Appendix A. Function List

Table of Contents

Algebra
Calculus
Combinatorics
Complex Numbers
Data Sets
Date & Time
Economics
Microeconomics
Exponents & Logarithms
Geometry
Circle
Cone
Cube
Cylinder
Parallelogram
Prism
Pyramid
Rectangle
Sphere
Square
Trapezoid
Triangle
Logical
Matrices & Vectors
Miscellaneous
Number Theory
Arithmetics
Integers
Number Bases
Polynomials
Rounding
Special Functions
Statistics
Descriptive Statistics
Distribution
Means
Moments
Regression
Statistical Tests
Step Functions
Trigonometry
Utilities

Algebra

Find Linear Function

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 of a sequence

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(x^2, 1, 5) = 1^2 * 2^2 * 3^2 * 4^2 * 5^2 = 1440

Arguments. 

  • Factor expression: a free value

  • Lower limit (i): an integer

  • Upper limit (n): an integer

  • Index variable: an unknown variable/symbol (optional, default: x)

Requirement.  "Upper limit (n)" >= "Lower limit (i)"

Solve equation

solve(Equation[, With respect to])

Arguments. 

  • Equation: a free value

  • With respect to: an unknown variable/symbol (optional, default: x)

Solve for multiple variables

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")

Solve for two variables

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)

Summation

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(x^2, 1, 5) = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 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: x)

Requirement.  "Upper limit (n)" >= "Lower limit (i)"

Calculus

Differentiate

diff(Function[, With respect to][, Order])

Arguments. 

  • Function: a free value

  • With respect to: an unknown variable/symbol (optional, default: x)

  • Order: an integer >= 1 and <= 2147483647 (optional, default: 1)

Extreme Values

extremum(Function[, With respect to])

Arguments. 

  • Function: a free value

  • With respect to: an unknown variable/symbol (optional, default: x)

Integrate

integrate(Function[, Variable of integration][, Lower limit][, Upper limit])

Arguments. 

  • Function: a free value

  • Variable of integration: an unknown variable/symbol (optional, default: x)

  • Lower limit: a free value (optional, default: undefined)

  • Upper limit: a free value (optional, default: undefined)

Combinatorics

Binomial Coefficient

binomial(Exponent, Index)

Arguments. 

  • Exponent: an integer >= 1

  • Index: an integer >= 0 and <= 18446744073709551615

Requirement.  "Exponent" >= "Index"

Combinations

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 is 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: a free value

  • Size: a free value

Derangements

derangements(Number of elements)

Returns the number of possible rearrangements of an ordered list, of a certain size, where none of the objects are on their original position. If the original list is [1, 2, 3], the possible derangements is [2, 3, 1] and [3, 1, 2], and thus the number of derangements is 2.

Arguments. 

  • Number of elements: an integer >= 1

Double Factorial

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

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

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) = (3^3) * (2^2) * (1^1) = 108

Arguments. 

  • Value: an integer >= 1

Multifactorial

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

Permutations (Variations)

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 is 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: a free value

  • Size: a free value

Superfactorial

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

Complex Numbers

Complex Conjugate

conj(Complex number)

Arguments. 

  • Complex number: a number

Imaginary Part

im(Complex number)

Arguments. 

  • Complex number: a number

Principal Argument

arg(Complex number)

Arguments. 

  • Complex number: a number

Real Part

re(Complex number)

Arguments. 

  • Complex number: a number

Data Sets

Elements

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.

Arguments. 

  • Element: an object from "Elements" (use symbol, number, or name)

  • Property: name of a data property (symbol, number, name, class, weight, 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

  • Weight: weight, mass

  • Boiling Point: boiling

  • Melting Point: melting

  • Density: density

    Density at 295K

Planets

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 (planet)" (http://www.wikipedia.org/wiki/Jupiter_(planet)),

"Mars (planet)" (http://www.wikipedia.org/wiki/Mars_(planet)),

"Mercury (planet)" (http://www.wikipedia.org/wiki/Mercury_(planet)),

"Neptune (planet)" (http://www.wikipedia.org/wiki/Neptune_(planet)),

"Pluto (planet)" (http://www.wikipedia.org/wiki/Pluto_(planet)),

"Saturn (planet)" (http://www.wikipedia.org/wiki/Saturn_(planet)),

"Uranus (planet)" (http://www.wikipedia.org/wiki/Uranus_(planet)), and

"Venus (planet)" (http://en.wikipedia.org/wiki/Venus_(planet)),

licensed under the GNU Free Documentation License (http://www.gnu.org/copyleft/fdl.html)

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: inclination

  • Number of Satellites: satellites

  • Mass: mass

  • Mean Density: density

  • Surface Area: area

  • Equatorial Gravity: gravity

  • Mean Surface Temperature: temperature

Date & Time

Add Days

addDays(Date, Days)

Arguments. 

  • Date: a date (Y-M-D)

  • Days: an integer >= -9223372036854775808 and <= 9223372036854775807

Add Months

addMonths(Date, Months)

Arguments. 

  • Date: a date (Y-M-D)

  • Months: an integer >= -9223372036854775808 and <= 9223372036854775807

Add Time

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/d)"

Add Years

addYears(Date, Years)

Arguments. 

  • Date: a date (Y-M-D)

  • Years: an integer >= -9223372036854775808 and <= 9223372036854775807

Current Time

time()

Date to Unix Timestamp

timestamp([Date])

Arguments. 

  • Date: a date (Y-M-D) (optional, default: now)

Day of Month

day([Date])

Arguments. 

  • Date: a date (Y-M-D) (optional, default: today)

Day of Week

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)

Day of Year

yearday([Date])

Arguments. 

  • Date: a date (Y-M-D) (optional, default: today)

Days between two dates

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)

Local Date Format

localdate([Date])

Arguments. 

  • Date: a date (Y-M-D) (optional, default: today)

Month

month([Date])

Arguments. 

  • Date: a date (Y-M-D) (optional, default: today)

Standard Date Format

isodate([Date])

Arguments. 

  • Date: a date (Y-M-D) (optional, default: today)

Unix Timestamp to Date

stamptodate(Timestamp)

Arguments. 

  • Timestamp: an integer >= -9223372036854775808 and <= 9223372036854775807

Week of Year

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

year([Date])

Arguments. 

  • Date: a date (Y-M-D) (optional, default: today)

Years between two dates

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)

Economics

Accrued interest of security paying at maturity

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)

Accrued interest of security with periodic interest payments

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)

Amount received at maturity for a security bond

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

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

Discount rate for a security

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)

Dollar Decimal

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

Dollar Fraction

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

Effective Interest Rate

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

Future 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)

Interest paid on a given period of an investment (ISPMT)

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

Interest rate for a fully invested security

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 Bond

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 Interest Rate

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

Number of coupons to be paid

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)

Payment for a loan

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 year) 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)

Payment of an annuity going towards interest (IPMT)

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)

Payment of an annuity going towards principal (PPMT)

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)

Periods for investment to attain desired value

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

Periods of an investment

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)

Present Value

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)

Price per $100 face value of a discounted security

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)

Price per $100 face value of a security

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)

Return on continuously compounded interest

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

Straight Line Depreciation

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

Sum-of-Years Digits Depreciation

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

Treasury Bill Equivalent

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

Treasury Bill Price

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

Treasury Bill Yield

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

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

Microeconomics

Elasticity

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)

Exponents & Logarithms

10 raised the to power X

exp10(Exponent)

Arguments. 

  • Exponent: a free value

2 raised the to power X

exp2(Exponent)

Arguments. 

  • Exponent: a free value

Base-10 Logarithm

log10(Value)

Returns the base n logarithm.

Arguments. 

  • Value: a number >= 0

Base-2 Logarithm

log2(Value)

Returns the base n logarithm.

Arguments. 

  • Value: a number >= 0

Base-N Logarithm

log(Value[, Base])

Arguments. 

  • Value: a number that is nonzero

  • Base: a number that is nonzero (optional, default: e)

Complex Exponential (Cis)

cis(Exponent)

Arguments. 

  • Exponent: a free value

Cube Root

cbrt(Value)

Arguments. 

  • Value: a free value

Exponential (e^x)

exp(Exponent)

Arguments. 

  • Exponent: a free value

Lambert W Function (Omega Function, Product Log)

lambertw(Value)

productlog

Returns the inverse function for mx*e^x as ln() does for e^x.

Arguments. 

  • Value: a real number

Natural Logarithm

ln(Value)

Arguments. 

  • Value: a number that is nonzero

Nth root

root(Base, Exponent)

Arguments. 

  • Base: a free value

  • Exponent: a free value

Square

sq(Value)

Arguments. 

  • Value: a free value

Square Root

sqrt(Value)

Arguments. 

  • Value: a free value

Square root (x * pi)

sqrtpi(Non-negative value)

Returns the non-negative square root of x * pi

Arguments. 

  • Non-negative value: a number >= 0

X raised to the power Y

pow(Base, Exponent)

Arguments. 

  • Base: a free value

  • Exponent: a free value

Geometry

Circle

Circle Area

circle(Radius)

Calculates the area of a circle using the radius

Arguments. 

  • Radius: a free value

Circle Circumference

circumference(Radius)

Calculates the area of a circle using the radius

Arguments. 

  • Radius: a free value

Cone

Cone Volume

cone(Radius, Height)

Arguments. 

  • Radius: a free value

  • Height: a free value

Surface Area of Cone

cone_sa(Radius, Height)

Arguments. 

  • Radius: a free value

  • Height: a free value

Cube

Cube Volume

cube(Length of side)

Arguments. 

  • Length of side: a free value

Surface Area of Cube

cube_sa(Length of side)

Arguments. 

  • Length of side: a free value

Cylinder

Cylinder Volume

cylinder(Radius, Height)

Arguments. 

  • Radius: a free value

  • Height: a free value

Surface Area of Cylinder

cylinder_sa(Radius, Height)

Arguments. 

  • Radius: a free value

  • Height: a free value

Parallelogram

Parallelogram Area

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

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

Prism

Surface Area of Rectangular Prism

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

Volume of Rectangular Prism

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

Volume of Triangular Prism

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

Pyramid

Height of Regular Tetrahedron

tetrahedron_height(Length of side)

Arguments. 

  • Length of side: a free value

Height of Square Pyramid

sqpyramid_height(Length of side)

Arguments. 

  • Length of side: a free value

Pyramid Volume

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

Surface Area of Regular Tetrahedron

tetrahedron_sa(Length of side)

Arguments. 

  • Length of side: a free value

Surface Area of Square Pyramid

sqpyramid_sa(Length of side)

Arguments. 

  • Length of side: a free value

Volume of Regular Tetrahedron

tetrahedron(Length of side)

Arguments. 

  • Length of side: a free value

Volume of Square Pyramid

sqpyramid(Length of side)

Arguments. 

  • Length of side: a free value

Rectangle

Rectangle Area

rect(Length, Width)

Arguments. 

  • Length: a free value

  • Width: a free value

Rectangle Perimeter

rect_perimeter(Length, Width)

Arguments. 

  • Length: a free value

  • Width: a free value

Sphere

Sphere Volume

sphere(Radius)

Arguments. 

  • Radius: a free value

Surface Area of Sphere

sphere_sa(Radius)

Arguments. 

  • Radius: a free value

Square

Square Area

square(Length of side)

Arguments. 

  • Length of side: a free value

Square Perimeter

square_perimeter(Length of side)

Arguments. 

  • Length of side: a free value

Trapezoid

Trapezoid Area

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

Triangle

Hypotenuse

hypot(Side A, Side B)

Arguments. 

  • Side A: a free value

  • Side B: a free value

Triangle Area

triangle(Base, Height)

Arguments. 

  • Base: a free value

  • Height: a free value

Triangle Perimeter

triangle_perimeter(Side A, Side B)

Arguments. 

  • Side A: a free value

  • Side B: a free value

Logical

Bitwise Exclusive OR

bitxor(Value 1, Value 2)

Arguments. 

  • Value 1: an integer or a vector

  • Value 2: an integer or a vector

Bitwise Shift

shift(Number, Bits)

Arguments. 

  • Number: an integer

  • Bits: an integer >= -9223372036854775808 and <= 9223372036854775807

For...Do

for(Initial value of counter, Counter variable, For condition, Counter update function, Initial value, Do function, Value variable)

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...Then...Else

if(Condition, Expression if condition is met, Expression if condition is NOT met)

Tests a condition and returns a value depending on the result.

Arguments. 

  • Condition: a real number

  • Expression if condition is met: a free value

  • Expression if condition is NOT met: a free value

Logical Exclusive OR

xor(Value 1, Value 2)

Arguments. 

  • Value 1: a free value

  • Value 2: a free value

Matrices & Vectors

Adjugate (Adjoint)

adj(Matrix)

Calculates the adjugate or adjoint of a matrix.

Arguments. 

  • Matrix: a square matrix

Cofactor

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

columns(Matrix)

Returns the number of columns in a matrix.

Arguments. 

  • Matrix: a matrix

Construct Matrix

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

Construct Vector

vector([argument 1], ...)

Returns a vector with listed elements.

Arguments. 

  • 1: a free value (optional)

Convert Matrix to Vector

matrix2vector(Matrix)

Puts each element of a matrix in vertical order in a vector.

Arguments. 

  • Matrix: a matrix

Cross Product

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"

Determinant

det(Matrix)

Calculates the determinant of a matrix.

Arguments. 

  • Matrix: a square matrix

Dimension

dimension(Vector)

Returns the number of elements in a vector.

Arguments. 

  • Vector: a vector

Element

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)

Elements

elements(Matrix or vector)

Returns the number of elements in a matrix or vector.

Arguments. 

  • Matrix or vector: a vector

Export To CSV File

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: ,)

Extract Column as Vector

column(Matrix, Column)

Returns a column in a matrix as a vector.

Arguments. 

  • Matrix: a matrix

  • Column: an integer >= 1 and <= 4294967295

Extract row as vector

row(Matrix, Row)

Returns a row in a matrix as a vector.

Arguments. 

  • Matrix: a matrix

  • Row: an integer >= 1 and <= 4294967295

Generate Vector

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: x)

  • Use step size: a boolean (0 or 1) (optional, default: 0)

Identity

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 CSV File

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: ,)

Matrix Area

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

Matrix Inverse

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

Merge Vectors

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 (length)

norm(Vector)

Calculates the norm/length of a vector.

Arguments. 

  • Vector: a vector

Permanent

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

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)

Rows

rows(Matrix)

Returns the number of rows in a matrix.

Arguments. 

  • Matrix: a matrix

Sort

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

transpose(Matrix)

Returns the transpose of a matrix.

Arguments. 

  • Matrix: a matrix

Vector Limits

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

Miscellaneous

Body Mass Index (BMI)

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

Roman Number

roman(Roman number)

Returns the value of a roman number.

Arguments. 

  • Roman number: a text string

Number Theory

Absolute Value

abs(Value)

Arguments. 

  • Value: a number

Fibonacci Number

fibonacci(Index (n))

Returns the n-th term of the Fibonacci sequence.

Arguments. 

  • Index (n): an integer >= 0

Greatest Common Divisor

gcd(1st value, 2nd value)

Arguments. 

  • 1st value: a free value that is rational (polynomial)

  • 2nd value: a free value that is rational (polynomial)

Least Common Multiple

lcm(1st value, 2nd value)

Arguments. 

  • 1st value: a free value that is rational (polynomial)

  • 2nd value: a free value that is rational (polynomial)

Arithmetics

Add

add(Terms)

Arguments. 

  • Terms: a vector

Denominator

denominator(Number)

Arguments. 

  • Number: a rational number

Divide

divide(Numerator, Denominator)

Arguments. 

  • Numerator: a free value

  • Denominator: a free value

Modulus

mod(Numerator, Denominator)

Arguments. 

  • Numerator: a real number

  • Denominator: a real number that is nonzero

Multiply

multiply(Factors)

Arguments. 

  • Factors: a vector

Negate

neg(Value)

Arguments. 

  • Value: a free value

Numerator

numerator(Number)

Arguments. 

  • Number: a rational number

Raise

raise(Base, Exponent)

Arguments. 

  • Base: a free value

  • Exponent: a free value

Reciprocal

inv(Value)

Arguments. 

  • Value: a free value

Remainder

rem(Numerator, Denominator)

Arguments. 

  • Numerator: a real number

  • Denominator: a real number that is nonzero

Signum

sgn(Number)

Arguments. 

  • Number: a number

Subtract

subtract(Terms)

Arguments. 

  • Terms: a vector

Integers

Even

even(Number)

Arguments. 

  • Number: an integer

Odd

odd(Number)

Arguments. 

  • Number: an integer

Number Bases

Binary

bin(Binary number)

Returns an integer from a binary number

Arguments. 

  • Binary number: a text string

Hexadecimal

hex(Hexadecimal number)

Returns a value from a hexadecimal number

Arguments. 

  • Hexadecimal number: a text string

Number Base

base(Number, Base)

Returns an integer from a number of specified base between 2 and 36

Arguments. 

  • Number: a text string

  • Base: an integer >= 2 and <= 36

Octal

oct(Octal number)

Returns an integer from an octal number

Arguments. 

  • Octal number: a text string

Polynomials

Coefficient

coeff(Polynomial, Number[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Number: an integer >= 0

  • Variable: an unknown variable/symbol (optional, default: x)

Content Part

pcontent(Polynomial[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Variable: an unknown variable/symbol (optional, default: x)

Leading Coefficient

lcoeff(Polynomial[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Variable: an unknown variable/symbol (optional, default: x)

Lowest Degree (Valuation)

ldegree(Polynomial[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Variable: an unknown variable/symbol (optional, default: x)

Polynomial Degree

degree(Polynomial[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Variable: an unknown variable/symbol (optional, default: x)

Primitive Part

primpart(Polynomial[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Variable: an unknown variable/symbol (optional, default: x)

Trailing Coefficient

tcoeff(Polynomial[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Variable: an unknown variable/symbol (optional, default: x)

Unit Part

punit(Polynomial[, Variable])

Arguments. 

  • Polynomial: a free value that is rational (polynomial)

  • Variable: an unknown variable/symbol (optional, default: x)

Rounding

Extract Fractional Part

frac(Value)

Arguments. 

  • Value: a real number

Extract Integer Part

int(Value)

Arguments. 

  • Value: a real number

Round

round(Value)

Arguments. 

  • Value: a real number

Round Downwards

floor(Value)

Arguments. 

  • Value: a real number

Round Towards Zero

trunc(Value)

Arguments. 

  • Value: a real number

Round Upwards

ceil(Value)

Arguments. 

  • Value: a real number

Special Functions

Airy Function

airy(argument 1)

Arguments. 

  • 1: a number >= -500 and <= 500

Bessel Function of the First Kind

besselj(Order, Argument)

Arguments. 

  • Order: an integer >= -9223372036854775808 and <= 9223372036854775807

  • Argument: a real number

Bessel Function of the Second Kind

bessely(Order, Argument)

Arguments. 

  • Order: an integer >= -9223372036854775808 and <= 9223372036854775807

  • Argument: a real number

Beta Function

beta(argument 1, argument 2)

Arguments. 

  • 1: a number

  • 2: a number

Complementary Error Function

erfc(argument 1)

Arguments. 

  • 1: a real number

Digamma Function

digamma(argument 1)

psi

Arguments. 

  • 1: a real number

Error Function

erf(argument 1)

Arguments. 

  • 1: a real number

Gamma Function

gamma(argument 1)

Arguments. 

  • 1: a real number

Kronecker Delta

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)

Riemann Zeta

zeta(Integral point)

Arguments. 

  • Integral point: an integer >= 1 and <= 9223372036854775807

Statistics

Random Number

rand([Ceil])

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)

Random Number Between Limits

randbetween(Bottom, Top)

Returns an integer between (including) bottom and top.

Arguments. 

  • Bottom: an integer

  • Top: an integer

Requirement.  "Bottom"<="Top"

Descriptive Statistics

Decile

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)

Interquartile Range

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

max(Vector)

Returns the highest value.

Arguments. 

  • Vector: a vector

Median

median(Data)

Arguments. 

  • Data: a vector

Min

min(Vector)

Returns the lowest value.

Arguments. 

  • Vector: a vector

Mode

mode(Vector)

Returns the most frequently occurring value.

Arguments. 

  • Vector: a vector

Number of Samples

number(Data)

Returns the number of samples.

Arguments. 

  • Data: a vector

Percentile

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

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

range(Data)

Calculates the difference between the min and max value.

Arguments. 

  • Data: a vector

Sum (total)

total(Data)

Arguments. 

  • Data: a vector

Distribution

Logistic Distribution

logistic(X, Scale)

Returns the probability density p(x) at x for a logistic distribution with scale parameter. (from Gnumeric)

Arguments. 

  • X: a free value

  • Scale: a number >= 0

Pareto Distribution

pareto(X, Exponent, Scale)

Returns the probability density p(x) at x for a Pareto distribution with exponent and scale. (from Gnumeric)

Arguments. 

  • X: a free value

  • Exponent: a number >= 0

  • Scale: a number >= 0

Rayleigh Distribution

rayleigh(X, Sigma)

Returns the probability density p(x) at x for a Rayleigh distribution with scale parameter sigma. (from Gnumeric)

Arguments. 

  • X: a free value

  • Sigma: a number >= 0

Rayleigh Tail Distribution

rayleightail(X, Lower limit, Sigma)

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

  • Sigma: a number >= 0

Means

Geometric Mean

geomean(Data)

Arguments. 

  • Data: a vector

Harmonic Mean

harmmean(Data)

Arguments. 

  • Data: a vector

Mean

mean(Data)

average

Arguments. 

  • Data: a vector

Quadratic Mean (RMS)

rms(Data)

Arguments. 

  • Data: a vector

Trimmed Mean

trimmean(Data, Trimmed percentage (at each end))

Arguments. 

  • Data: a vector

  • Trimmed percentage (at each end): a free value

Weighted Mean

weighmean(Data, Weights)

Arguments. 

  • Data: a vector

  • Weights: a vector

Winsorized Mean

winsormean(Data, Winsorized percentage (at each end))

Arguments. 

  • Data: a vector

  • Winsorized percentage (at each end): a free value

Moments

Covariance

cov(Data 1, Data 2)

covar

Arguments. 

  • Data 1: a vector

  • Data 2: a vector

Mean Deviation

meandev(Data)

Arguments. 

  • Data: a vector

Pooled Variance

poolvar(Data 1, Data 2)

Arguments. 

  • Data 1: a vector

  • Data 2: a vector

Standard Deviation (entire population)

stdevp(Data)

Arguments. 

  • Data: a vector

Standard Deviation (random sampling)

stdev(Data)

Arguments. 

  • Data: a vector

Standard Error

stderr(Data)

Arguments. 

  • Data: a vector

Variance (entire population)

varp(Data)

Arguments. 

  • Data: a vector

Variance (random sampling)

var(Data)

Arguments. 

  • Data: a vector

Regression

Pearson's Correlation Coefficient

pearson(Data 1, Data 2)

correl

Arguments. 

  • Data 1: a vector

  • Data 2: a vector

Requirement.  dimension("Data 1")=dimension("Data 2")

Spearman's Rho

spearman(Data 1, Data 2)

Arguments. 

  • Data 1: a vector

  • Data 2: a vector

Requirement.  dimension("Data 1")=dimension("Data 2")

Statistical Correlation

cor(Data 1, Data 2)

Arguments. 

  • Data 1: a vector

  • Data 2: a vector

Statistical Tests

Paired T-Test

pttest(Data 1, Data 2)

Arguments. 

  • Data 1: a vector

  • Data 2: a vector

Unpaired T-Test

ttest(Data 1, Data 2)

Arguments. 

  • Data 1: a vector

  • Data 2: a vector

Step Functions

Heaviside Step Function

heaviside(Value)

Discontinuous function also known as "unit step function". Returns 0 if x < 0, 1 if x > 0, and 1/2 if x = 0.

Arguments. 

  • Value: a real number

Logit Transformation

logit(Value)

Arguments. 

  • Value: a number

Ramp Function

ramp(Value)

Arguments. 

  • Value: a real number

Rectangular Function

rectangular(Value)

Arguments. 

  • Value: a real number

Sigmoid Function

sigmoid(Value)

Arguments. 

  • Value: a number

Triangular Function

triangular(Value)

Arguments. 

  • Value: a real number

Trigonometry

Cosecant

csc(Angle)

Arguments. 

  • Angle: an angle or a number (using the default angle unit)

Cosine

cos(Angle)

Arguments. 

  • Angle: an angle or a number (using the default angle unit)

Cotangent

cot(Angle)

Arguments. 

  • Angle: an angle or a number (using the default angle unit)

Four-quadrant Inverse Tangent

atan2(Y, X)

Computes the principal value of the argument function applied to the complex number x+iy.

Arguments. 

  • Y: a real number

  • X: a real number

Hyperbolic Cosecant

csch(argument 1)

Arguments. 

  • 1: a free value

Hyperbolic Cosine

cosh(argument 1)

Arguments. 

  • 1: a number

Hyperbolic Cotangent

coth(argument 1)

Arguments. 

  • 1: a free value

Hyperbolic Secant

sech(argument 1)

Arguments. 

  • 1: a free value

Hyperbolic Sine

sinh(argument 1)

Arguments. 

  • 1: a number

Hyperbolic Tangent

tanh(argument 1)

Arguments. 

  • 1: a number

Inverse Cosecant

acsc(argument 1)

Arguments. 

  • 1: a free value

Inverse Cosine

acos(argument 1)

Arguments. 

  • 1: a number

Inverse Cotangent

acot(argument 1)

Arguments. 

  • 1: a free value

Inverse Hyperbolic Cosecant

acsch(argument 1)

Arguments. 

  • 1: a free value

Inverse Hyperbolic Cosine

acosh(argument 1)

Arguments. 

  • 1: a number

Inverse Hyperbolic Cotangent

acoth(argument 1)

Arguments. 

  • 1: a free value

Inverse Hyperbolic Secant

asech(argument 1)

Arguments. 

  • 1: a free value

Inverse Hyperbolic Sine

asinh(argument 1)

Arguments. 

  • 1: a number

Inverse Hyperbolic Tangent

atanh(argument 1)

Arguments. 

  • 1: a number

Inverse Secant

asec(argument 1)

Arguments. 

  • 1: a free value

Inverse Sine

asin(argument 1)

Arguments. 

  • 1: a number

Inverse Tangent

atan(argument 1)

Arguments. 

  • 1: a number

Radians to Default Angle Unit

radtodef(Radians)

Arguments. 

  • Radians: a free value

Secant

sec(Angle)

Arguments. 

  • Angle: an angle or a number (using the default angle unit)

Sine

sin(Angle)

Arguments. 

  • Angle: an angle or a number (using the default angle unit)

Tangent

tan(Angle)

Arguments. 

  • Angle: an angle or a number (using the default angle unit)

Utilities

ASCII Char

char(Value)

Arguments. 

  • Value: an integer >= 32 and <= 127

ASCII Value

code(Character)

Arguments. 

  • Character: a text string that fulfills the condition: "len(Character) = 1"

Concatenate Strings

concatenate(Text string 1[, Text string 2], ...)

Arguments. 

  • Text string 1: a text string

  • Text string 2: a text string (optional)

Custom Sum of Elements

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, default: "")

  • Vector variable: an unknown variable/symbol (optional, default: "")

Display Error

error(Message)

Arguments. 

  • Message: a text string

Display Message

message(Message)

Arguments. 

  • Message: a text string

Display Warning

warning(Message)

Arguments. 

  • Message: a text string

Function

function(Expression, Arguments)

Arguments. 

  • Expression: a text string

  • Arguments: a vector

Is Integer

isInteger(Value)

Arguments. 

  • Value: a free value

Is Number

isNumber(Value)

Arguments. 

  • Value: a free value

Is Rational

isRational(Value)

Arguments. 

  • Value: a free value

Is Real

isReal(Value)

Arguments. 

  • Value: a free value

Length of string

len(Text)

Arguments. 

  • Text: a text string

Plot Functions and Vectors

plot(Expression or vector[, Minimum x value][, Maximum x value][, Number of samples / Step size][, X variable][, Use step size])

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([x^2, 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: 100)

  • X variable: an unknown variable/symbol (optional, default: x)

  • Use step size: a boolean (0 or 1) (optional, default: 0)

Requirement.  "Minimum x value" < "Maximum x value"

Process Matrix Elements

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, default: "")

  • Column variable: an unknown variable/symbol (optional, default: "")

  • Matrix variable: an unknown variable/symbol (optional, default: "")

Process Vector Elements

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, default: "")

  • Vector variable: an unknown variable/symbol (optional, default: "")

RPN Stack Register

register(Index)

Returns the value of a RPN stack register.

Arguments. 

  • Index: an integer >= 1 and <= 4294967295

RPN Stack Vector

stack()

Returns the RPN stack as a vector.

Replace

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)

Represents Integer

representsInteger(Value)

Arguments. 

  • Value: a free value

Represents Number

representsNumber(Value)

Arguments. 

  • Value: a free value

Represents Rational

representsRational(Value)

Arguments. 

  • Value: a free value

Represents Real

representsReal(Value)

Arguments. 

  • Value: a free value

Save as Variable

save(Value, Name[, Category][, Title])

Arguments. 

  • Value: a free value

  • Name: a text string

  • Category: a text string (optional, default: Temporary)

  • Title: a text string (optional)

Select Vector Elements

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: x)

  • Select first match: a boolean (0 or 1) (optional, default: 0)

Strip Units

nounit(Expression)

strip_units

Removes all units from an expression. The expression is calculated before the removal.

Arguments. 

  • Expression: a free value

Title

title(Name)

Arguments. 

  • Name: a valid function, unit or variable name