summer

This packages seeks to implement summation notation and product notation (Sigma and Pi notation) in R in a style similar to symbolic algebraic systems.

Installation:

if(!require(summer))

{ 

  install.packages("devtools")
  library(devtools)  
  devtools::install_github("mlanier/summer")
  library(summer)
 }else{
  library(summer)}

R Topics documented

1. summation_notation
2. product_notation
3. Riemann Zeta Function
4. Complex Exponentiation
5. Complex Zeta Function ##Sigma Notation

Usage

summation_notation(i=1,n=100,formula="x")

Arguments

i The start index of the summation.

n The end index of the summation.

formula A string in terms of x to be parsed by the summation_notation function.

Details

Summation notation will return errors messages if the formula does not contain any 'x' substrings. If the end user mixes 'x's and other variables the summation may run returning an incorrect value.

Examples

summation_notation(i=1,n=100,formula="x")

summation_notation(i=0,n=100,formula="x^4")

Pi notation

Usage

product_notation(i=1,n=100,formula="x")

Arguments

i The start index of the prodcut.

n The end index of the product.

formula A string in terms of x to be parsed by the product_notation function.

Details

Product notation will return errors messages if the formula does not contain any 'x' substrings. If the end user mixes 'x's and other variables the product may run returning an incorrect value.

Examples

product_notation(i=1,n=6,formula="x")

Riemann Zeta Function

Usage

Zeta(s=5)

Arguments

s The argument of the Zeta functions.

Details

This function calculates the Zeta function for a given argument s.

Examples

Calculate Apery's Constant.

Zeta(3)

Complex Exponentiation

Usage

c_Expo(a=2,b=7)

Arguments

a The base b The coefficent of the complex exponent ie bi.

Details

Consider the value a to the bi. b must be an integer. a to the bi is multivalued, this function gives only one value. To check equivelence its reccomended that the user pass the returned value to the Mod function.

Examples

Calculate 2 to the 7i.

c_Expo(2,7)

Complex Zeta Function

Usage

c_Zeta(a=3,b=3)

Arguments

a The real part of the argument a+bi. b The imaginary part of the argument a+bi.

Details

Experimental. This method uses a Monte Carlo calculation to evalulate the Euler integral. To check equivelence its recommended that the user pass the returned value to the Mod function.

Examples

Calculate the Zeta function evaluated at 2+2**i

c_Zeta(2,2)

Depends

stringr pander pracma

In the event that this package throws errors run the following in command:

if (!require('pander')) {
 devtools::install_github('Rapporter/pander')
}

if (!require('stringr')) {
install.packages('stringr')
}


if(!require('pracma')){
install.packages('pracma')
}

library(pracma)
library(pander)
library(stringr)