Matchers

nat

(match 0 nat {[<o> #t] [_ #f]}) ;=>#t (match 1 nat {[<o> #t] [_ #f]}) ;=>#f (match 10 nat {[<s $n> n]}) ;=>9 (match 0 nat {[<s <o>> #t] [_ #f]}) ;=>#f

integer

(match 10 integer {[,10 #t] [_ #f]}) ;=>#t (match 10 nat {[$n n]}) ;=>10

Sequences

nats

(take 10 nats);=>{1 2 3 4 5 6 7 8 9 10}

nats0

(take 10 nats0);=>{0 1 2 3 4 5 6 7 8 9}

odds

(take 10 odds);=>{1 3 5 7 9 11 13 15 17 19}

evens

(take 10 evens);=>{2 4 6 8 10 12 14 16 18 20}

primes

(take 10 primes);=>{2 3 5 7 11 13 17 19 23 29}

fibs

(take 10 fibs);=>{1 1 2 3 5 8 13 21 34 55}

Natural numbers

divisor?

(divisor? 10 5);=>#t

find-factor

(find-factor 100);=>2

p-f

(p-f 100);=>{2 2 5 5}

n-adic

(n-adic 2 5);=>{1 0 1} (n-adic 5 5);=>{1 0}

odd?

(odd? 3);=>#t (odd? 4);=>#f

even?

(even? 4);=>#t (even? 5);=>#f

prime?

(prime? 17);=>#t (prime? 18);=>#f

square?

(square? 9);=>#t (square? 10);=>#f

gcd

(gcd {10 20 5 40});=>5

fact

(fact 10);=>3628800

perm

(perm 5 2);=>20

comb

(comb 5 2);=>10

Integers

power

(power 2 10);=>1024

sum

(sum (take 5 nats));=>15

product

(product (take 5 nats));=>120

Decimal fractions

rtod

(rtod 10 6/35);=>[0 {1 7 1 4 2 8 5 7 1 4}]

rtod'

(rtod' 6/35);=>[0 {1} {7 1 4 2 8 5}]

show-decimal

(show-decimal 10 6/35);=>"0.1714285714"

show-decimal'

(show-decimal' 6/35);=>"0.1 714285 ..."

regular-continued-fraction

(rtof (regular-continued-fraction {1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2})) ;=>1.4142135623730951

continued-fraction

(rtof (continued-fraction {3 7 15 1 292 1 1 1 2 1 3 1 14 2 1 1 2 2 2 2 1 84 2 1 1 15 3 13} {1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1})) ;=>3.141592653589793

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