Spacetime Functions.Pdf

Basic functions
These are the basic calculator functions :
• • • •

Plus or Add : + Minus or Subtract : Multiply : * Divide : /

Examples

Mod(m,n)
Mod(m,n) calculates m-n*floor(m/n)
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The sign of Mod(m,n) always equals the sign of n

Sqrt(z)
sqrt(z) takes the square root of a given number. Number can be either real or complex. There are different ways to enter this function :
•• •

directly as : sqrt() keyboard shortcut : CTRL + SHIFT + R through dedicated key : √

Power (^)
The power function ^ raises a given number to the given power.

Examples

NRoot(z,n)
nRoot(z, n, [mode]) finds the nth root of a given value.
• • • •

n = root z = input value, either real or complex mode = 0 : returns ONLY real roots (except for complex z) mode = 1 : returns ALLroots, real and complex

All roots are returned in a list

Examples

Factorial(n) or n!
Factorial(n), also written as n!, returns the number of ways n elements can be ordered.
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n! = 1 * 2 * 3 * ..... (n-1) * n

NCr(n,r)
nCr(n,r) returns the number of unordered subsets of r elements out of a set of n elements
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nCr(n,r) = n! / ((n-r)! * r!)

NPr(n,r)
nPr(n,r) returns the numberof permutations of a subset of r elements from a set of n elements
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nPr(n,r) = n! / (n-r)!

Binomial(n,r)
Binomial(n,r) finds the binomial coefficient. Binomial(n,r) can be used with symbolic and numerical values. This function is equivalent as the function nCr(n,r) which can only be used with numerical values.

Examples

Multinomial(nList)
Multinomial([nList]) finds the Multinomialcoefficient of nList.

Examples

Pochhammer(n,k)
Pochhammer(n,k) finds the value of n*(n+1)*(n+2)*..*(n+k-1)

Examples

Floor(z)
Floor(z) returns the greatest integer of the given value. If z is a complex number, then floor works on both the real and the imaginary part.

Examples

Ceil(z)
Ceil(z) returns the smallest integer of the given value. If z is a complex number, then ceilworks on both the real and the imaginary part.

Examples

Sign(z)
Sign(z) returns the sign of a given value. If z is a complex number, then sign returns z/abs(z).

Examples

FPart(x)
fPart(x) returns the fractional part of x.

Examples

Round(number, digits)
Round(number, digits) rounds a given a given number to the requested number of digits.

Examples

z can be a real orcomplex value. In case of a complex value, both real & imaginary part will be rounded. Please note that the maximum displayed number of digits can never exceed the Options setting : Precision

Re(z)
Re(z) returns the real part of a complex number.

Im(z)
Im(z) returns the imaginary part of a complex number.

Abs(z)
Abs(z) returns the complex modulus (or magnitude) of a complex number.Arg(z)
Arg(z) returns the argument (or phase) of a complex number.
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Arg(z) returns the value in radians when Options - Angles - Radians is set, in degrees otherwise.

Example

Conj(z)
Conj(z) returns the complex conjugate of a complex number.

Exp(z) or e^(z)
exp(z) or e^z raises e (base of natural logarithm) to the power z. This function can be entered as:
• • •

directly : exp()keyboard shortcut : CTRL + SHIFT + e followed by ^ decdicated key e followed by ^

Examples

Ln(z)
ln(z) takes the natural logarithm (base: e) of the given number z. z can be either real or complex.

Examples

Log(z)
log(z) takes the common or Briggs logarithm (base: 10) of the given number z. z can be either real or complex.

[edit] Examples

Log(n,z)
log(n,z) takes the logarithmwith base: n of the given number z. z can be either real or complex.

Examples

TrigExpand(function)
TrigExpand(function) splits up sums and integer multiples that appear in arguments of trigonometric functions and expands products of trigonometric functions into sums of powers.

Examples

TrigReduce(function)
TrigReduce(function) rewrites products and powers of trigonometric...