6.5 One-Line Functions

As you use FriCAS, you will find that you will write many short functions function:one-line definition to codify sequences of operations that you often perform. In this section we write some simple one-line functions.

This is a simple recursive factorial function for positive integers.

fac n == if n < 3 then n else n * fac(n-1)

_{Type: Void}

fac 10

\[\]

3628800

_{Type: PositiveInteger}

This function computes 1+1/2+1/3+...+1/n.

s n == reduce(+,[1/i for i in 1..n])

_{Type: Void}

s 50

\[\]

139432375772240549607593099044504245996706400

_{Type: Fraction Integer}

This function computes a Mersenne number, several of which are prime. Mersenne number

mersenne i == 2^i - 1

_{Type: Void}

If you type mersenne, FriCAS shows you the function definition.

mersenne

\[\]

mersennei==2i-1

_{Type: FunctionCalled mersenne}

Generate a stream of Mersenne numbers.

[mersenne i for i in 1..]

\[\]

[1,3,7,15,31,63,127,255,511,1023,…]

_{Type: Stream Integer}

Create a stream of those values of i such that mersenne(i) is prime.

mersenneIndex := [n for n in 1.. | prime?(mersenne(n))]

Compiling function mersenne with type PositiveInteger -> Integer

\[\]

[2,3,5,7,13,17,19,31,61,89,…]

_{Type: Stream PositiveInteger}

Finally, write a function that returns the n-th Mersenne prime.

mersennePrime n == mersenne mersenneIndex(n)

_{Type: Void}

mersennePrime 5

\[\]

8191

_{Type: PositiveInteger}