Fraction Scripts

 

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--fAdd on fAdd tFraction1, tFraction2   -- Adds two given fractions   tWorkingFraction1 = fMakeImproper(tFraction1)   tWorkingFraction2 = fMakeImproper(tFraction2)   -- Convert fractions to use a common denominator   tNewDenominator = tWorkingFraction1.denominator * tWorkingFraction2.denominator     tWorkingFraction1 = fChangeDenominator(tWorkingFraction1, tNewDenominator)   tWorkingFraction2 = fChangeDenominator(tWorkingFraction2, tNewDenominator)   -- Add them together and make into a proper fraction   tCombinedNumerator = tWorkingFraction1.numerator + tWorkingFraction2.numerator   tSumFraction = fNew(tCombinedNumerator, tNewDenominator)   tSumFraction = fMakeProper(tSumFraction)   -- Return the total   return tSumFraction end --fAddAndSimplify on fAddAndSimplify tFraction1, tFraction2     -- Adds two fractions and simplifies the result   tAddedFraction = fAdd(tFraction1, tFraction2)   tSimplifiedFraction = fSimplify(tAddedFraction)   -- Return the final fraction   return tSimplifiedFraction end --fAreEqual on fAreEqual tFraction1, tFraction2   -- Returns whether two fractions are equal   tComparison = fCompare(tFraction1, tFraction2)   if tComparison = #equal then tAreEqual = TRUE   else tAreEqual = FALSE   -- Returns TRUE or FALSE   return tAreEqual end --fChangeDenominator on fChangeDenominator tFraction, tNewDenominator     -- Converts a fraction into using given denominator   -- Returns -1 instead of the converted fraction if conversion is impossible   -- Check it can be converted   tCanChange = TRUE   -- Check that numerator can be evenly divided into the new denominator   tScale = (tFraction.denominator + 0.0) / tNewDenominator   tNewNumerator = integer(tFraction.numerator / tScale)   if (tFraction.numerator / tScale) <> tNewNumerator then     tCanChange = FALSE   end if   if tCanChange = TRUE then     -- Can convert so do so     tConvertedFraction = fCopy(tFraction)     tConvertedFraction.numerator = tNewNumerator     tConvertedFraction.denominator = tNewDenominator   else     -- Cannot convert, so return -1     tConvertedFraction = -1   end if   -- Return converted (or otherwise) fraction   return tConvertedFraction end --fCompare on fCompare tFraction1, tFraction2   -- Compares the second fraction against the first   tFraction1Value = fGetDecimalValue(tFraction1)   tFraction2Value = fGetDecimalValue(tFraction2)   if tFraction1Value = tFraction2Value then tComparison = #equal   else if tFraction2Value < tFraction1Value then tComparison = #lessthan   else tComparison = #greaterthan   -- Returns the comparison   return tComparison end --fCopy on fCopy tFraction   -- Duplicates the fraction   return duplicate(tFraction) end --fFractionToString on fFractionToString tFraction   -- Make a fraction variable into a string   if tFraction.whole <> 0 then tString = string(tFraction.whole) & " "   else tString = EMPTY   tString = tString & string(tFraction.numerator) & "/" & string(tFraction.denominator)   -- Return the string   return tString end --fGetCommonDenominators on fGetCommonDenominators tFraction1, tFraction2, tUpperLimit     tlValidDenominators = []   tlFraction1ValidDenominators = []   tlFraction2ValidDenominators = []   -- Get lists of valid denominators for fractions   repeat with a = 1 to tUpperLimit     if fIsDenominator(tFraction1, a) then       add tlFraction1ValidDenominators, a     end if     if fIsDenominator(tFraction2, a) then       add tlFraction2ValidDenominators, a     end if   end repeat   -- Compare lists and only return values in both   repeat with a = 1 to count(tlFraction1ValidDenominators)     if getone(tlFraction2ValidDenominators, tlFraction1ValidDenominators[a]) > 0 then       add tlValidDenominators, tlFraction1ValidDenominators[a]     end if   end repeat     -- Return list of valid denominators   return tlValidDenominators end --fGetDecimalValue on fGetDecimalValue tFraction   -- Returns the decimal value of a fraction   if tFraction.denominator <= 0 then return -1   tDecimalValue = tFraction.whole + (tFraction.numerator + 0.0) / tFraction.denominator   -- Returns the decimal value   return tDecimalValue end --fGetDenominators on fGetDenominators tFraction, tUpperLimit     tlValidDenominators = []   -- Get a list of valid denominators for fraction   repeat with a = 1 to tUpperLimit     if fIsDenominator(tFraction, a) then       add tlValidDenominators, a     end if   end repeat   -- Return list of valid denominators   return tlValidDenominators end --fGetLowestCommonDenominator on fGetLowestCommonDenominator tFraction1, tFraction2     -- Finds the lowest common denominator   tMaximumDenominator = tFraction1.denominator * tFraction2.denominator   repeat with a = 1 to tMaximumDenominator     if fIsDenominator(tFraction1, a) and fIsDenominator(tFraction2, a) then       tLowestCommonDenominator = a       exit repeat     end if   end repeat   -- Return the lowest common denominator   return tLowestCommonDenominator end --fGetLowestDenominator on fGetLowestDenominator tFraction     -- Find lowest denominator by simply starting at 1 and working up to current denominator   tLowestDenominator = tFraction.denominator   repeat with a = 1 to tFraction.denominator     if fChangeDenominator(tFraction, a) <> -1 then       tLowestDenominator = a       exit repeat     end if   end repeat   -- Return the lowest found denominator   return tLowestDenominator end --fGetType on fGetType tFraction   -- Gets the type of the given fraction   if fIsProper(tFraction) then tFractionType = #proper   else     if fIsImproper(tFraction) then tFractionType = #improper     else tFractionType = #mixed   end if   -- Return fraction type   return tFractionType end --fGetWhole on fGetWhole tFraction   -- Gets the whole part of any sort of fraction   tWorkingFraction = fMakeProper(tFraction)   tWhole = tWorkingFraction.whole   -- Return just the whole part   return tWhole end --fIsCommonDenominator on fIsCommonDenominator tFraction1, tFraction2, tDenominator     -- Checks whether a denominator is valid for two fractions   tIsCommonDenominator = TRUE   if fChangeDenominator(tFraction1, tDenominator) = -1 then tIsCommonDenominator = FALSE   if fChangeDenominator(tFraction2, tDenominator) = -1 then tIsCommonDenominator = FALSE   -- Return TRUE or FALSE   return tIsCommonDenominator end --fIsDenominator on fIsDenominator tFraction, tDenominator     -- Checks whether a denominator is a valid denominator for a fraction   if fChangeDenominator(tFraction, tDenominator) = -1 then tIsDenominator = FALSE   else tIsDenominator = TRUE   -- Returns TRUE or FALSE   return tIsDenominator end --fIsImproper on fIsImproper tFraction     -- Checks whether a fraction is improper   tIsImproper = TRUE   if tFraction.whole > 0 then tIsImproper = FALSE   if tFraction.numerator < tFraction.denominator then tIsImproper = FALSE   -- Returns TRUE or FALSE   return tIsImproper --fIsMixed on fIsMixed tFraction     -- Checks whether a fraction is mixed   tIsMixed = TRUE   if tFraction.numerator < tFraction.denominator then     tIsMixed = FALSE   else     if tFraction.whole = 0 then       tIsMixed = FALSE     end if   end if   -- Returns TRUE or FALSE   return tIsMixed end --fIsProper on fIsProper tFraction     -- Checks whether a fraction is proper   tIsProper = TRUE   if tFraction.numerator >= tFraction.denominator then tIsProper = FALSE   -- Returns TRUE or FALSE   return tIsProper end --fJustFraction on fJustFraction tFraction     -- Returns a fraction with top limit of 1 unit   tJustFraction = fMakeProper(tFraction)   if (tJustFraction.numerator = 0) and (tJustFraction.whole > 0) then     tJustFraction.numerator = tJustFraction.denominator   end if   tJustFraction.whole = 0   -- Returns just the fraction   return tJustFraction end --fMakeFraction on fMakeFraction tDecimalValue     -- Convert a decimal value into a fraction and simplify the result   if tDecimalValue <0 then     tNewFraction = -1   else     tDecimalValue = value(string(tDecimalValue)) * 10000     tNewFraction = fMakeProper(fSimplify(fNew(tDecimalValue, 10000)))   end if   -- Return the fraction (or error)   return tNewFraction end --fMakeImproper on fMakeImproper tFraction     -- Make into improper fraction   tImproperFraction = fNew()   tNumerators = tFraction.numerator + tFraction.whole * tFraction.denominator   tImproperFraction.numerator = tNumerators   tImproperFraction.denominator = tFraction.denominator   tImproperFraction.whole = 0   -- Return converted fraction   return tImproperFraction end --fMakeMixed on fMakeMixed tFraction, tWholeUsed     -- Make into a mixed fraction (Returns -1 if impossible)   tMixedFraction = fCopy(tFraction)   tImproperFraction = fMakeImproper(tFraction)   tNumeratorsToDelete = tWholeUsed * tFraction.denominator   -- Check there are enough numerators to subtract from   if tNumeratorsToDelete <= tFraction.numerator then     tMixedFraction = fMakeProper(tFraction)   else     tMixedFraction.numerator = tMixedFraction.numerator - tNumeratorsToDelete     tMixedFraction.whole = tWholeUsed   end if   -- Return converted fraction   return tMixedFraction end --fMakeProper on fMakeProper tFraction     -- Make into proper fraction   tProperFraction = fNew()   tNumerators = tFraction.numerator + tFraction.whole * tFraction.denominator   tProperFraction.numerator = tNumerators mod tFraction.denominator   tProperFraction.denominator = tFraction.denominator   tProperFraction.whole = tNumerators / tFraction.denominator   -- Return converted fraction   return tProperFraction end --fNew on fNew tNumerator, tDenominator, tWhole   -- Initialise and return a fraction property list   if voidP(tWhole) then tWhole = 0   if (voidP(tDenominator)) and (voidP(tNumerator)) then tDenominator = 1   if (voidP(tDenominator)) and (not(voidP(tNumerator))) then tDenominator = tNumerator   if voidP(tNumerator) then tNumerator = 0   -- If values are not integers then call fMakeFraction instead   if (tNumerator <> integer(tNumerator)) or (tDenominator <> integer(tDenominator)) or (tWhole <> integer(tWhole)) then     tNewFraction = fMakeFraction(tNumerator / tDenominator + tWhole * tDenominator)   else     tNewFraction = [#numerator: integer(tNumerator), #denominator: integer(tDenominator), #whole: integer(tWhole)]   end if   -- Return fraction property list   return tNewFraction end --fRemoveWhole on fRemoveWhole tFraction   -- Removes the whole part from any type of fraction   tJustFraction = fMakeProper(tFraction)   tJustFraction.whole = 0   -- Return just the fractional part   return tJustFraction end --fSimplify on fSimplify tFraction   -- Uses the other routines to simplify the fraction   tLowestDenominator = fGetLowestDenominator(tFraction)   tSimplifiedFraction = fChangeDenominator(tFraction, tLowestDenominator)   -- Return the simplified fraction   return tSimplifiedFraction end --fStringToFraction on fStringToFraction tString   -- Make a string into a fraction 'variable type'   tFraction = fNew()   if tString contains " " then     tFraction.whole = value(tString.char[1..(offset(" ", tString) - 1)])     tString = tString.char[(offset(" ", tString) + 1)..length(tString)]   else     tFraction.whole = 0   end if   tFraction.numerator = value(tString.char[1..(offset("/", tString) - 1)])   tFraction.denominator = value(tString.char[(offset("/", tString) + 1)..length(tString)])   -- Return the fraction   return tFraction end --fSubtract on fSubtract tFraction1, tFraction2   -- Subtracts two given fractions   tWorkingFraction1 = fMakeImproper(tFraction1)   tWorkingFraction2 = fMakeImproper(tFraction2)   -- Convert fractions to use a common denominator   tNewDenominator = tWorkingFraction1.denominator * tWorkingFraction2.denominator     tWorkingFraction1 = fChangeDenominator(tWorkingFraction1, tNewDenominator)   tWorkingFraction2 = fChangeDenominator(tWorkingFraction2, tNewDenominator)   -- Subtract them and make into a proper fraction   tSubtractedNumerator = tWorkingFraction1.numerator - tWorkingFraction2.numerator   -- If numerator is no longer positive return an error   if tSubtractedNumerator < 0 then     tSumFraction = -1   else     tSumFraction = fNew(tSubtractedNumerator, tNewDenominator)     tSumFraction = fMakeProper(tSumFraction)   end if   -- Return the total (or error code)   return tSumFraction end