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.
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[, With respect to])
Arguments.
Equation: a free value
With respect to: an unknown variable/symbol (optional, default: x)
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)
sum(Term expression, Lower limit (i), Upper limit (n)[, Index variable])
Σ
Corresponds to the sum symbol. Adds terms for each x ranging from the lower to the upper limit.
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)"
beta(argument 1, argument 2)
Arguments.
1: an integer
2: an integer
gamma(argument 1)
Arguments.
1: a number
im(Complex number)
Arguments.
Complex number: a number
re(Complex number)
Arguments.
Complex number: a number
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 (optional, default: 1)
extremum(Function[, With respect to])
Arguments.
Function: a free value
With respect to: an unknown variable/symbol (optional, default: x)
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)
binomial(Exponent, Index)
Arguments.
Exponent: an integer >= 1
Index: an integer >= 0
Requirement. "Exponent">="Index"
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(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
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.
ex. factorial2(5) = 5!! = 5 * 3 * 1 = 15
Arguments.
Value: an integer >= -1
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.
ex. factorial(5) = 5! = 5 * 4 * 3 * 2 * 1 = 120
Arguments.
Value: an integer
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).
ex. hyperfactorial(3) = (3^3) * (2^2) * (1^1) = 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.
ex. multifactorial(18, 4) = 18!!!! = 18 * 14 * 10 * 6 * 2 = 30 240
Arguments.
Value: an integer >= 0
Factorial: an integer >= 1
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(Value)
Calculates the superfactorial of an integer. Multiplies the factorial of the argument with the factorial of every lesser positive integer (1! * 2! ... n!).
ex. superfactorial(5) = 5! * 4! * 3! * 2! * 1! = 34 560
Arguments.
Value: an integer >= 0
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
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
addDays(Date, Days)
Arguments.
Date: a date
Days: an integer
addMonths(Date, Months)
Arguments.
Date: a date
Months: an integer
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
Time: a free value that fulfills the condition: "isNumber(Time/day)"
addYears(Date, Years)
Arguments.
Date: a date
Years: an integer
time()
timestamp([Date])
Arguments.
Date: a date (optional, default: now)
day([Date])
Arguments.
Date: a date (optional, default: today)
weekday([Date][, Week begins on Sunday])
Arguments.
Date: a date (optional, default: today)
Week begins on Sunday: a boolean (0 or 1) (optional, default: 0)
yearday([Date])
Arguments.
Date: a date (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
Second date: a date
Day counting basis: an integer >= 0 and <= 4 (optional, default: 1)
Financial function mode: a boolean (0 or 1) (optional, default: 0)
localdate([Date])
Arguments.
Date: a date (optional, default: today)
month([Date])
Arguments.
Date: a date (optional, default: today)
isodate([Date])
Arguments.
Date: a date (optional, default: today)
stamptodate(Timestamp)
Arguments.
Timestamp: an integer
week([Date][, Week begins on Sunday])
Arguments.
Date: a date (optional, default: today)
Week begins on Sunday: a boolean (0 or 1) (optional, default: 0)
year([Date])
Arguments.
Date: a date (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
Second date: a date
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
Settlement date: a date
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
First interest: a date
Settlement date: a date
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
Maturity date: a date
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
Maturity date: a date
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
Maturity date: a date
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
Maturity date: a date
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 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 result by 12).
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
Maturity date: a date
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
Maturity date: a date
Issue date: a date
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
Maturity date: a date
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
Maturity date: a date
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
Maturity date: a date
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...
Ex. 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 free value
cbrt(Value)
∛
Arguments.
Value: a free value
exp(Exponent)
Arguments.
Exponent: a free value
lambertw(Value)
productlog
Returns the inverse function for mx*e^x as ln() does for e^x.
Arguments.
Value: a real number
ln(Value)
Arguments.
Value: a number that is nonzero
root(Base, Exponent)
Arguments.
Base: a free value
Exponent: a free value
sq(Value)
Arguments.
Value: a free value
sqrt(Value)
√
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
pow(Base, Exponent)
Arguments.
Base: a free value
Exponent: a free value
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
bitxor(Value 1, Value 2)
Arguments.
Value 1: an integer or a vector
Value 2: an integer or a vector
shift(Number, Bits)
Arguments.
Number: an integer
Bits: an integer
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(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
xor(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
Column: an integer >= 1
columns(Matrix)
Returns the number of columns in a matrix.
Arguments.
Matrix: a 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
Columns: an integer >= 1
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
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
Column: an integer (optional, default: 0)
elements(Matrix or vector)
Returns the number of elements in a matrix or vector.
Arguments.
Matrix or vector: a vector
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
row(Matrix, Row)
Returns a row in a matrix as a vector.
Arguments.
Matrix: a matrix
Row: an integer >= 1
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(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 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 (optional, default: 1)
Separator: a text string (optional, default: ,)
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
Start column: an integer >= 1
End row: an integer >= 1
End column: an integer >= 1
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
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)
Calculates the norm/length of a vector.
Arguments.
Vector: a vector
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.
ex. rank([6, 1, 4]) = [3, 1, 2]
Arguments.
Vector: a vector
Ascending: a boolean (0 or 1) (optional, default: 1)
rows(Matrix)
Returns the number of rows in a matrix.
Arguments.
Matrix: a matrix
sort(Vector[, Ascending])
Returns a sorted vector.
ex. 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
Upper limit: an integer
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).
Arguments.
Weight: a free value
Length: a free value
fibonacci(Index (n))
Returns the n-th term of the Fibonacci sequence.
Arguments.
Index (n): an integer >= 0
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)
zeta(Integral point)
Arguments.
Integral point: an integer >= 1 and <= 2.1474836E9
roman(Roman number)
Returns the value of a roman number.
Arguments.
Roman number: a text string
abs(Value)
Arguments.
Value: a number
gcd(1st value, 2nd value)
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)
add(Terms)
Arguments.
Terms: a vector
denominator(Number)
Arguments.
Number: a rational number
divide(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
multiply(Factors)
Arguments.
Factors: a vector
neg(Value)
Arguments.
Value: a free value
numerator(Number)
Arguments.
Number: a rational number
raise(Base, Exponent)
Arguments.
Base: a free value
Exponent: a free value
inv(Value)
Arguments.
Value: a free value
rem(Numerator, Denominator)
Arguments.
Numerator: a real number
Denominator: a real number that is nonzero
sgn(Number)
Arguments.
Number: a number
subtract(Terms)
Arguments.
Terms: a vector
bin(Binary number)
Returns an integer from a binary number
Arguments.
Binary number: a text string
hex(Hexadecimal number)
Returns a value from a hexadecimal number
Arguments.
Hexadecimal number: a text string
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
oct(Octal number)
Returns an integer from an octal number
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: x)
pcontent(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: x)
lcoeff(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: x)
ldegree(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: x)
degree(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: x)
primpart(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: x)
tcoeff(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: x)
punit(Polynomial[, Variable])
Arguments.
Polynomial: a free value that is rational (polynomial)
Variable: an unknown variable/symbol (optional, default: x)
frac(Value)
Arguments.
Value: a real number
int(Value)
Arguments.
Value: a real number
round(Value)
Arguments.
Value: a real number
floor(Value)
Arguments.
Value: a real number
trunc(Value)
Arguments.
Value: a real number
ceil(Value)
Arguments.
Value: a real 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)
randbetween(Bottom, Top)
Returns an integer between (including) bottom and top.
Arguments.
Bottom: an integer
Top: an integer
Requirement. "Bottom"<="Top"
decile(Data, Decile)
Arguments.
Data: a vector
Decile: a number >= 0 and <= 100
iqr(Data)
Calculates the difference between the first and third quartile.
Arguments.
Data: a vector
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 (%))
Arguments.
Vector: a vector
Percentile (%): a number > 0 and < 99
quartile(Data, Quartile)
Arguments.
Data: a vector
Quartile: an integer >= 1 and <= 3
range(Data)
Calculates the difference between the min and max value.
Arguments.
Data: a vector
total(Data)
Arguments.
Data: a vector
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(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(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
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
geomean(Data)
Arguments.
Data: a vector
harmmean(Data)
Arguments.
Data: a vector
mean(Data)
average
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
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
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(Value)
Arguments.
Value: a number
ramp(Value)
Arguments.
Value: a real number
rectangular(Value)
Arguments.
Value: a real number
sigmoid(Value)
Arguments.
Value: a number
triangular(Value)
Arguments.
Value: a real 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)
csch(argument 1)
Arguments.
1: a free value
cosh(argument 1)
Arguments.
1: a number
coth(argument 1)
Arguments.
1: a free value
sech(argument 1)
Arguments.
1: a free value
sinh(argument 1)
Arguments.
1: a number
tanh(argument 1)
Arguments.
1: a free value
acsc(argument 1)
Arguments.
1: a free value
acos(argument 1)
Arguments.
1: a number
acot(argument 1)
Arguments.
1: a free value
acsch(argument 1)
Arguments.
1: a free value
acosh(argument 1)
Arguments.
1: a number
acoth(argument 1)
Arguments.
1: a free value
asech(argument 1)
Arguments.
1: a free value
asinh(argument 1)
Arguments.
1: a number
atanh(argument 1)
Arguments.
1: a number
asec(argument 1)
Arguments.
1: a free value
asin(argument 1)
Arguments.
1: a number
atan(argument 1)
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)
char(Value)
Arguments.
Value: an integer >= 32 and <= 127
code(Character)
Arguments.
Character: a text string that fulfills the condition: "len(Character) = 1"
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
Last element: an integer
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: "")
error(Message)
Arguments.
Message: a text string
message(Message)
Arguments.
Message: a text string
warning(Message)
Arguments.
Message: a text string
function(Expression, Arguments)
Arguments.
Expression: a text string
Arguments: a vector
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
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(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: "")
register(Index)
Returns the value of a RPN stack register.
Arguments.
Index: an integer >= 1
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])
Arguments.
Value: a free value
Name: a text string
Category: a text string (optional, default: Temporary)
Title: a text string (optional)
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)
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