9.28 Fraction

The Fraction domain implements quotients. The elements must belong to a domain of category IntegralDomain: multiplication must be commutative and the product of two non-zero elements must not be zero. This allows you to make fractions of most things you would think of, but don’t expect to create a fraction of two matrices! The abbreviation for Fraction is FRAC.

Use / to create a fraction.

a := 11/12

\[\]

1112

_{Type: Fraction Integer}

b := 23/24

\[\]

2324

_{Type: Fraction Integer}

The standard arithmetic operations are available.

3 - a*b^2 + a + b/a

\[\]

31327176032

_{Type: Fraction Integer}

Extract the numerator and denominator by using numernumerFraction and denomdenomFraction, respectively.

numer(a)

\[\]

11

_{Type: PositiveInteger}

denom(b)

\[\]

24

_{Type: PositiveInteger}

Operations like maxmaxFraction, minminFraction, negative?negative?Fraction, positive?positive?Fraction and zero?zero?Fraction are all available if they are provided for the numerators and denominators. See IntegerXmpPage for examples.

Don’t expect a useful answer from factorfactorFraction, gcdgcdFraction or lcmlcmFraction if you apply them to fractions.

r := (x^2 + 2*x + 1)/(x^2 - 2*x + 1)

\[\]

x2+2x+1x2-2x+1

_{Type: Fraction Polynomial Integer}

Since all non-zero fractions are invertible, these operations have trivial definitions.

factor(r)

\[\]

x2+2x+1x2-2x+1

_{Type: Factored Fraction Polynomial Integer}

Use mapmapFraction to apply factorfactorFraction to the numerator and denominator, which is probably what you mean.

map(factor,r)

\[\]

(x+1)2(x-1)2

_{Type: Fraction Factored Polynomial Integer}

Other forms of fractions are available. Use continuedFraction to create a continued fraction.

continuedFraction(7/12)

\[\]

_{Type: ContinuedFraction Integer}

Use partialFraction to create a partial fraction. See ContinuedFractionXmpPage and PartialFractionXmpPage for additional information and examples.

partialFraction(7,12)

\[\]

1-322+13

_{Type: PartialFraction Integer}

Use conversion to create alternative views of fractions with objects moved in and out of the numerator and denominator.

g := 2/3 + 4/5*%i

\[\]

23+45i

_{Type: Complex Fraction Integer}

Conversion is discussed in detail in Section ugTypesConvertPage .

g :: FRAC COMPLEX INT

\[\]

10+12i15

_{Type: Fraction Complex Integer}