# Some calculations with natural numbers and
# conversion from Celsius toFahrenheit
# A. Heck
# 19-11-2018

one  <- 1
two <- 2
three <- one + two
cat("The type of the R object", three, "is", typeof(three), "\n")
cat(one, '+', two, '=', three, "\n")

cat('6 / 8 =', 6 / 8, "\n")
cat('8 / 6 =', 8 / 6, "\n")
quotient <- 8 %/% 6; rest <-  8 %% 6; 
cat('8 %/% 6 =', quotient, 'en 8 %% 6 =', rest, "\n")

The type of the R object 3 is double 
1 + 2 = 3 
6 / 8 = 0.75 
8 / 6 = 1.333333 
8 %/% 6 = 1 en 8 %% 6 = 2 

The first lines are meant as documentation

We can separate R instructions (if they are complete) with an empty line to have a better overview in the program file.

The next three lines show you how to store values in self-chosen names called variables and use those names in further calculations. The next four statements show that you can print multiple things one after the other: texts, in the form of a string object, are separated with a double quote " and R separates parts in the result of the cat statement with a space. The newline escape character \n is used to force a new line.

Another way to specify a string object is to use the single quote ', but don't mix the two types of quotes: "gives error' is incorrect, but "Marthe's bike" is a good string with a quote in the middle.

The last two R instructions show calculations with natural numbers: / is for 'ordinary division', which may or may not return a fraction in the form of a floating-pointed number. Not every fraction can be represented as a finite floating-point number: in this case $8/6 = 4/3$ is only stored in 16 decimal places. The operator %/% is for 'divide with remainder' and %% is the symbol for the modulo operator.

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We summarise the basic numerical operations with numbers:

$$\begin{array}{l|c|l} \textit{Operation} & \textit{Operator} & \textit{Explanation} \\ \hline\hline \text{addition} & x+y & x\text{ and }y\text{ are integers or floating-point numbers.} \\ \hline \text{difference} & x-y & x\text{ and }y\text{ are integers or floating-point numbers.} \\ \hline \text{product} & x*y & x\text{ and }y\text{ are integers or floating-point numbers.} \\ \hline \text{quotiënt} & x/y & x\text{ and }y\text{ are integers or floating-point numbers..}\\[-2pt] & & \text{The result is a floating-point number.} \\ \hline \text{integer division} & x\;\%/\%\;y & x\text{ and }y\text{ are integers or floating-point numbers.}\\[-2pt] & & \text{The result is the greatest integer less than or}\\ & & \text{equal to the quotiënt.} \\ \hline \text{remainder in division} & x\;\%\%\;y & x\text{ and }y\text{ are integers.}\\[-2pt] & & \text{The result is the remainder in division of }x\text{ by }y\text{.} \\ \hline \text{exponentiation} & x \;\mathtt{\hat{\;}} \;y & x\text{ and }y\text{ are integers or floating-point numbers.} \\ \hline \text{floating-point conversion} & \mathtt{as.double}(x) & \text{Convert the numerical value of }x\\[-2pt] & & \text{into a floating-point number.}\\ \hline \text{integer conversion} & \mathtt{as.integer}(x) & \text{convert the numerical value of }x\text{ to an integer.}\\[-2pt] & & \text{ Cut off the decimal representation; do not round off.}\\ \hline \text{absolute value} & \mathtt{abs}(x)& \text{Compute the absolute vale of }x\text{.} \\ \hline \text{rounding} & \mathtt{round}(x) & \text{Round the numerical value of }x\text{ to the nearest integer.}\\ & \mathtt{round}(x, \text{digits=}n) & \text{Round }x\text{ up to }n\text{ decimals.}\\ \hline \text{sign} & \mathtt{sign}(x) & \text{The result is } \left\{ \begin{array}{ll} -1 & \text{if }x \lt 0 \\ 0 & \text{if }x=0 \\ 1 & \text{if }x\gt 0 \end{array} \right. \\ \hline \text{factorial} & \mathtt{factorial}(n) & n! \end{array}$$

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The associated data types for variables are

$$\begin{array}{l|c|l} \textit{Type} & \textit{Example} & \textit{Explanation} \\ \hline\hline \text{integer} & 12 & \text{Integer values} \\ \hline \text{double} & 12.345 & \text{Approximations of real number in a maximum of 16 decimals} \\ \hline \text{character} & \text{"Hello"} & \text{Collection of characters. A string must always be between quotation marks} \\ \hline \text{logical} & \text{TRUE} & \text{Outcome of a logical logische test. Two possible values: TRUE of FALSE}\\ \hline \end{array}$$

You can check the data type of a variable with the typeof function. You can convert data types with the functions as.double, as.integer, and as.character .