public void RationalCanonicalize()
{
using (var a = new HugeRational(198, 15))
{
a.Denominator.Value = -a.Denominator;
Assert.AreEqual("198/-15", a.ToString());
a.Canonicalize();
Assert.AreEqual("-66/5", a.ToString());
}
}
public void RationalCanonicalize()
{
using (var a = new HugeRational(198, 15))
{
a.Denominator.Value = -a.Denominator;
Assert.AreEqual("198/-15", a.ToString());
a.Canonicalize();
Assert.AreEqual("-66/5", a.ToString());
}
}
public void RationalToStringHex()
{
var n = "-23429abcdef298357462983fedcba345623984756";
var d = "17607ef654eb9a13ffa163c75";
var s = n + "/" + d;
using (var a = new HugeRational(s, 16))
{
Assert.AreEqual(s, a.ToString(16, true));
Assert.AreEqual(s.ToUpper(), a.ToString(16));
}
}
public void RationalFromLong()
{
using (var a = new HugeRational())
{
var b = Platform.Si(-0x784739ABCDEF4876, -0xF84776);
var d = Platform.Ui(12764787846358441471, 3628273133);
a.SetTo(b, d);
Assert.AreEqual(b.ToString() + "/" + d.ToString(), a.ToString());
a.SetTo(b);
Assert.AreEqual(b.ToString() + "/1", a.ToString());
}
}
public void RationalFromLong()
{
using (var a = new HugeRational())
{
var b = Platform.Si(-0x784739ABCDEF4876, -0xF84776);
var d = Platform.Ui(12764787846358441471, 3628273133);
a.SetTo(b, d);
Assert.AreEqual(b.ToString() + "/" + d.ToString(), a.ToString());
a.SetTo(b);
Assert.AreEqual(b.ToString() + "/1", a.ToString());
}
}
public void RationalConstructorFromDoubleNegative()
{
using (var a = new HugeRational(-123456789123456.75))
{
Assert.AreEqual("-493827156493827/4", a.ToString());
}
}
public void RationalConstructorFromDoubleNegative()
{
using (var a = new HugeRational(-123456789123456.75))
{
Assert.AreEqual("-493827156493827/4", a.ToString());
}
}
public void RationalStringAssignmentHexPrefix()
{
using (var i = new HugeInt("362736035870515331128527330659"))
{
var d = i.ToString(16);
var n = "143210ABCDEF32123457ACDB324598799";
using (var a = new HugeRational("0x" + n + "/0x" + d))
{
Assert.AreEqual(n + "/" + d, a.ToString(16));
Assert.AreEqual(n + "/" + d, a.ToString(16, false));
Assert.AreEqual((n + "/" + d).ToLower(), a.ToString(16, true));
a.SetTo("-0x" + n + "/0x17");
Assert.AreEqual("-" + n + "/17", a.ToString(16));
}
}
}
public void RationalSwap()
{
var strA = "-222509832503450298345029835740293845720/115756986668303657898962467957";
var strB = "2039847290878794872059384789347534534/590872612825179551336102196593";
using (var a = new HugeRational(strA))
using (var b = new HugeRational(strB))
{
var aValue = a._value();
var bValue = b._value();
var an = a.Numerator;
var ad = a.Denominator;
var bn = b.Numerator;
var bd = b.Denominator;
a.Swap(b);
Assert.AreEqual(aValue, a._value());
Assert.AreEqual(bValue, b._value());
Assert.AreEqual(strB, a.ToString());
Assert.AreEqual(strA, b.ToString());
Assert.AreEqual(strB, string.Format("{0}/{1}", an, ad));
Assert.AreEqual(strA, string.Format("{0}/{1}", bn, bd));
}
}
public void RationalConstructorFromIntExpression()
{
using (var a = new HugeInt("2340958273409578234095823045723490587"))
using (var b = new HugeRational(a + 1))
{
Assert.AreEqual("2340958273409578234095823045723490588/1", b.ToString());
}
}
public void RationalFromString()
{
using (var a = new HugeRational())
{
var n = "98762934876529834765234123984761/115756986668303657898962467957";
a.SetTo(n);
Assert.AreEqual(n, a.ToString());
n = "-98ABCDEF876529834765234123984761/17607EF654EB9A13FFA163C75";
a.SetTo(n, 16);
Assert.AreEqual(n, a.ToString(16));
n = "-98ABCDEF876529834765234123984761";
a.SetTo(n, 16);
Assert.AreEqual(n + "/1", a.ToString(16));
}
}
public void RationalConstructorFromFloatExpression()
{
using (var a = new HugeFloat("2340958273409578234.25"))
using (var b = new HugeRational(a + 1))
{
Assert.AreEqual("9363833093638312941/4", b.ToString());
}
}
public void RationalAssignFloat2()
{
using(var a = new HugeFloat("222509832503450298342455029.125"))
using(var b = new HugeRational("1/3"))
{
b.SetTo(a);
Assert.AreEqual("1780078660027602386739640233/8", b.ToString());
}
}
public void RationalAssignFloat()
{
using (var a = new HugeFloat("9363833093638312937.25"))
using (var b = new HugeRational())
{
b.SetTo(a);
Assert.AreEqual("37455332374553251749/4", b.ToString());
}
}
public void RationalAssignCopy()
{
using (var a = new HugeRational("-222509832503450298345029835740293845720/115756986668303657898962467957"))
using (var b = new HugeRational())
{
b.Value = a;
Assert.AreEqual("-222509832503450298345029835740293845720/115756986668303657898962467957", b.ToString());
}
}
public void RationalAssignFloat2()
{
using (var a = new HugeFloat("222509832503450298342455029.125"))
using (var b = new HugeRational("1/3"))
{
b.SetTo(a);
Assert.AreEqual("1780078660027602386739640233/8", b.ToString());
}
}
public void RationalAssignFloat()
{
using (var a = new HugeFloat("9363833093638312937.25"))
using (var b = new HugeRational())
{
b.SetTo(a);
Assert.AreEqual("37455332374553251749/4", b.ToString());
}
}
public void RationalAssignInt()
{
using (var a = new HugeInt("222509832503450298345029835740293845720"))
using (var b = new HugeRational("1/3"))
{
b.SetTo(a);
Assert.AreEqual("222509832503450298345029835740293845720/1", b.ToString());
}
}
public void RationalAssignInt()
{
using (var a = new HugeInt("222509832503450298345029835740293845720"))
using (var b = new HugeRational("1/3"))
{
b.SetTo(a);
Assert.AreEqual("222509832503450298345029835740293845720/1", b.ToString());
}
}
private void VerifyPartialResult(MpirRandom rnd, RationalExpression expr, long expected)
{
rnd.Seed(123);
using (var r = new HugeRational())
{
r.Value = expr;
Assert.AreEqual(expected.ToString() + "/1", r.ToString());
}
}
public void RationalStringConstructorNumeratorOnly()
{
var n = "5432109876543212345789023245987";
using (var a = new HugeRational(n))
{
Assert.AreEqual(128 / MpirSettings.BITS_PER_LIMB, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(n + "/1", a.ToString());
}
}
public void RationalStringConstructor()
{
var n = "5432109876543212345789023245987/362736035870515331128527330659";
using (var a = new HugeRational(n))
{
Assert.AreEqual(128 / MpirSettings.BITS_PER_LIMB, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(n, a.ToString());
}
}
public void RationalToStringDecimal()
{
var n = "-23429384756298357462983476598345623984756";
var d = "115756986668303657898962467957";
var s = n + "/" + d;
using (var a = new HugeRational(s))
{
Assert.AreEqual(s, a.ToString());
}
}
public void RationalDivideLimbBy()
{
using (var a = new HugeRational("115756986668303657898962467957/39458029384750298767200622330399462537522498"))
{
var b = Platform.Ui(5931690917503076532, 3367900313);
a.Value = b / a;
Assert.AreEqual(Platform.Select(
"234052834524092854092874502983745029345723092857791404165816936/115756986668303657898962467957",
"132890709515263728644898490080347139295153795258741874/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalDivideSignedLimbBy()
{
using (var a = new HugeRational("115756986668303657898962467957/39458029384750298767200622330399462537522498"))
{
var b = Platform.Si(-5931690917503076532, -1500450271);
a.Value = b / a;
Assert.AreEqual(Platform.Select(
"-234052834524092854092874502983745029345723092857791404165816936/115756986668303657898962467957",
"-59204810883474549052577139687016525102679979792696958/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalMultiplyLimbBy()
{
using (var a = new HugeRational("90234098723098475098479385345098345/115756986668303657898962467957"))
{
var b = Platform.Ui(17390538260286101342, 1500450271);
a.Value = b * a;
Assert.AreEqual(Platform.Select(
"1569219546226477273686601978789044606491747469626478990/115756986668303657898962467957",
"135391777882513860921200145428966240276901495/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalMultiplySignedLimbBy()
{
using (var a = new HugeRational("90234098723098475098479385345098345/115756986668303657898962467957"))
{
var b = Platform.Si(-7390538260286101342, -1987450271);
a.Value = b * a;
Assert.AreEqual(Platform.Select(
"-666878558995492522701808125338061156491747469626478990/115756986668303657898962467957",
"-179335783960662818294159606092029134291901495/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalStringConstructorHexPrefix()
{
using (var i = new HugeInt("362736035870515331128527330659"))
{
var d = i.ToString(16);
var n = "143210ABCDEF32123457ACDB324598799";
using (var a = new HugeRational("0x" + n + "/0x" + d))
{
Assert.AreEqual(n + "/" + d, a.ToString(16));
Assert.AreEqual(i, a.Denominator);
}
}
}
public void RationalConstructorFromLongNegative()
{
var n = Platform.Si(-123456789123456, -1234567891);
var d = Platform.Ui(12764787846358441471U, 2860486313U);
using (var a = new HugeRational(n, d))
{
Assert.AreEqual(1, a.NumeratorNumberOfLimbsAllocated());
Assert.AreEqual(-1, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsAllocated());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsUsed());
Assert.AreEqual(n + "/" + d, a.ToString());
}
}
public void RationalConstructorFromULong()
{
var n = Platform.Ui(ulong.MaxValue, uint.MaxValue);
var d = Platform.Ui(12764787846358441471U, 2860486313U);
using (var a = new HugeRational(n, d))
{
Assert.AreEqual(1, a.NumeratorNumberOfLimbsAllocated());
Assert.AreEqual(1, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsAllocated());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsUsed());
Assert.AreEqual(n.ToString(), a.Numerator.ToString());
Assert.AreEqual(n.ToString() + "/" + d, a.ToString());
}
}
public void RationalToStringTruncated()
{
using (var d = new HugeInt("115756986668303657898962467957"))
using (var e = new HugeInt(d ^ 10))
{
var s = e.ToString(10);
var n = string.Concat("123456789".Select(c => new string(c, 30)));
using (var a = new HugeRational(n + "/" + s))
{
Assert.AreEqual(n + "/" + s, a.ToString(10));
Assert.AreEqual("..." + n.Substring(n.Length - 256) + "/..." + s.Substring(s.Length - 256), a.ToString());
a.Value = -a;
Assert.AreEqual("-..." + n.Substring(n.Length - 256) + "/..." + s.Substring(s.Length - 256), a.ToString());
}
}
}
public void RationalInputOutputStrHex()
{
using (var a = new HugeRational("0x10123456789ABCDEF0123456789ABCDEF0123456789ABCDEF/361720912810755408215708460645842859722715865206816237944587"))
using (var b = new HugeRational())
using (var ms = new MemoryStream())
{
a.Value = a ^ 100;
using (var writer = new StreamWriter(ms, Encoding.UTF8, 1024, true))
a.Write(writer, 16);
ms.Position = 0;
using (var reader = new StreamReader(ms, Encoding.UTF8, false, 1024, true))
b.Read(reader, 16);
Assert.AreEqual(a, b);
Assert.AreEqual(ms.Length, ms.Position);
Assert.AreEqual((char)0xFEFF + a.ToString(16), Encoding.UTF8.GetString(ms.ToArray()));
}
}
public void RationalCompoundOperators()
{
using (var a = new HugeRational("938475092834705928347523452345/115756986668303657898962467957"))
{
a.Value += 1;
a.Value *= 10;
Assert.AreEqual("10542320795030095862464859203020/115756986668303657898962467957", a.ToString());
}
}
public void RationalDivideHugeRational()
{
using (var a = new HugeRational("115756986668303657898962467957/394580293847502987609283945873594873409587"))
using (var b = new HugeRational("593169091750307653294"))
{
a.Value = a / b;
Assert.AreEqual("115756986668303657898962467957/234052834524092854092760134269509268758750275703033222451729578", a.ToString());
}
}
public void RationalConstructorFromFloatExpression()
{
using (var a = new HugeFloat("2340958273409578234.25"))
using (var b = new HugeRational(a + 1))
{
Assert.AreEqual("9363833093638312941/4", b.ToString());
}
}
public void RationalStringAssignmentHexPrefix()
{
using (var i = new HugeInt("362736035870515331128527330659"))
{
var d = i.ToString(16);
var n = "143210ABCDEF32123457ACDB324598799";
using (var a = new HugeRational("0x" + n + "/0x" + d))
{
Assert.AreEqual(n + "/" + d, a.ToString(16));
Assert.AreEqual(n + "/" + d, a.ToString(16, false));
Assert.AreEqual((n + "/" + d).ToLower(), a.ToString(16, true));
a.SetTo("-0x" + n + "/0x17");
Assert.AreEqual("-" + n + "/17", a.ToString(16));
}
}
}
public void RationalStringConstructorHexPrefix()
{
using (var i = new HugeInt("362736035870515331128527330659"))
{
var d = i.ToString(16);
var n = "143210ABCDEF32123457ACDB324598799";
using (var a = new HugeRational("0x" + n + "/0x" + d))
{
Assert.AreEqual(n + "/" + d, a.ToString(16));
Assert.AreEqual(i, a.Denominator);
}
}
}
public void RationalShiftRight()
{
using (var a = new HugeRational("ABCDEF052834524092854092874502983745029345723098457209305983434345/17607EF654EB9A13FFA163C75", 16))
{
uint b = 96;
a.Value = a >> b;
Assert.AreEqual("ABCDEF052834524092854092874502983745029345723098457209305983434345/17607EF654EB9A13FFA163C75000000000000000000000000", a.ToString(16));
}
}
public void RationalConstructorFromLongNegative()
{
var n = Platform.Si(-123456789123456, -1234567891);
var d = Platform.Ui(12764787846358441471U, 2860486313U);
using (var a = new HugeRational(n, d))
{
Assert.AreEqual(1, a.NumeratorNumberOfLimbsAllocated());
Assert.AreEqual(-1, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsAllocated());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsUsed());
Assert.AreEqual(n + "/" + d, a.ToString());
}
}
public void RationalNegate()
{
using (var a = new HugeRational("24092854092874502983745029345723098457209/115756986668303657898962467957"))
{
a.Value = -a;
Assert.AreEqual("-24092854092874502983745029345723098457209/115756986668303657898962467957", a.ToString());
a.Value = -a;
Assert.AreEqual("24092854092874502983745029345723098457209/115756986668303657898962467957", a.ToString());
}
}
public void RationalMultiplyLimbBy()
{
using (var a = new HugeRational("90234098723098475098479385345098345/115756986668303657898962467957"))
{
var b = Platform.Ui(17390538260286101342, 1500450271);
a.Value = b * a;
Assert.AreEqual(Platform.Select(
"1569219546226477273686601978789044606491747469626478990/115756986668303657898962467957",
"135391777882513860921200145428966240276901495/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalAssignInt2()
{
using (var a = new HugeInt("222509832503450298345029835740293845719"))
using (var d = new HugeInt("115756986668303657898962467957"))
using (var b = new HugeRational("1/3"))
{
b.SetTo(a, d);
Assert.AreEqual("222509832503450298345029835740293845719/115756986668303657898962467957", b.ToString());
b.SetTo(b.Numerator - b.Denominator, b.Denominator * 5);
Assert.AreEqual(a - d, b.Numerator);
Assert.AreEqual(d * 5, b.Denominator);
}
}
public void RationalAssignCopy()
{
using (var a = new HugeRational("-222509832503450298345029835740293845720/115756986668303657898962467957"))
using (var b = new HugeRational())
{
b.Value = a;
Assert.AreEqual("-222509832503450298345029835740293845720/115756986668303657898962467957", b.ToString());
}
}
public void RationalCompoundOperators()
{
using (var a = new HugeRational("938475092834705928347523452345/115756986668303657898962467957"))
{
a.Value += 1;
a.Value *= 10;
Assert.AreEqual("10542320795030095862464859203020/115756986668303657898962467957", a.ToString());
}
}
public void RationalMultiplySignedLimbBy()
{
using (var a = new HugeRational("90234098723098475098479385345098345/115756986668303657898962467957"))
{
var b = Platform.Si(-7390538260286101342, -1987450271);
a.Value = b * a;
Assert.AreEqual(Platform.Select(
"-666878558995492522701808125338061156491747469626478990/115756986668303657898962467957",
"-179335783960662818294159606092029134291901495/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalToStringDecimal()
{
var n = "-23429384756298357462983476598345623984756";
var d = "115756986668303657898962467957";
var s = n + "/" + d;
using (var a = new HugeRational(s))
{
Assert.AreEqual(s, a.ToString());
}
}
public void RationalShiftLeft()
{
using (var a = new HugeRational("-12345700987ABCDEF2345CBDEFA245230948/17607EF654EB9A13FFA163C75", 16))
{
uint b = 40;
a.Value = a << b;
Assert.AreEqual("-12345700987ABCDEF2345CBDEFA2452309480000000000/17607EF654EB9A13FFA163C75", a.ToString(16));
}
}
public void RationalToStringHex()
{
var n = "-23429abcdef298357462983fedcba345623984756";
var d = "17607ef654eb9a13ffa163c75";
var s = n + "/" + d;
using (var a = new HugeRational(s, 16))
{
Assert.AreEqual(s, a.ToString(16, true));
Assert.AreEqual(s.ToUpper(), a.ToString(16));
}
}
public void RationalInputOutputStrBinary()
{
using (var a = new HugeRational("0x10123456789ABCDEF0123456789ABCDEF0123456789ABCDEF/361720912810755408215708460645842859722715865206816237944587"))
using (var b = new HugeRational())
using (var ms = new MemoryStream())
{
a.Value = a ^ 100;
using (var writer = new StreamWriter(ms, Encoding.UTF8, 1024, true))
a.Write(writer, 2);
ms.Position = 0;
using (var reader = new StreamReader(ms, Encoding.UTF8, false, 1024, true))
b.Read(reader, 2);
Assert.AreEqual(a, b);
Assert.AreEqual(ms.Length, ms.Position);
Assert.AreEqual((char)0xFEFF + a.ToString(2), Encoding.UTF8.GetString(ms.ToArray()));
}
}
public void RationalToStringTruncated()
{
using (var d = new HugeInt("115756986668303657898962467957"))
using (var e = new HugeInt(d ^ 10))
{
var s = e.ToString(10);
var n = string.Concat("123456789".Select(c => new string(c, 30)));
using (var a = new HugeRational(n + "/" + s))
{
Assert.AreEqual(n + "/" + s, a.ToString(10));
Assert.AreEqual("..." + n.Substring(n.Length - 256) + "/..." + s.Substring(s.Length - 256), a.ToString());
a.Value = -a;
Assert.AreEqual("-..." + n.Substring(n.Length - 256) + "/..." + s.Substring(s.Length - 256), a.ToString());
}
}
}
public void RationalConstructorFromULong()
{
var n = Platform.Ui(ulong.MaxValue, uint.MaxValue);
var d = Platform.Ui(12764787846358441471U, 2860486313U);
using (var a = new HugeRational(n, d))
{
Assert.AreEqual(1, a.NumeratorNumberOfLimbsAllocated());
Assert.AreEqual(1, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsAllocated());
Assert.AreEqual(1, a.DenominatorNumberOfLimbsUsed());
Assert.AreEqual(n.ToString(), a.Numerator.ToString());
Assert.AreEqual(n.ToString() + "/" + d, a.ToString());
}
}
public void RationalFromString()
{
using (var a = new HugeRational())
{
var n = "98762934876529834765234123984761/115756986668303657898962467957";
a.SetTo(n);
Assert.AreEqual(n, a.ToString());
n = "-98ABCDEF876529834765234123984761/17607EF654EB9A13FFA163C75";
a.SetTo(n, 16);
Assert.AreEqual(n, a.ToString(16));
n = "-98ABCDEF876529834765234123984761";
a.SetTo(n, 16);
Assert.AreEqual(n + "/1", a.ToString(16));
}
}
public void RationalStringConstructor()
{
var n = "5432109876543212345789023245987/362736035870515331128527330659";
using (var a = new HugeRational(n))
{
Assert.AreEqual(128 / MpirSettings.BITS_PER_LIMB, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(n, a.ToString());
}
}
public void RationalDivideHugeRational()
{
using (var a = new HugeRational("115756986668303657898962467957/394580293847502987609283945873594873409587"))
using (var b = new HugeRational("593169091750307653294"))
{
a.Value = a / b;
Assert.AreEqual("115756986668303657898962467957/234052834524092854092760134269509268758750275703033222451729578", a.ToString());
}
}
public void RationalStringConstructorNumeratorOnly()
{
var n = "5432109876543212345789023245987";
using(var a = new HugeRational(n))
{
Assert.AreEqual(128 / MpirSettings.BITS_PER_LIMB, a.NumeratorNumberOfLimbsUsed());
Assert.AreEqual(n + "/1", a.ToString());
}
}
public void RationalDivideLimbBy()
{
using(var a = new HugeRational("115756986668303657898962467957/39458029384750298767200622330399462537522498"))
{
var b = Platform.Ui(5931690917503076532, 3367900313);
a.Value = b / a;
Assert.AreEqual(Platform.Select(
"234052834524092854092874502983745029345723092857791404165816936/115756986668303657898962467957",
"132890709515263728644898490080347139295153795258741874/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalInvert()
{
using (var a = new HugeRational("-24092854092874502983745029345723098457209/115756986668303657898962467957"))
{
a.Value = a.Invert();
Assert.AreEqual("-115756986668303657898962467957/24092854092874502983745029345723098457209", a.ToString());
a.Value = a.Invert();
Assert.AreEqual("-24092854092874502983745029345723098457209/115756986668303657898962467957", a.ToString());
}
}
public void RationalDivideSignedLimbBy()
{
using(var a = new HugeRational("115756986668303657898962467957/39458029384750298767200622330399462537522498"))
{
var b = Platform.Si(-5931690917503076532, -1500450271);
a.Value = b / a;
Assert.AreEqual(Platform.Select(
"-234052834524092854092874502983745029345723092857791404165816936/115756986668303657898962467957",
"-59204810883474549052577139687016525102679979792696958/115756986668303657898962467957"),
a.ToString());
}
}
public void RationalConstructorFromIntExpression()
{
using (var a = new HugeInt("2340958273409578234095823045723490587"))
using (var b = new HugeRational(a + 1))
{
Assert.AreEqual("2340958273409578234095823045723490588/1", b.ToString());
}
}
public void RationalAssignInt2()
{
using (var a = new HugeInt("222509832503450298345029835740293845719"))
using (var d = new HugeInt("115756986668303657898962467957"))
using (var b = new HugeRational("1/3"))
{
b.SetTo(a, d);
Assert.AreEqual("222509832503450298345029835740293845719/115756986668303657898962467957", b.ToString());
b.SetTo(b.Numerator - b.Denominator, b.Denominator * 5);
Assert.AreEqual(a - d, b.Numerator);
Assert.AreEqual(d * 5, b.Denominator);
}
}