AlgebraicFraction $-$ an object for holding abstract fractional representations.

fields

numerator: an ArrayList of each numerator component

denominator: an ArrayList of each denominator component

methods

AlgebraicFraction$($num$,$ denom$)$: The values of each cell of the num array should be put in to the

numerator ArrayList and the values of each cell in the denom array should be put into the denominator

ArrayList. Then the fraction should be reduced with the below Fraction reducing algorithm.

multiply$($otherFraction$)$ should return a new AlgebraicFraction from the combination of the two

fractions. See Fraction multiplication algorithm.

toString $()$ : this method should return a String representation of the $($reduced$)$ fraction. The parts of the

numerator should be prefixed by a $"("$ then separated by single spaces followed by $")/("$ and then the

parts of the denominator should be separated by spaces and then ended with a $")".$

Fraction reducing algorithm

For each Object n in the num array $($passed into the constructor$)$:

if n is in the numerator ArrayList and n is in the denominator ArrayList

remove $n$ from the numerator array list

remove $n$ from the denominatory array list

Fraction multiplication algorithm

to multiply fractions a and b

combine the numerators of fractions a and $b$

combine the denominators of fractions a and $b$

make a new fraction with the combined numerators and denominators

$($reduce$)$

Fraction multiplication example

$\frac{abc}{\text{d}\text{e}\text{f}}$ times e $r$

combined numerator: $)$

combined denominator: $(d$ e $f$ a e $r)$

new fraction $($ abcdfg $)/($d e $f$ a e $r)$

reduced: c g$)/($ e e r$)$