emmy.bigfraction — org.mentat/emmy 0.32.0

A CLJS bigfraction is a coprime pair of JavaScript BigInts, with the sign carried in the numerator.

->normal-form cljs

(->normal-form a b)

We assume we are given two BigInts, with b > 0. The GCD is divided out, and the sign is carried in the numerator.

->real cljs

(->real q)

Coerce a fraction to real by performing the division in the floating point domain

abs cljs

(abs x)

Absolute value of the fraction x.

add cljs

(add x y)

Returns the sum of x and y.

bigint-gcd cljs

(bigint-gcd a b)

GCD assuming a and b are BigInts > 0

ceil cljs

(ceil x)

Ceiling. Result is a BigInt.

cmp cljs

(cmp x y)

Compares the fractions x and y, returning -1, 0, or 1.

denominator cljs

(denominator x)

div cljs

(div x y)

Returns the quotient of x and y.

division-by-zero cljs

(division-by-zero)

Throws JS exception used to signal an attempt to construct a fraction with zero denominator.

eq cljs

(eq x y)

floor cljs

(floor x)

Floor. Result is a BigInt.

gcd cljs

(gcd x y)

integer-> cljs

(integer-> n)

Create a fraction with unit denominator.

integer-power cljs

(integer-power x n)

Raises the fraction x to the integer power n.

invert cljs

(invert x)

Returns the reciprocal of x, but throws if $x=0$.

make cljs

(make a b)

Produces a fraction in canonical form. Note that the canonical form of an integer is an integer, so if (one? b) you just get a.

mul cljs

(mul x y)

Returns the product of x and y.

neg cljs

(neg x)

Negation of the fraction x.

neg? cljs

(neg? x)

True if $x<0$.

numerator cljs

(numerator x)

one? cljs

(one? x)

Returns true iff x is a unit fraction.

promote cljs

(promote x)

If the fraction has a unit denominator, return the numerator, else the fraction.

quotient cljs

(quotient x y)

Fractions form a field, so somewhat dubiously the function returns the largest integer N for which $Ny\le x$.

real-> cljs

(real-> x)

Clojure converts the real to BigDecimal and rationalizes from that. The JVM documentation explains that the BigDecimal value will correspond to what would be printed for the double value. We attempt to do the same thing here by converting to a string and converting from there.

remainder cljs

(remainder x y)

If $q$ is (quotient x y), returns $x-qy$.

sub cljs

(sub x y)

Returns the difference of x and y.

zero? cljs

(zero? x)

Returns true iff x is a zero fraction.