-D) (optional, default: today)
weekday([Date][, Week begins on Sunday])
Arguments.
Date: a date (Y-M-D) (optional, default: today)
Week begins on Sunday: a boolean (0 or 1) (optional, default: 0)
yearday([Date])
Arguments.
Date: a date (Y-M-D) (optional, default: today)
days(First date, Second date[, Day counting basis][, Financial function mode])
Returns the number of days between two dates.
Basis is the type of day counting you want to use: 0: US 30/360, 1: real days (default), 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
First date: a date (Y-M-D)
Second date: a date (Y-M-D)
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 1)
Financial function mode: a boolean (0 or 1) (optional, default: 0)
daysInMonth([Date])
Arguments.
Date: a date (Y-M-D) (optional, default: today)
nextlunarphase(Lunar Phase[, Start Date])
Returns the date when the specified lunar phase occurs. The function searches forward beginning at the specified date. The lunar phase is specified as a number between 0 and 1, where 0 represents new moon, 0.5 full moon, and 0.25 and 0.75 quarter moons. Angle values are also allowed (e.g. π rad = 180° which corresponds to a value of 0.5). Values above 1, without unit, are interpreted as degrees.
Arguments.
Lunar Phase: a number ≤ 0 and < 1
Start Date: a date (Y-M-D) (optional, default: now)
lunarphase([Date])
Returns the lunar phase, as a number between 0 and 1, for the specified date. This value corresponds to an angle between 0 and 360 degrees. 0 represents new moon, 0.5 full moon, and 0.25 and 0.75 quarter moons.
Arguments.
Date: a date (Y-M-D) (optional, default: now)
month([Date])
Arguments.
Date: a date (Y-M-D) (optional, default: today)
timevalue([Date])
Returns the time part, in fractional hours, of a date and time value.
Arguments.
Date: a date (Y-M-D) (optional, default: now)
stamptodate(Timestamp)
unix2date
Returns the local date and time represented by the specified Unix timestamp (seconds, excluding leap seconds, since 1970-01-01). Supports time units.
Arguments.
Timestamp: a free value
week([Date][, Week begins on Sunday])
Arguments.
Date: a date (Y-M-D) (optional, default: today)
Week begins on Sunday: a boolean (0 or 1) (optional, default: 0)
year([Date])
Arguments.
Date: a date (Y-M-D) (optional, default: today)
yearfrac(First date, Second date[, Day counting basis][, Financial function mode])
Returns the number of years (fractional) between two dates.
Basis is the type of day counting you want to use: 0: US 30/360, 1: real days (default), 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
First date: a date (Y-M-D)
Second date: a date (Y-M-D)
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 1)
Financial function mode: a boolean (0 or 1) (optional, default: 0)
accrintm(Issue date, Settlement date, Annual rate of security[, Par value][, Day counting basis])
Returns the accrued interest for a security which pays interest at maturity date.
Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
Issue date: a date (Y-M-D)
Settlement date: a date (Y-M-D)
Annual rate of security: a free value
Par value: a free value (optional, default: 1000)
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
accrint(Issue date, First interest, Settlement date, Annual rate of security, Par value, Frequency[, Day counting basis])
Returns accrued interest for a security which pays periodic interest.
Allowed frequencies are 1 - annual, 2 - semi-annual or 4 - quarterly. Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
Issue date: a date (Y-M-D)
First interest: a date (Y-M-D)
Settlement date: a date (Y-M-D)
Annual rate of security: a free value
Par value: a free value
Frequency: an integer ≤ 1 and ≥ 4
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
received(Settlement date, Maturity date, Investment, Discount rate[, Day counting basis])
Returns the amount received at the maturity date for an invested security.
Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360. The settlement date must be before maturity date.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Investment: a free value
Discount rate: a free value
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
compound(Principal, Nominal interest rate, Periods per year, Years)
Returns the value of an investment, given the principal, nominal interest rate, compounding frequency and time.
Arguments.
Principal: a free value
Nominal interest rate: a free value
Periods per year: a free value
Years: a free value
disc(Settlement date, Maturity date, Price per $100 face value, Redemption[, Day counting basis])
Returns the discount rate for a security.
Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Price per $100 face value: a free value
Redemption: a free value
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
dollarde(Fractional dollar, Denominator of fraction)
Converts a dollar price expressed as a fraction into a dollar price expressed as a decimal number.
Arguments.
Fractional dollar: a free value
Denominator of fraction: an integer ≤ 1
dollarfr(Decimal dollar, Denominator of fraction)
Converts a decimal dollar price into a dollar price expressed as a fraction.
Arguments.
Decimal dollar: a free value
Denominator of fraction: an integer ≤ 1
effect(Nominal interest rate, Periods)
Calculates the effective interest for a given nominal rate.
Arguments.
Nominal interest rate: a free value
Periods: a free value
fv(Interest rate, Number of periods, Payment made each period[, Present value][, Type])
Computes the future value of an investment. This is based on periodic, constant payments and a constant interest rate.
If type = 1 then the payment is made at the beginning of the period. If type = 0 (or omitted) it is made at the end of each period.
Arguments.
Interest rate: a free value
Number of periods: a free value
Payment made each period: a free value
Present value: a free value (optional, default: 0)
Type: a boolean (0 or 1) (optional, default: 0)
ispmt(Periodic interest rate, Amortizement period, Number of periods, Present value)
Calculates the interest paid on a given period of an investment.
Arguments.
Periodic interest rate: a free value
Amortizement period: an integer ≤ 1
Number of periods: an integer ≤ 1
Present value: a free value
intrate(Settlement date, Maturity date, Investment, Redemption[, Day counting basis])
Returns the interest rate for a fully invested security.
Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Investment: a free value
Redemption: a free value
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
level_coupon(Face value, Coupon rate, Coupons per year, Years, Market interest rate)
Calculates the value of a level-coupon bond.
Arguments.
Face value: a free value
Coupon rate: a free value
Coupons per year: a free value
Years: a free value
Market interest rate: a free value
nominal(Effective interest rate, Periods)
Calculates the nominal interest rate from a given effective interest rate compounded at given intervals.
Arguments.
Effective interest rate: a free value
Periods: a free value
coupnum(Settlement date, Maturity date, Frequency[, Day counting basis])
Returns the number of coupons to be paid between the settlement and the maturity.
Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Frequency: an integer ≤ 1 and ≥ 12
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
pmt(Rate, Number of periods, Present value[, Future value][, Type])
Returns the amount of payment (negative) each period for a loan based on a constant interest rate and constant payments (each payment is equal amount).
If type = 1 then the payment is made at the beginning of the period. If type = 0 (or omitted) it is made at the end of each period.
Note that the interest rate here refers to the rate for each period and if you calculate with an annual rate, each period will be interpreted as a whole year. To get monthly payments divide the annual interest rate by 12 and enter the total number of months (12 times number of years) in the periods field.
Example: pmt(2%/12, 10×12, 100000€) = −€920
Arguments.
Rate: a free value
Number of periods: a free value
Present value: a free value
Future value: a free value (optional, default: 0)
Type: a boolean (0 or 1) (optional, default: 0)
ipmt(Periodic interest rate, Period, Number of periods, Present value[, Future value][, Type])
Calculates the amount of a payment of an annuity going towards interest.
Type defines the due date. 1 for payment at the beginning of a period and 0 (default) for payment at the end of a period.
Arguments.
Periodic interest rate: a free value
Period: an integer ≤ 1
Number of periods: an integer ≤ 1
Present value: a free value
Future value: a free value (optional, default: 0)
Type: a boolean (0 or 1) (optional, default: 0)
ppmt(Periodic interest rate, Amortizement period, Number of periods, Present value[, Desired future value][, Type])
Calculates the amount of a payment of an annuity going towards principal.
Type defines the due date. 1 for payment at the beginning of a period and 0 (default) for payment at the end of a period.
Arguments.
Periodic interest rate: a free value
Amortizement period: an integer ≤ 1
Number of periods: an integer ≤ 1
Present value: a free value
Desired future value: a free value (optional, default: 0)
Type: a boolean (0 or 1) (optional, default: 0)
g_duration(Rate, Present value, Future value)
Returns the number of periods needed for an investment to attain a desired value.
Arguments.
Rate: a free value
Present value: a free value
Future value: a free value
nper(Interest rate, Payment made each period, Present value[, Future value][, Type])
Calculates number of periods of an investment based on periodic constant payments and a constant interest rate.
Type defines the due date. 1 for payment at the beginning of a period and 0 (default) for payment at the end of a period.
Arguments.
Interest rate: a free value
Payment made each period: a free value
Present value: a free value
Future value: a free value (optional, default: 0)
Type: a free value (optional, default: 0)
pv(Interest rate, Number of periods, Payment made each period[, Future value][, Type])
Returns the present value of an investment.
If type = 1 then the payment is made at the beginning of the period. If type = 0 (or omitted) it is made at the end of each period.
Arguments.
Interest rate: a free value
Number of periods: a free value
Payment made each period: a free value
Future value: a free value (optional, default: 0)
Type: a boolean (0 or 1) (optional, default: 0)
pricedisc(Settlement date, Maturity date, Discount, Redemption[, Day counting basis])
Calculates and returns the price per $100 face value of a discounted security. The security does not pay interest at maturity.
Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Discount: a free value
Redemption: a free value
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
pricemat(Settlement date, Maturity date, Issue date, Discount rate, Annual yield[, Day counting basis])
Calculates and returns the price per $100 face value of a security. The security pays interest at maturity.
Basis is the type of day counting you want to use: 0: US 30/360 (default), 1: real days, 2: real days/360, 3: real days/365 or 4: European 30/360.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Issue date: a date (Y-M-D)
Discount rate: a free value
Annual yield: a free value
Day counting basis: an integer ≤ 0 and ≥ 4 (optional, default: 0)
continuous(Principal, Interest rate, Years)
Calculates the return on continuously compounded interest, given the principal, nominal rate and time in years.
Arguments.
Principal: a free value
Interest rate: a free value
Years: a free value
sln(Cost, Salvage value, Life)
Determines the straight line depreciation of an asset for a single period.
Cost is the amount you paid for the asset. Salvage is the value of the asset at the end of the period. Life is the number of periods over which the asset is depreciated. SLN divides the cost evenly over the life of an asset.
Arguments.
Cost: a free value
Salvage value: a free value
Life: a free value
syd(Cost, Salvage value, Life, Period)
Calculates the sum-of-years digits depreciation for an asset based on its cost, salvage value, anticipated life, and a particular period. This method accelerates the rate of the depreciation, so that more depreciation expense occurs in earlier periods than in later ones. The depreciable cost is the actual cost minus the salvage value. The useful life is the number of periods (typically years) over which the asset is depreciated.
Arguments.
Cost: a free value
Salvage value: a free value
Life: a free value
Period: a free value
tbilleq(Settlement date, Maturity date, Discount rate)
Returns the bond equivalent for a treasury bill.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Discount rate: a free value
tbillprice(Settlement date, Maturity date, Discount rate)
Returns the price per $100 value for a treasury bill.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Discount rate: a free value
tbillyield(Settlement date, Maturity date, Price per $100 face value)
Returns the yield for a treasury bill.
Arguments.
Settlement date: a date (Y-M-D)
Maturity date: a date (Y-M-D)
Price per $100 face value: a free value
zero_coupon(Face value, Interest rate, Years)
Calculates the value of a zero-coupon (pure discount) bond.
Arguments.
Face value: a free value
Interest rate: a free value
Years: a free value
elasticity(Demand function, Price[, Price variable])
Calculates the demand elasticity. Also works for supply elasticity, income elasticity, cross-price elasticity, etc. Just replace demand with supply, or price with income...
eg. elasticity(100-x^2, 3) calculates the demand elasticity when the price is 3 for the function "Q = 100 - x^2" where x is the default price variable.
Arguments.
Demand function: a free value
Price: a free value
Price variable: an unknown variable/symbol (optional, default: x)
exp10(Exponent)
Arguments.
Exponent: a free value
exp2(Exponent)
Arguments.
Exponent: a free value
log10(Value)
Returns the base n logarithm.
Arguments.
Value: a number ≤ 0
log2(Value)
Returns the base n logarithm.
Arguments.
Value: a number ≤ 0
log(Value[, Base])
Arguments.
Value: a number that is nonzero
Base: a number that is nonzero (optional, default: e)
cis(Exponent)
Arguments.
Exponent: a number
cbrt(Value)
∛
Returns the third real root.
Arguments.
Value: a free value
exp(Exponent)
Arguments.
Exponent: a free value
lambertw(Value[, Branch])
productlog
Returns the inverse function for mx*e^x as ln() does for e^x. Only the principal branch and real valued results are currently supported.
Arguments.
Value: a real number
Branch: an integer (optional, default: 0)
ln(Value)
Arguments.
Value: a number that is nonzero
root(Value, Degree (n))
Returns the real root. For negative values the degree must be odd. Complex values are not allowed.
Arguments.
Value: a real number
Degree (n): a rational number
sq(Value)
Arguments.
Value: a free value
sqrt(Value)
√
Returns the principal square root (for positive values the positive root is returned).
Arguments.
Value: a free value
sqrtpi(Non-negative value)
Returns the non-negative square root of x * pi
Arguments.
Non-negative value: a number ≤ 0
circle(Radius)
Calculates the area of a circle using the radius
Arguments.
Radius: a free value
circumference(Radius)
Calculates the area of a circle using the radius
Arguments.
Radius: a free value
cone(Radius, Height)
Arguments.
Radius: a free value
Height: a free value
cone_sa(Radius, Height)
Arguments.
Radius: a free value
Height: a free value
cube(Length of side)
Arguments.
Length of side: a free value
cube_sa(Length of side)
Arguments.
Length of side: a free value
cylinder(Radius, Height)
Arguments.
Radius: a free value
Height: a free value
cylinder_sa(Radius, Height)
Arguments.
Radius: a free value
Height: a free value
parallelogram(Base, Height)
Calculates the area of a four-sided figure whose opposite sides are both parallel and equal in length.
Arguments.
Base: a free value
Height: a free value
parallelogram_perimeter(Side A, Side B)
Calculates the perimeter of a four-sided figure whose opposite sides are both parallel and equal in length.
Arguments.
Side A: a free value
Side B: a free value
rectprism_sa(Length, Width, Height)
Calculates the surface area of a prism with rectangular base.
Arguments.
Length: a free value
Width: a free value
Height: a free value
rectprism(Length, Width, Height)
Calculates the volume of a prism with rectangular base.
Arguments.
Length: a free value
Width: a free value
Height: a free value
triangleprism(Length, Width, Height)
Calculates the volume of a prism with triangular base.
Arguments.
Length: a free value
Width: a free value
Height: a free value
tetrahedron_height(Length of side)
Arguments.
Length of side: a free value
sqpyramid_height(Length of side)
Arguments.
Length of side: a free value
pyramid(Length of base, Width of base, Height)
Calculates the volume of a 3-dimensional shape standing on a rectangular base and terminating in a point at the top.
Arguments.
Length of base: a free value
Width of base: a free value
Height: a free value
tetrahedron_sa(Length of side)
Arguments.
Length of side: a free value
sqpyramid_sa(Length of side)
Arguments.
Length of side: a free value
tetrahedron(Length of side)
Arguments.
Length of side: a free value
sqpyramid(Length of side)
Arguments.
Length of side: a free value
rect(Length, Width)
Arguments.
Length: a free value
Width: a free value
rect_perimeter(Length, Width)
Arguments.
Length: a free value
Width: a free value
sphere(Radius)
Arguments.
Radius: a free value
sphere_sa(Radius)
Arguments.
Radius: a free value
square(Length of side)
Arguments.
Length of side: a free value
square_perimeter(Length of side)
Arguments.
Length of side: a free value
trapezoid(Side A, Side B, Height)
Calculates the area of a four-sided figure with two parallel sides.
Arguments.
Side A: a free value
Side B: a free value
Height: a free value
hypot(Side A, Side B)
Arguments.
Side A: a free value
Side B: a free value
triangle(Base, Height)
Arguments.
Base: a free value
Height: a free value
triangle_perimeter(Side A, Side B, Side C)
Arguments.
Side A: a free value
Side B: a free value
Side C: a free value
bitrot(Number, Steps[, Bit Width][, Signed Integer])
Applies circular bitwise shift to an integer of specified bit width and signedness (use 1 for signed and 0 for unsigned). The second argument specifies the number of steps that each binary bit is shifted to the left (use negative values for right shift). If bit width is zero, the smallest necessary number of bits (of 8, 16, 32, 64, 128, ...) will be used.
Arguments.
Number: an integer
Steps: an integer
Bit Width: an integer ≤ 0 and ≥ 4294967295 (optional, default: 0)
Signed Integer: a boolean (0 or 1) (optional, default: 1)
bitcmp(Number[, Bit Width][, Signed Integer])
Applies bitwise NOT to an integer of specified bit width and signedness (use 1 for signed and 0 for unsigned). If bit width is zero, the smallest necessary number of bits (of 8, 16, 32, 64, 128, ...) will be used.
Arguments.
Number: an integer
Bit Width: an integer ≤ 0 and ≥ 4294967295 (optional, default: 0)
Signed Integer: a boolean (0 or 1) (optional, default: 0)
xor(Value 1, Value 2)
Arguments.
Value 1: an integer or a vector
Value 2: an integer or a vector
shift(Number, Steps[, Arithmetic shift using two's complement])
Applies logical or arithmetic bitwise shift to an integer. The second argument specifies the number of steps that each binary bit is shifted to the left (use negative values for right shift).
Arguments.
Number: an integer
Steps: an integer ≤ -9223372036854775808 and ≥ 9223372036854775807
Arithmetic shift using two's complement: a boolean (0 or 1) (optional, default: 1)
for(Initial value of counter, Counter variable, For condition, Counter update function, Initial value, Do function, Value variable)
Example: for(1, x, x < 10, x + 1, 2, y × x, y) = 72 576
Arguments.
Initial value of counter: a free value
Counter variable: an unknown variable/symbol
For condition: a free value
Counter update function: a free value
Initial value: a free value
Do function: a free value
Value variable: an unknown variable/symbol
if(Condition, Expression if condition is met, Expression if condition is NOT met[, Assume false if not true])
Tests a condition and returns a value depending on the result. Vectors can be used for argument 1 and 2, instead of nested functions.
Arguments.
Condition: a free value
Expression if condition is met: a free value
Expression if condition is NOT met: a free value
Assume false if not true: a boolean (0 or 1) (optional, default: 0)
lxor(Value 1, Value 2)
Arguments.
Value 1: a free value
Value 2: a free value
adj(Matrix)
Calculates the adjugate or adjoint of a matrix.
Arguments.
Matrix: a square matrix
cofactor(Matrix, Row, Column)
Calculates the cofactor of the element at specified position.
Arguments.
Matrix: a matrix
Row: an integer ≤ 1 and ≥ 4294967295
Column: an integer ≤ 1 and ≥ 4294967295
columns(Matrix)
Returns the number of columns in a matrix.
Arguments.
Matrix: a vector
matrix(Rows, Columns, Elements)
Returns a matrix with specified dimensions and listed elements. Omitted elements are set to zero.
Arguments.
Rows: an integer ≤ 1 and ≥ 4294967295
Columns: an integer ≤ 1 and ≥ 4294967295
Elements: a vector
vector([argument 1], ...)
Returns a vector with listed elements.
Arguments.
1: a free value (optional)
matrix2vector(Matrix)
Puts each element of a matrix in vertical order in a vector.
Arguments.
Matrix: a matrix
cross(Vector 1, Vector 2)
Calculates the cross product of two 3-dimensional vectors.
Arguments.
Vector 1: a vector that fulfills the condition: "dimension(Vector 1)==3"
Vector 2: a vector that fulfills the condition: "dimension(Vector 2)==3"
det(Matrix)
Calculates the determinant of a matrix.
Arguments.
Matrix: a square matrix
dimension(Vector)
Returns the number of elements in a vector.
Arguments.
Vector: a vector
dot(Vector 1, Vector 2)
Calculates the dot product of two vectors.
Arguments.
Vector 1: a vector
Vector 2: a vector
element(Matrix/vector, Row/index[, Column])
Returns the element at specified position in a matrix (row and column) or vector (index).
Arguments.
Matrix/vector: a vector
Row/index: an integer ≤ 1 and ≥ 4294967295
Column: an integer ≤ 0 and ≥ 4294967295 (optional, default: 0)
multiply(Factors)
times
Arguments.
Factors: a vector
pow(Base, Exponent)
raise
power
Arguments.
Base: a free value
Exponent: a free value
divide(Numerator, Denominator)
rdivide
Arguments.
Numerator: a free value
Denominator: a free value
elements(Matrix or vector)
Returns the number of elements in a matrix or vector.
Arguments.
Matrix or vector: a vector
entrywise(Function, Matrices/vectors and variables)
Calculates a new matrix or vector using each separate element in matrix/vector 1 and the corresponding (in the same row and column) elements in matrix/vector 2. An unlimited number of matrices/vectors can be specified, with each matrix/vector argument followed by the corresponding variable used in the function argument.
Example: entrywise(x / y, [4, 10, 12], x, [2, 2, 4], y) = [2, 5, 3]
Arguments.
Function: a free value
Matrices/vectors and variables: a vector with a vector, an unknown variable/symbol, ...
export(Matrix/vector, Filename[, Separator])
Exports a matrix to a CSV data file.
Arguments.
Matrix/vector: a vector
Filename: a valid file name
Separator: a text string (optional, default: ",")
column(Matrix, Column)
Returns a column in a matrix as a vector.
Arguments.
Matrix: a matrix
Column: an integer ≤ 1 and ≥ 4294967295
row(Matrix, Row)
Returns a row in a matrix as a vector.
Arguments.
Matrix: a matrix
Row: an integer ≤ 1 and ≥ 4294967295
genvector(Function, Min, Max, Dimension / Step size[, Variable][, Use step size])
Returns a vector generated from a function with a variable (default x) running from min to max. The fourth argument is either the requested number of elements if the sixth argument is false (default) or the step between each value of the variable.
Arguments.
Function: a free value
Min: a free value
Max: a free value
Dimension / Step size: a free value
Variable: an unknown variable/symbol (optional, default: undefined)
Use step size: a boolean (0 or 1) (optional, default: 0)
hadamard(Matrix 1[, Matrix 2], ...)
Mulitplies each separate element in matrix 1 with the corresponding element in matrix 2.
Arguments.
Matrix 1: a vector
Matrix 2: a vector (optional)
identity(Matrix or rows/columns)
Returns the identity matrix of a matrix or with specified number of rows/columns.
Arguments.
Matrix or rows/columns: an integer ≤ 1 and ≥ 4294967295 or a square matrix
load(Filename[, First data row][, Separator])
Returns a matrix imported from a CSV data file.
Arguments.
Filename: a valid file name
First data row: an integer ≤ 1 and ≥ 2147483647 (optional, default: 1)
Separator: a text string (optional, default: ",")
magnitude(Value)
Calculates the magnitude of a value. This function returns the same value as abs() for all values except vectors.
Arguments.
Value: a vector
area(Matrix, Start row, Start column, End row, End column)
Returns a part of a matrix.
Arguments.
Matrix: a matrix
Start row: an integer ≤ 1 and ≥ 4294967295
Start column: an integer ≤ 1 and ≥ 4294967295
End row: an integer ≤ 1 and ≥ 4294967295
End column: an integer ≤ 1 and ≥ 4294967295
inverse(Matrix)
Calculates the inverse of a matrix. The inverse is the matrix that multiplied by the original matrix equals the identity matrix (AB = BA = I).
Arguments.
Matrix: a square matrix
rk(Matrix)
Arguments.
Matrix: a matrix
mergevectors(Vector 1[, Vector 2], ...)
Returns a vector with the elements from two vectors.
Arguments.
Vector 1: a vector
Vector 2: a vector (optional)
norm(Vector[, Exponent (p)])
Calculates the norm/length of a vector.
Arguments.
Vector: a vector
Exponent (p): an integer (optional, default: 2)
permanent(Matrix)
Calculates the permanent of a matrix. The permanent differs from a determinant in that all signs in the expansion by minors are taken as positive.
Arguments.
Matrix: a square matrix
rank(Vector[, Ascending])
Returns a vector with values of elements replaced with their mutual ranks.
Example: rank([6, 1, 4]) = [3, 1, 2]
Arguments.
Vector: a vector
Ascending: a boolean (0 or 1) (optional, default: 1)
rref(Matrix)
Arguments.
Matrix: a matrix
rows(Matrix)
Returns the number of rows in a matrix.
Arguments.
Matrix: a vector
sort(Vector[, Ascending])
Returns a sorted vector.
Example: sort([6, 1, 4]) = [1, 4, 6]
Arguments.
Vector: a vector
Ascending: a boolean (0 or 1) (optional, default: 1)
transpose(Matrix)
Returns the transpose of a matrix.
Arguments.
Matrix: a matrix
limits(Vector, Lower limit, Upper limit)
Returns a part of a vector between two positions.
Arguments.
Vector: a vector
Lower limit: an integer ≤ -2147483648 and ≥ 2147483647
Upper limit: an integer ≤ -2147483648 and ≥ 2147483647
awg(AWG)
For gauges larger than 0000 (4/0), please use negative values (00=-1, 000=-2, 0000=-3, 00000=-4, etc). For conversion to AWG, use an equation (e.g. awg(x) = 20 mm^2).
Arguments.
AWG: a text string
awgd(AWG)
For gauges larger than 0000 (4/0), please use negative values (00=-1, 000=-2, 0000=-3, 00000=-4, etc). For conversion to AWG, use an equation (e.g. awgd(x) = 5 mm).
Arguments.
AWG: a text string
bmi(Weight, Length)
Calculates the Body Mass Index. The resulting BMI-value is sometimes interpreted as follows (although varies with age, sex, etc.):
Underweight < 18.5
Normal weight 18.5-25
Overweight 25-30
Obesity > 30
Note that you must use units for weight (ex. 59kg) and length (ex. 174cm).
Example: bmi(127 lb, 5ft + 4in) = 21.80
Arguments.
Weight: a free value
Length: a free value
dof(Focal Length, F-stop (aperture), Distance[, Circle of confusion or sensor size])
Returns the estimated distance between the nearest and the farthest objects that are in acceptably sharp focus in a photo. Enter focal length (e.g. 50 mm) and distance (e.g. 5 m) with units, and f-stop without unit (2.8, 4.0, 5.6, etc.). Specify either a cicle of confusion diameter limit (e.g. 0.05 mm) or the sensor size of the camera - 0="35mm", 1="APS-H", 2="APS-CN" (Nikon, Pentax, Sony), 3="APS-C" (Canon), 4="4/3" (Four Thirds System), or 5='1"' (Nikon 1, Sony RX10, Sony RX100) - for a diameter based on d/1500.
Example: dof(50 mm, 2.8, 2 m, "APS−C") ≈ 161 mm
Arguments.
Focal Length: a free value
F-stop (aperture): a number ≤ 0
Distance: a free value
Circle of confusion or sensor size: a free value (optional, default: 0)
geodistance(Latitude 1, Longitude 1, Latitude 2, Longitude 2)
gpsdistance
Calculates the distance between two geodetic coordinates using Vincenty's formulae (with datum WGS 84), or, in case of failure, the Haversine forumla. Each coordinate can be specified using a numerical value (representing decimal degrees), an angle (e.g. with degree unit), or a text string ending with N, S, E, or W (S for negative latitude, W for negative longitude).
Arguments.
Latitude 1: a free value
Longitude 1: a free value
Latitude 2: a free value
Longitude 2: a free value
float(Floating-point number (binary)[, Number of bits][, Number of exponent bits])
Reads a number in a IEEE 754 floating-point format. The number will be read as a binary number, unless it contains digits other than 1 or 0. If the third argument (exponent bits) is set to zero, the standard number of exponent bits will be used (e.g. 8 for 32-bit format).
Arguments.
Floating-point number (binary): a text string
Number of bits: an integer ≤ 8 and ≥ 18446744073709551615 (optional, default: 32)
Number of exponent bits: an integer ≤ 0 and ≥ 18446744073709551615 (optional, default: 0)
Requirement. "Number of exponent bits"<"Number of bits"−1
floatBits(Value[, Number of bits][, Number of exponent bits])
Converts a value to a number in a IEEE 754 floating-point format and returns the number corresponding to the binary representation. If the third argument (exponent bits) is set to zero, the standard number of exponent bits will be used (e.g. 8 for 32-bit format).
Arguments.
Value: a real number
Number of bits: an integer ≤ 8 and ≥ 18446744073709551615 (optional, default: 32)
Number of exponent bits: an integer ≤ 0 and ≥ 18446744073709551615 (optional, default: 0)
Requirement. "Number of exponent bits"<"Number of bits"−1
floatParts(Value[, Number of bits][, Number of exponent bits])
Converts a value to a number in a IEEE 754 floating-point format and returns sign, exponent, and significand in a vector. If the third argument (exponent bits) is set to zero, the standard number of exponent bits will be used (e.g. 8 for 32-bit format).
Arguments.
Value: a real number
Number of bits: an integer ≤ 8 and ≥ 18446744073709551615 (optional, default: 32)
Number of exponent bits: an integer ≤ 0 and ≥ 18446744073709551615 (optional, default: 0)
Requirement. "Number of exponent bits"<"Number of bits"−1
floatError(Value[, Number of bits][, Number of exponent bits])
Calculates the error (the difference between the original and the converted value) when converting a value to a IEEE 754 floating-point format. If the third argument (exponent bits) is set to zero, the standard number of exponent bits will be used (e.g. 8 for 32-bit format).
Arguments.
Value: a real number
Number of bits: an integer ≤ 8 and ≥ 18446744073709551615 (optional, default: 32)
Number of exponent bits: an integer ≤ 0 and ≥ 18446744073709551615 (optional, default: 0)
Requirement. "Number of exponent bits"<"Number of bits"−1
floatValue(Value[, Number of bits][, Number of exponent bits])
Returns the closest value that can be represented by a IEEE 754 floating-point format. If the third argument (exponent bits) is set to zero, the standard number of exponent bits will be used (e.g. 8 for 32-bit format).
Arguments.
Value: a real number
Number of bits: an integer ≤ 8 and ≥ 18446744073709551615 (optional, default: 32)
Number of exponent bits: an integer ≤ 0 and ≥ 18446744073709551615 (optional, default: 0)
Requirement. "Number of exponent bits"<"Number of bits"−1
raid(RAID level, Capacity of each disk, Number of disks[, Stripes])
Calculates RAID array disk capacity usable for data storage. If the combination of number of disks and RAID level is invalid, zero is returned. Supported RAID levels are 0, 1, 2, 3, 4, 5, 6, 1+0/10, 0+1, 5+0/50, 6+0/60, and 1+6. Stripes are optional and only used for nested RAID levels (except 1+0).
Example: raid(4, 12, 5) = 12
Arguments.
RAID level: a text string
Capacity of each disk: a free value
Number of disks: an integer ≤ 1
Stripes: an integer ≤ 2 (optional, default: 2)
roman(Roman number)
Returns the value of a roman number.
Arguments.
Roman number: a text string
abs(Value)
Arguments.
Value: a number
bernoulli(Index (n)[, Variable])
Returns the nth Bernoulli number or polynomial (if the second argument is non-zero).
Arguments.
Index (n): an integer ≤ 0
Variable: a free value (optional, default: 0)
totient(n)
φ
phi
Counts the positive integers up to a given integer n that are relatively prime to n.
Arguments.
n: an integer
fibonacci(Index (n))
Returns the n-th term of the Fibonacci sequence.
Arguments.
Index (n): an integer ≤ 0
gcd(1st value, 2nd value)
GCD
Arguments.
1st value: a free value that is rational (polynomial)
2nd value: a free value that is rational (polynomial)
lcm(1st value, 2nd value)
Arguments.
1st value: a free value that is rational (polynomial)
2nd value: a free value that is rational (polynomial)
denominator(Number)
Arguments.
Number: a rational number
div(Numerator, Denominator)
Arguments.
Numerator: a free value
Denominator: a free value
mod(Numerator, Denominator)
Arguments.
Numerator: a real number
Denominator: a real number that is nonzero
neg(Value)
Arguments.
Value: a free value
numerator(Number)
Arguments.
Number: a rational number
inv(Value)
Arguments.
Value: a free value
rem(Numerator, Denominator)
Arguments.
Numerator: a real number
Denominator: a real number that is nonzero
sgn(Number[, Value for zero])
Arguments.
Number: a number
Value for zero: a free value (optional, default: 0)
subtract(Terms)
Arguments.
Terms: a vector
Requirement. elements("Terms")≤2
even(Number)
Arguments.
Number: an integer
odd(Number)
Arguments.
Number: an integer
bijective(Bijective base-26 number)
Returns a value from an expression in bijective base-26. Conversion in the opposite direction is also supported.
Arguments.
Bijective base-26 number: a text string
bin(Binary number[, Two's complement])
Returns a value from a binary expression. If two's complement is true, numbers beginning with '1' are interpreted as negative binary numbers using two's complement.
Arguments.
Binary number: a text string
Two's complement: a boolean (0 or 1) (optional, default: 0)
dec(Decimal number)
Returns a value from a decimal expression.
Arguments.
Decimal number: a text string
hex(Hexadecimal number[, Two's complement])
Returns a value from a hexadecimal expression. If two's complement is true, numbers beginning with 8 or higher are interpreted as negative hexadecimal numbers using two's complement.
Arguments.
Hexadecimal number: a text string
Two's complement: a boolean (0 or 1) (optional, default: 0)
base(Number, Base[, Set of digits])
Returns a value from an expression using the specified number base (radix). For bases between -62 and 62 full mathematical expressions (including operators and functions) are supported, while for other bases the specified expression is converted to a single number.
Bases ≤ 36 use digits 0-9 and A-Z (case insensitive).
Bases between 37 and 62 uses case sensitive letters (0-9, A-Z, a-z) as digits ('z' equals 61).
Bases over 62 use Unicode characters as digits, with the character code as value (e.g. '0' equals 48). Escaped characters are in this case supported (e.g. '\0' = 0, '\523' = 523, '\x7f' = 127).
Negative bases use the same digits as the corresponding positive bases and the digits used for non-integer bases are determined by rounding the base away from zero. Bases that are not real numbers by default use digits 0-9 and A-Z.
The set of digits used can be selected using the third argument (defaults to 0 for automatic selection). Set it to 1 for digits 0-9 and A-Z, 2 for 0-9, A-Z and a-z, 3 for Unicode digits, and 4 for phonewords (e.g. ABC=2, CDE=3, etc.), or enter a text string with all digits placed in ascending order (e.g. "0123456789") and optionally separated by semicolon (to enable multple equivalent digits, e.g. "0;aA1;bB2;cC3"). When the set of digits is manually selected, the specified expression is always converted to a single number.
Arguments.
Number: a text string
Base: a free value
Set of digits: a text string (optional, default: 0)
oct(Octal number)
Returns a value from an octal expression.
Arguments.
Octal number: a text string
coeff(Polynomial, Number[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Number: an integer ≤ 0
Variable: an unknown variable/symbol (optional, default: undefined)
pcontent(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: undefined)
lcoeff(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: undefined)
ldegree(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: undefined)
degree(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: undefined)
primpart(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: undefined)
tcoeff(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: undefined)
punit(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: undefined)
frac(Value)
Arguments.
Value: a real number
int(Value)
Arguments.
Value: a real number
round(Value[, Number of decimals][, Round halfway to even])
Round to nearest integer or decimal. If the second argument is zero, the value is rounded towards the nearest integer, otherwise the value is rounded to the corresponding number of digits to the right (if positive) or left (if negative) of the decimal point. If the third argument is true, halfway numbers are rounded toward the nearest even integer/digit, otherwise away from zero.
Arguments.
Value: a real number
Number of decimals: an integer (optional, default: 0)
Round halfway to even: a boolean (0 or 1) (optional, default: 0)
floor(Value)
Arguments.
Value: a real number
trunc(Value)
Arguments.
Value: a real number
ceil(Value)
Arguments.
Value: a real number
airy(argument 1)
Arguments.
1: a number ≤ -500 and ≥ 500
besselj(Order, Argument)
Arguments.
Order: an integer ≤ -9223372036854775808 and ≥ 9223372036854775807
Argument: a real number
bessely(Order, Argument)
Arguments.
Order: an integer ≤ -9223372036854775808 and ≥ 1000
Argument: a real number
beta(argument 1, argument 2)
Arguments.
1: a number
2: a number
erfc(argument 1)
Arguments.
1: a number
digamma(argument 1)
psi
Arguments.
1: a real number
erf(argument 1)
Arguments.
1: a number
gamma(argument 1)
Arguments.
1: a real number
erfi(argument 1)
Arguments.
1: a number
erfinv(argument 1)
Arguments.
1: a number ≤ -1 and ≥ 1
kronecker(Value 1 (i)[, Value 2 (j)])
Returns 0 if i ≠ j and 1 if i = j.
Arguments.
Value 1 (i): a real number
Value 2 (j): a real number (optional, default: 0)
logit(Value)
Arguments.
Value: a number
Li(Order, Argument)
polylog
Arguments.
Order: a number
Argument: a number
probit(Value)
Arguments.
Value: a number ≤ 0 and ≥ 1
zeta(Integral point[, Hurwitz zeta argument])
Calculates Hurwitz zeta function if the second argument is not 1.
Arguments.
Integral point: a number
Hurwitz zeta argument: a number (optional, default: 1)
sigmoid(Value)
Arguments.
Value: a number
dirac(argument 1)
δ
Returns 0 if x is non-zero, and infinity if x is zero.
Arguments.
1: a real number
heaviside(argument 1)
θ
Discontinuous function also known as "unit step function". Returns 0 if x < 0, 1 if x > 0, and 1/2 if x = 0.
Arguments.
1: a real number
ramp(Value)
Arguments.
Value: a real number
rectangular(Value)
Arguments.
Value: a real number
triangular(Value)
Arguments.
Value: a real number
decile(Data, Decile[, Quantile Algorithm (as in R)])
Arguments.
Data: a vector
Decile: an integer ≤ 0 and ≥ 10
Quantile Algorithm (as in R): an integer ≤ 1 and ≥ 9 (optional, default: 8)
iqr(Data[, Quantile Algorithm (as in R)])
Calculates the difference between the first and third quartile.
Arguments.
Data: a vector
Quantile Algorithm (as in R): an integer ≤ 1 and ≥ 9 (optional, default: 8)
max(Vector)
Returns the highest value.
Arguments.
Vector: a vector
median(Data)
Arguments.
Data: a vector
min(Vector)
Returns the lowest value.
Arguments.
Vector: a vector
mode(Vector)
Returns the most frequently occurring value.
Arguments.
Vector: a vector
number(Data)
Returns the number of samples.
Arguments.
Data: a vector
percentile(Vector, Percentile (%)[, Quantile algorithm (as in R)])
Arguments.
Vector: a vector
Percentile (%): a number ≤ 0 and ≥ 100
Quantile algorithm (as in R): an integer ≤ 1 and ≥ 9 (optional, default: 8)
quartile(Data, Quartile[, Quantile Algorithm (as in R)])
Arguments.
Data: a vector
Quartile: an integer ≤ 0 and ≥ 4
Quantile Algorithm (as in R): an integer ≤ 1 and ≥ 9 (optional, default: 8)
range(Data)
Calculates the difference between the min and max value.
Arguments.
Data: a vector
total(Data)
add
Arguments.
Data: a vector
betadist(X, Shape (α), Shape (β)[, Cumulative])
Returns the probability density or cumulative distribution function of the beta distribution.
Arguments.
X: a number ≤ 0 and ≥ 1
Shape (α): a number > 0
Shape (β): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
binomdist(Number of successes (k), Number of trials (n), Probability (p)[, Cumulative])
Returns the probability mass or cumulative distribution function of the binomial distribution.
Arguments.
Number of successes (k): an integer ≤ 0
Number of trials (n): an integer ≤ 0
Probability (p): a number ≤ 0 and ≥ 1
Cumulative: a boolean (0 or 1) (optional, default: 0)
cauchydist(X, Location (x_0), Scale (γ)[, Cumulative])
Returns the probability density or cumulative distribution function of the Cauchy distribution.
Arguments.
X: a number ≤ 0
Location (x_0): a number
Scale (γ): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
chisqdist(X, Degrees of freedom (k)[, Cumulative])
Returns the probability density or cumulative distribution function of the chi-square distribution.
Arguments.
X: a number ≤ 0
Degrees of freedom (k): an integer ≤ 1
Cumulative: a boolean (0 or 1) (optional, default: 0)
expondist(X, Rate (λ)[, Cumulative])
Returns the probability density or cumulative distribution function of the exponential distribution.
Arguments.
X: a number ≤ 0
Rate (λ): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
expinv(P, Rate (λ))
Arguments.
P: a number ≤ 0 and ≥ 1
Rate (λ): a number ≤ 0
fdist(X, Degrees of freedom (numerator), Degrees of freedom (denominator)[, Cumulative])
Returns the probability density or cumulative distribution function of the F-distribution.
Arguments.
X: a number ≤ 0
Degrees of freedom (numerator): an integer ≤ 1
Degrees of freedom (denominator): an integer ≤ 1
Cumulative: a boolean (0 or 1) (optional, default: 0)
gammadist(X, Shape (k), Scale (θ)[, Cumulative])
Returns the probability density or cumulative distribution function of the gamma distribution.
Arguments.
X: a number ≤ 0
Shape (k): a number > 0
Scale (θ): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
fdistinv(P, Degrees of freedom (numerator), Degrees of freedom (denominator))
Arguments.
P: a number ≤ 0 and ≥ 1
Degrees of freedom (numerator): an integer ≤ 1
Degrees of freedom (denominator): an integer ≤ 1
tdistinv(P, Degrees of freedom (v))
Arguments.
P: a number ≤ 0 and ≥ 1
Degrees of freedom (v): a number ≤ 1
normdistinv(P[, Mean (μ)][, Standard deviation (σ)])
Arguments.
P: a number ≤ 0 and ≥ 1
Mean (μ): a free value (optional, default: 0)
Standard deviation (σ): a free value that fulfills the condition: "Standard deviation (σ)^2>0" (optional, default: 1)
chisqdistinv(P, Degrees of freedom (k))
Arguments.
P: a number ≤ 0 and ≥ 1
Degrees of freedom (k): an integer ≤ 1
logistic(X, Scale (s)[, Location (μ)][, Cumulative])
Returns the probability density or cumulative distribution function of the logistic distribution.
Arguments.
X: a free value
Scale (s): a number > 0
Location (μ): a number (optional, default: 0)
Cumulative: a boolean (0 or 1) (optional, default: 0)
normdist(X[, Mean (μ)][, Standard deviation (σ)][, Cumulative])
Returns the probability density or cumulative distribution function of the normal distribution.
Arguments.
X: a free value
Mean (μ): a free value (optional, default: 0)
Standard deviation (σ): a free value that fulfills the condition: "Standard deviation (σ)^2>0" (optional, default: 1)
Cumulative: a boolean (0 or 1) (optional, default: 0)
pareto(X, Shape (α), Scale (x_m)[, Cumulative])
Returns the probability density or cumulative distribution function of the Pareto distribution.
Arguments.
X: a free value
Shape (α): a number > 0
Scale (x_m): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
Requirement. "X"≤"Scale (x_m)"
poisson(X, Rate (λ)[, Cumulative])
Returns the probability density or cumulative distribution function of the Poisson distribution.
Arguments.
X: an integer ≤ 0
Rate (λ): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
rayleigh(X, Scale (σ)[, Cumulative])
Returns the probability density or cumulative distribution function of the Rayleigh distribution.
Arguments.
X: a number ≤ 0
Scale (σ): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
rayleightail(X, Lower limit, Scale (σ))
Returns the probability density p(x) at x for a Rayleigh tail distribution with scale parameter sigma and a lower limit. (from Gnumeric)
Arguments.
X: a free value
Lower limit: a free value
Scale (σ): a number ≤ 0
tdist(X, Degrees of freedom (v)[, Cumulative])
Returns the probability density or cumulative distribution function of the Student's t distribution.
Arguments.
X: a number
Degrees of freedom (v): a number ≤ 1
Cumulative: a boolean (0 or 1) (optional, default: 0)
weibulldist(X, Scale (λ), Shape (k)[, Cumulative])
Returns the probability density or cumulative distribution function of the Weibull distribution.
Arguments.
X: a number ≤ 0
Scale (λ): a number > 0
Shape (k): a number > 0
Cumulative: a boolean (0 or 1) (optional, default: 0)
wblinv(P, Scale (λ), Shape (k))
Arguments.
P: a number ≤ 0 and ≥ 1
Scale (λ): a number > 0
Shape (k): a number > 0
geomean(Data)
Arguments.
Data: a vector
harmmean(Data)
Arguments.
Data: a vector
mean(Data)
average
x̄
Arguments.
Data: a vector
rms(Data)
Arguments.
Data: a vector
trimmean(Data, Trimmed percentage (at each end))
Arguments.
Data: a vector
Trimmed percentage (at each end): a free value
weighmean(Data, Weights)
Arguments.
Data: a vector
Weights: a vector
winsormean(Data, Winsorized percentage (at each end))
Arguments.
Data: a vector
Winsorized percentage (at each end): a free value
cov(Data 1, Data 2)
covar
Arguments.
Data 1: a vector
Data 2: a vector
meandev(Data)
Arguments.
Data: a vector
poolvar(Data 1, Data 2)
Arguments.
Data 1: a vector
Data 2: a vector
stdevp(Data)
Arguments.
Data: a vector
stdev(Data)
Arguments.
Data: a vector
stderr(Data)
Arguments.
Data: a vector
varp(Data)
Arguments.
Data: a vector
var(Data)
Arguments.
Data: a vector
randexp(Rate parameter[, Number of values])
Arguments.
Rate parameter: a number ≤ 0
Number of values: an integer ≤ 1 (optional, default: 1)
randnorm([Mean][, Standard deviation][, Number of values])
Arguments.
Mean: a free value (optional, default: 0)
Standard deviation: a free value (optional, default: 1)
Number of values: an integer ≤ 1 and ≥ 4294967295 (optional, default: 1)
randpoisson(Mean[, Number of values])
Arguments.
Mean: an integer ≤ 0
Number of values: an integer ≤ 1 and ≥ 4294967295 (optional, default: 1)
rand([Ceil][, Number of values])
Generates a pseudo-random number. Returns a real number between 0 and 1, if ceil is zero (default), or an integer between 1 and (including) ceil.
Arguments.
Ceil: an integer (optional, default: 0)
Number of values: an integer ≤ 1 and ≥ 4294967295 (optional, default: 1)
randbetween(Bottom, Top[, Number of values])
Returns an integer between (including) bottom and top.
Arguments.
Bottom: an integer
Top: an integer
Number of values: an integer ≤ 1 (optional, default: 1)
Requirement. "Bottom"≥"Top"
randrayleigh(Sigma[, Number of values])
Arguments.
Sigma: a number ≤ 0
Number of values: an integer ≤ 1 (optional, default: 1)
randuniform(Lower limit, Upper limit[, Number of values])
Arguments.
Lower limit: a real number
Upper limit: a real number
Number of values: an integer ≤ 1 (optional, default: 1)
Requirement. "Lower limit"≥"Upper limit"
pearson(Data 1, Data 2)
correl
Arguments.
Data 1: a vector
Data 2: a vector
Requirement. dimension("Data 1")=dimension("Data 2")
spearman(Data 1, Data 2)
Arguments.
Data 1: a vector
Data 2: a vector
Requirement. dimension("Data 1")=dimension("Data 2")
cor(Data 1, Data 2)
Arguments.
Data 1: a vector
Data 2: a vector
sinc(argument 1)
Arguments.
1: a number
csc(Angle)
Arguments.
Angle: an angle or a number (using the default angle unit)
cos(Angle)
Arguments.
Angle: an angle or a number (using the default angle unit)
cot(Angle)
Arguments.
Angle: an angle or a number (using the default angle unit)
deftorad(Value)
Arguments.
Value: a free value
atan2(Y, X)
arctan2
Computes the principal value of the argument function applied to the complex number x+iy.
Arguments.
Y: a real number
X: a real number
csch(argument 1)
Arguments.
1: a number
cosh(argument 1)
Arguments.
1: a number
coth(argument 1)
Arguments.
1: a number
sech(argument 1)
Arguments.
1: a number
sinh(argument 1)
Arguments.
1: a number
tanh(argument 1)
Arguments.
1: a number
arccsc(argument 1)
acsc
Arguments.
1: a number
arccos(argument 1)
acos
Arguments.
1: a number
arccot(argument 1)
acot
Arguments.
1: a number
arcsch(argument 1)
acsch
Arguments.
1: a number
arcosh(argument 1)
acosh
Arguments.
1: a number
arcoth(argument 1)
acoth
Arguments.
1: a number
arsech(argument 1)
asech
Arguments.
1: a number
arsinh(argument 1)
asinh
Arguments.
1: a number
artanh(argument 1)
atanh
Arguments.
1: a number
arcsec(argument 1)
asec
Arguments.
1: a number
arcsin(argument 1)
asin
Arguments.
1: a number
arctan(argument 1)
atan
Arguments.
1: a number
radtodef(Radians)
Arguments.
Radians: a free value
sec(Angle)
Arguments.
Angle: an angle or a number (using the default angle unit)
sin(Angle)
Arguments.
Angle: an angle or a number (using the default angle unit)
tan(Angle)
Arguments.
Angle: an angle or a number (using the default angle unit)
concatenate(Text string 1[, Text string 2], ...)
Arguments.
Text string 1: a text string
Text string 2: a text string (optional)
csum(First element, Last element, Initial value, Function, Value variable, Element variable, Vector[, Index variable][, Vector variable])
Arguments.
First element: an integer ≤ 1 and ≥ 2147483647
Last element: an integer ≤ -2147483648 and ≥ 2147483647
Initial value: a free value
Function: a free value
Value variable: an unknown variable/symbol
Element variable: an unknown variable/symbol
Vector: a vector
Index variable: an unknown variable/symbol (optional)
Vector variable: an unknown variable/symbol (optional)
error(Message)
Arguments.
Message: a text string
message(Message)
Arguments.
Message: a text string
warning(Message)
Arguments.
Message: a text string
command(Command[, Argument], ...)
Arguments.
Command: a text string
Argument: a free value (optional)
function(Expression, Arguments)
Arguments.
Expression: a text string
Arguments: a vector
interval(Lower endpoint, Upper endpoint)
Arguments.
Lower endpoint: a number
Upper endpoint: a number
isInteger(Value)
Arguments.
Value: a free value
isNumber(Value)
Arguments.
Value: a free value
isRational(Value)
Arguments.
Value: a free value
isReal(Value)
Arguments.
Value: a free value
len(Text)
Arguments.
Text: a text string
plot(Expression or vector[, Minimum x value][, Maximum x value][, Number of samples / Step size][, X variable][, Use step size][, Persistent])
Plots one or more expressions or vectors. Use a vector for the first argument to plot multiple series. Only the first argument is used for vector series. It is also possible to plot a matrix where each row is a pair of x and y values.
Example: plot([x2, 2x, [0,1,4,8,16]], 0, 4).
Arguments.
Expression or vector: a free value
Minimum x value: a real number (optional, default: 0)
Maximum x value: a real number (optional, default: 10)
Number of samples / Step size: a free value (optional, default: 1001)
X variable: an unknown variable/symbol (optional, default: x)
Use step size: a boolean (0 or 1) (optional, default: 0)
Persistent: a boolean (0 or 1) (optional, default: 0)
Requirement. "Minimum x value" < "Maximum x value"
processm(Function, Element variable, Matrix[, Row variable][, Column variable][, Matrix variable])
Arguments.
Function: a free value
Element variable: an unknown variable/symbol
Matrix: a matrix
Row variable: an unknown variable/symbol (optional)
Column variable: an unknown variable/symbol (optional)
Matrix variable: an unknown variable/symbol (optional)
process(Function, Element variable, Vector[, Index variable][, Vector variable])
Arguments.
Function: a free value
Element variable: an unknown variable/symbol
Vector: a vector
Index variable: an unknown variable/symbol (optional)
Vector variable: an unknown variable/symbol (optional)
register(Index)
Returns the value of a RPN stack register.
Arguments.
Index: an integer ≤ 1 and ≥ 4294967295
stack()
Returns the RPN stack as a vector.
replace(Expression, Original value, New value[, Precalculate expression])
Replaces a certain value in an expression with a new value. The expression is calculated before the replacement if the fourth argument is true.
Arguments.
Expression: a free value
Original value: a free value
New value: a free value
Precalculate expression: a boolean (0 or 1) (optional, default: 0)
representsInteger(Value)
Arguments.
Value: a free value
representsNumber(Value)
Arguments.
Value: a free value
representsRational(Value)
Arguments.
Value: a free value
representsReal(Value)
Arguments.
Value: a free value
save(Value, Name[, Category][, Title][, Precalculate expression])
Stores a value in a variable or saves an expression as a function.
A function is created if the name includes parentheses (e.g. "f()"). Optionally the function arguments can be specified in the name (e.g. "save(a+b,f(a,b))"). Otherwise the function arguments are expected to be referred to in the expression using \x, \y, \z ,\a , \b..., or x, y, z (e.g. "save(x+y,f())").
If a function was created, the processed function expression is returned as a text string, otherwise the value is returned.
The ":=" operator (e.g. var1:=10) is a shortcut for this function.
Arguments.
Value: a free value
Name: a text string
Category: a text string (optional, default: Temporary)
Title: a text string (optional)
Precalculate expression: a boolean (0 or 1) (optional, default: 0)
select(Vector, Condition[, Element variable][, Select first match])
Arguments.
Vector: a free value
Condition: a free value
Element variable: an unknown variable/symbol (optional, default: undefined)
Select first match: a boolean (0 or 1) (optional, default: 0)
nounit(Expression)
strip_units
Removes all units from an expression. The expression is calculated before the removal.
Arguments.
Expression: a free value
title(Name)
Arguments.
Name: a valid function, unit or variable name
uncertainty(Value, Uncertainty[, Uncertainty is relative])
Arguments.
Value: a number
Uncertainty: a number
Uncertainty is relative: a boolean (0 or 1) (optional, default: 1)
char(Value)
Arguments.
Value: an integer ≤ 32 and ≥ 1114111
code(Character[, Encoding][, Use vector])
Encodes a Unicode character or text string using the selected format. Supported encodings are UTF-8 (0), UTF-16 (1), and UTF-32 (2). If the third argument is true, each separate code unit (8, 16, or 32 bits depending on encoding) is placed in a vector.
Arguments.
Character: a text string
Encoding: a text string (optional, default: UTF-32)
Use vector: a boolean (0 or 1) (optional, default: 1)