ComplexNum

java.lang.Object
- org.matheclipse.core.expression.ExprImpl
- - org.matheclipse.core.expression.ComplexNum

All Implemented Interfaces:

edu.jas.structure.AbelianGroupElem<IExpr>, edu.jas.structure.Element<IExpr>, edu.jas.structure.GcdRingElem<IExpr>, edu.jas.structure.MonoidElem<IExpr>, edu.jas.structure.RingElem<IExpr>, java.io.Serializable, java.lang.Comparable<IExpr>, org.apache.commons.math4.FieldElement<IExpr>, IComplexNum, IExpr, INumber
```
public class ComplexNum
extends ExprImpl
implements IComplexNum
```
IComplexNum implementation which wraps a org.apache.commons.math4.complex.Complex value to represent a numeric complex floating-point number.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static ComplexNum`	`I` The square root of -1.
`static ComplexNum`	`NaN` A complex number representing "NaN + NaNi"
`static ComplexNum`	`ONE` A complex number representing "1.0 + 0.0i"
`static ComplexNum`	`ZERO` A complex number representing "0.0 + 0.0i"

Fields inherited from interface org.matheclipse.core.interfaces.IExpr
ASTID, BLANKID, COMPLEXID, DOUBLECOMPLEXID, DOUBLEID, FRACTIONID, INTEGERID, METHODSYMBOLID, PATTERNID, STRINGID, SYMBOLID

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`<T> T`	`accept(IVisitor<T> visitor)` Accept a visitor with return type T
`boolean`	`accept(IVisitorBoolean visitor)` Accept a visitor with return type `boolean`
`int`	`accept(IVisitorInt visitor)` Accept a visitor with return type `int`
`long`	`accept(IVisitorLong visitor)` Accept a visitor with return type `long`
`org.apache.commons.math4.complex.Complex`	`add(org.apache.commons.math4.complex.Complex that)`
`ComplexNum`	`add(ComplexNum that)`
`IComplexNum`	`add(IComplexNum val)`
`ApcomplexNum`	`apcomplexNumValue(long precision)` Get a `Apcomplex` number wrapped into an `ApcomplexNum` object.
`org.apfloat.Apcomplex`	`apcomplexValue(long precision)`
`INumber`	`ceilFraction()` Returns the smallest (closest to negative infinity) `IInteger` value that is not less than `this` and is equal to a mathematical integer.
`int`	`compareAbsValueToOne()` Compare the absolute value of this number with `1` and return `1`, if the absolute value is greater than 1 `0`, if the absolute value equals 1 `-1`, if the absolute value is less than 1
`int`	`compareTo(org.apache.commons.math4.complex.Complex that)`
`int`	`compareTo(IExpr expr)` Compares this expression with the specified expression for order.
`ComplexNum`	`complexNumValue()` Get a `ComplexNum` number bject.
`int`	`complexSign()` Gets the signum value of a complex number
`org.apache.commons.math4.complex.Complex`	`complexValue()`
`IComplexNum`	`conjugate()` Conjugate this (complex-) number.
`double`	`dabs()` Return the absolute value of this complex number.
`static double`	`dabs(org.apache.commons.math4.complex.Complex c)`
`org.apache.commons.math4.complex.Complex`	`divide(org.apache.commons.math4.complex.Complex that)`
`ComplexNum`	`divide(ComplexNum that)`
`Num`	`eabs()` Get the absolute value for a given number
`boolean`	`equals(java.lang.Object obj)` Test if this is equal to b.
`boolean`	`equalsInt(int i)` Check if this number equals the given `int` number?
`IExpr`	`evaluate(EvalEngine engine)` Evaluate an expression
`INumber`	`floorFraction()` Returns the largest (closest to positive infinity) `IInteger` value that is not greater than `this` and is equal to a mathematical integer.
`org.apache.commons.math4.complex.Complex`	`getCMComplex()`
`ISignedNumber`	`getIm()` Returns the imaginary part of a complex number
`double`	`getImaginary()` Returns the imaginary part of a complex number
`double`	`getImaginaryPart()`
`ISignedNumber`	`getRe()` Returns the real part of a complex number
`double`	`getReal()` Returns the real part of a complex number
`double`	`getRealPart()`
`int`	`hashCode()` Hashcode of this Element.
`ISymbol`	`head()` If this object is an instance of `IAST` get the first element (offset 0) of the `IAST` list (i.e. get(0) ).
`int`	`hierarchy()` A unique integer ID for the implementation of this expression
`java.lang.String`	`internalFormString(boolean symbolsAsFactoryMethod, int depth)` Return the internal Java form of this expression.
`java.lang.String`	`internalJavaString(boolean symbolsAsFactoryMethod, int depth, boolean useOperators)` Return the internal Java form of this expression.
`java.lang.String`	`internalScalaString(boolean symbolsAsFactoryMethod, int depth)` Return the internal Scala form of this expression.
`IExpr`	`inverse()` Returns the multiplicative inverse of this object.
`boolean`	`isInfinite()`
`boolean`	`isNaN()`
`boolean`	`isSame(IExpr expression, double epsilon)` Test if this expression equals the given expression.
`boolean`	`isZero()` Test if this expression equals `0` in symbolic or numeric mode.
`ComplexNum`	`multiply(ComplexNum that)`
`IComplexNum`	`multiply(IComplexNum val)`
`ComplexNum`	`negate()` Negate this.
`protected static ComplexNum`	`newInstance(org.apache.commons.math4.complex.Complex value)` Be cautious with this method, no new internal couble complex is created
`INumber`	`opposite()` Returns an `IExpr` whose value is `(-1) * this`.
`IExpr`	`plus(IExpr that)` Returns an `IExpr` whose value is `(this + that)`.
`IComplexNum`	`pow(IComplexNum val)`
`org.apache.commons.math4.complex.Complex`	`subtract(org.apache.commons.math4.complex.Complex that)`
`ComplexNum`	`subtract(ComplexNum that)`
`IExpr`	`times(IExpr that)` Returns an `IExpr` whose value is `(this * that)`.
`java.lang.String`	`toString()`
`static ComplexNum`	`valueOf(org.apache.commons.math4.complex.Complex c)`
`static ComplexNum`	`valueOf(double real)`
`static ComplexNum`	`valueOf(double real, double imaginary)`
`static ComplexNum`	`valueOf(INum d)`

Methods inherited from class org.matheclipse.core.expression.ExprImpl
$div, $minus, $plus, $times, $up, abs, and, apply, apply, asType, copy, dec, divide, egcd, evalComplex, evalDouble, evalNumber, evalSignedNumber, factory, fullFormString, gcd, getAt, inc, leafCount, leaves, minus, mod, multiply, negative, optional, or, power, power, remainder, replaceAll, replaceAll, replacePart, replaceRepeated, replaceRepeated, replaceRepeated, replaceSlots, signum, subtract, sum, topHead, toScript, toScriptFactory, variables2Slots

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.matheclipse.core.interfaces.IExpr
$div, $minus, $plus, $times, $up, and, apply, apply, asType, dec, divide, evalComplex, evalDouble, evalNumber, evalSignedNumber, evaluateHead, fullFormString, getAt, getField, ifPresent, inc, isAllExpanded, isAnd, isArcCos, isArcCosh, isArcSin, isArcSinh, isArcTan, isArcTanh, isAST, isAST, isAST, isAST, isAST, isAST, isAST, isASTSizeGE, isAtom, isBlank, isComplex, isComplexInfinity, isComplexNumeric, isCondition, isConstant, isCos, isCosh, isDerivative, isDirectedInfinity, isE, isExpanded, isFalse, isFlatAST, isFraction, isFree, isFree, isFree, isFreeAST, isFreeAST, isFreeOfPatterns, isFunction, isGEOrdered, isGTOrdered, isIndeterminate, isInfinity, isInteger, isIntegerResult, isLEOrdered, isList, isListOfLists, isLog, isLTOrdered, isMatrix, isMember, isMember, isMinusOne, isModule, isNegative, isNegativeInfinity, isNegativeResult, isNonNegativeResult, isNot, isNumber, isNumEqualInteger, isNumEqualRational, isNumeric, isNumericFunction, isNumericMode, isNumIntValue, isOne, isONE, isOr, isOrderlessAST, isPattern, isPatternDefault, isPatternExpr, isPatternSequence, isPi, isPlus, isPlusTimesPower, isPolynomial, isPolynomial, isPolynomialOfMaxDegree, isPositive, isPositiveResult, isPower, isPresent, isRational, isRationalResult, isRationalValue, isRealResult, isRuleAST, isSame, isSequence, isSignedNumber, isSin, isSinh, isSlot, isSlotSequence, isSpan, isSymbol, isTan, isTanh, isTimes, isTrue, isUnit, isValue, isVariable, isVector, isZERO, leafCount, leaves, minus, mod, multiply, multiply, negative, ofNullable, optional, or, orElse, orElseGet, orElseThrow, power, power, reciprocal, replaceAll, replaceAll, replacePart, replaceRepeated, replaceRepeated, replaceSlots, signum, subtract, sum, timesDistributed, topHead, variables2Slots

Methods inherited from interface edu.jas.structure.RingElem
egcd, gcd

Methods inherited from interface edu.jas.structure.AbelianGroupElem
abs

Methods inherited from interface edu.jas.structure.MonoidElem
remainder

Methods inherited from interface edu.jas.structure.Element
copy, factory, toScript, toScriptFactory

- Field Detail
  - I
```
public static final ComplexNum I
```
    The square root of -1. A number representing "0.0 + 1.0i"
  - NaN
```
public static final ComplexNum NaN
```
    A complex number representing "NaN + NaNi"
  - ONE
```
public static final ComplexNum ONE
```
    A complex number representing "1.0 + 0.0i"
  - ZERO
```
public static final ComplexNum ZERO
```
    A complex number representing "0.0 + 0.0i"
- Method Detail
  - newInstance
```
protected static ComplexNum newInstance(org.apache.commons.math4.complex.Complex value)
```
    Be cautious with this method, no new internal couble complex is created
    
    Parameters:
    
    numerator -
    
    Returns:
  - valueOf
```
public static ComplexNum valueOf(INum d)
```
  - valueOf
```
public static ComplexNum valueOf(org.apache.commons.math4.complex.Complex c)
```
  - valueOf
```
public static ComplexNum valueOf(double real)
```
  - valueOf
```
public static ComplexNum valueOf(double real,
                                 double imaginary)
```
  - getImaginaryPart
```
public double getImaginaryPart()
```
    Specified by:
    
    getImaginaryPart in interface IComplexNum
    
    Returns:
  - getRealPart
```
public double getRealPart()
```
    Specified by:
    
    getRealPart in interface IComplexNum
    
    Returns:
  - isZero
```
public boolean isZero()
```
    Description copied from interface: IExpr
    
    Test if this expression equals 0 in symbolic or numeric mode.
    
    Specified by:
    
    isZero in interface IExpr
  - hierarchy
```
public int hierarchy()
```
    Description copied from interface: IExpr
    
    A unique integer ID for the implementation of this expression
    
    Specified by:
    
    hierarchy in interface IExpr
    
    Returns:
    
    a unique integer id for the implementation of this expression
  - add
```
public IComplexNum add(IComplexNum val)
```
    Specified by:
    
    add in interface IComplexNum
  - add
```
public ComplexNum add(ComplexNum that)
```
  - apcomplexValue
```
public org.apfloat.Apcomplex apcomplexValue(long precision)
```
  - apcomplexNumValue
```
public ApcomplexNum apcomplexNumValue(long precision)
```
    Description copied from interface: INumber
    
    Get a Apcomplex number wrapped into an ApcomplexNum object.
    
    Specified by:
    
    apcomplexNumValue in interface INumber
    
    Parameters:
    
    precision - set the precision of the resulting ApcomplexNum
    
    Returns:
    
    this signed number represented as an ApcomplexNum
  - complexNumValue
```
public ComplexNum complexNumValue()
```
    Description copied from interface: INumber
    
    Get a ComplexNum number bject.
    
    Specified by:
    
    complexNumValue in interface INumber
    
    Returns:
  - multiply
```
public IComplexNum multiply(IComplexNum val)
```
    Specified by:
    
    multiply in interface IComplexNum
  - pow
```
public IComplexNum pow(IComplexNum val)
```
    Specified by:
    
    pow in interface IComplexNum
  - add
```
public org.apache.commons.math4.complex.Complex add(org.apache.commons.math4.complex.Complex that)
```
    Parameters:
    
    that -
    
    Returns:
  - conjugate
```
public IComplexNum conjugate()
```
    Conjugate this (complex-) number.
    
    Specified by:
    
    conjugate in interface IComplexNum
    
    Specified by:
    
    conjugate in interface INumber
    
    Overrides:
    
    conjugate in class ExprImpl
    
    Returns:
    
    the conjugate complex number
  - divide
```
public org.apache.commons.math4.complex.Complex divide(org.apache.commons.math4.complex.Complex that)
```
    Parameters:
    
    that -
    
    Returns:
  - divide
```
public ComplexNum divide(ComplexNum that)
                  throws java.lang.ArithmeticException
```
    Throws:
    
    java.lang.ArithmeticException
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Description copied from interface: edu.jas.structure.Element
    
    Test if this is equal to b.
    
    Specified by:
    
    equals in interface edu.jas.structure.Element<IExpr>
    
    Overrides:
    
    equals in class java.lang.Object
    
    Returns:
    
    true if this is equal to b, else false.
  - evaluate
```
public IExpr evaluate(EvalEngine engine)
```
    Evaluate an expression
    
    Specified by:
    
    evaluate in interface IExpr
    
    Parameters:
    
    engine - the evaluation engine
    
    Returns:
    
    the evaluated Object or F.NIL if the evaluation is not possible (i.e. the evaluation doesn't change the object).
  - isSame
```
public boolean isSame(IExpr expression,
                      double epsilon)
```
    Description copied from interface: IExpr
    
    Test if this expression equals the given expression. If the compared expressions are of the same numeric type, they are equal to a given EPSILON
    
    Specified by:
    
    isSame in interface IExpr
  - dabs
```
public double dabs()
```
    Return the absolute value of this complex number.
    Returns NaN if either real or imaginary part is NaN and Double.POSITIVE_INFINITY if neither part is NaN, but at least one part takes an infinite value.
    
    Specified by:
    
    dabs in interface IComplexNum
    
    Returns:
    
    the absolute value
  - dabs
```
public static double dabs(org.apache.commons.math4.complex.Complex c)
```
  - eabs
```
public Num eabs()
```
    Description copied from interface: INumber
    
    Get the absolute value for a given number
    
    Specified by:
    
    eabs in interface INumber
    
    Returns:
  - compareAbsValueToOne
```
public int compareAbsValueToOne()
```
    Compare the absolute value of this number with 1 and return
    - 1, if the absolute value is greater than 1
    - 0, if the absolute value equals 1
    - -1, if the absolute value is less than 1
    Specified by:
    
    compareAbsValueToOne in interface INumber
    
    Returns:
  - getImaginary
```
public double getImaginary()
```
    Description copied from interface: INumber
    
    Returns the imaginary part of a complex number
    
    Specified by:
    
    getImaginary in interface INumber
    
    Returns:
    
    real part
  - getReal
```
public double getReal()
```
    Description copied from interface: INumber
    
    Returns the real part of a complex number
    
    Specified by:
    
    getReal in interface INumber
    
    Returns:
    
    real part
  - hashCode
```
public final int hashCode()
```
    Description copied from interface: edu.jas.structure.Element
    
    Hashcode of this Element.
    
    Specified by:
    
    hashCode in interface edu.jas.structure.Element<IExpr>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
  - isInfinite
```
public boolean isInfinite()
```
    Returns:
  - isNaN
```
public boolean isNaN()
```
    Returns:
  - multiply
```
public ComplexNum multiply(ComplexNum that)
```
    Parameters:
    
    that -
    
    Returns:
  - negate
```
public ComplexNum negate()
```
    Description copied from class: ExprImpl
    
    Negate this.
    
    Specified by:
    
    negate in interface edu.jas.structure.AbelianGroupElem<IExpr>
    
    Specified by:
    
    negate in interface org.apache.commons.math4.FieldElement<IExpr>
    
    Overrides:
    
    negate in class ExprImpl
    
    Returns:
  - opposite
```
public INumber opposite()
```
    Description copied from class: ExprImpl
    
    Returns an IExpr whose value is (-1) * this. Calculates F.eval(F.Times(F.CN1, this)) in the common case and uses a specialized implementation for derived number classes.
    
    Specified by:
    
    opposite in interface IExpr
    
    Specified by:
    
    opposite in interface INumber
    
    Overrides:
    
    opposite in class ExprImpl
    
    Returns:
    
    See Also:
    
    IExpr.negative()
  - plus
```
public IExpr plus(IExpr that)
```
    Description copied from class: ExprImpl
    
    Returns an IExpr whose value is (this + that). Calculates F.eval(F.Plus(this, that)) in the common case and uses a specialized implementation for derived number classes.
    
    Specified by:
    
    plus in interface IExpr
    
    Overrides:
    
    plus in class ExprImpl
    
    Parameters:
    
    that -
    
    Returns:
  - inverse
```
public IExpr inverse()
```
    Description copied from class: ExprImpl
    
    Returns the multiplicative inverse of this object. It is the object such as this.times(this.inverse()) == ONE , with ONE being the multiplicative identity. Calculates F.eval(F.Power(this, F.CN1)) in the common case and uses a specialized implmentation for derived number classes.
    
    Specified by:
    
    inverse in interface edu.jas.structure.MonoidElem<IExpr>
    
    Specified by:
    
    inverse in interface IExpr
    
    Overrides:
    
    inverse in class ExprImpl
    
    Returns:
    
    ONE / this.
  - subtract
```
public org.apache.commons.math4.complex.Complex subtract(org.apache.commons.math4.complex.Complex that)
```
    Parameters:
    
    that -
    
    Returns:
  - subtract
```
public ComplexNum subtract(ComplexNum that)
```
  - times
```
public IExpr times(IExpr that)
```
    Description copied from class: ExprImpl
    
    Returns an IExpr whose value is (this * that). Calculates F.eval(F.Times(this, that)) in the common case and uses a specialized implementation for derived number classes.
    
    Specified by:
    
    times in interface IExpr
    
    Overrides:
    
    times in class ExprImpl
    
    Parameters:
    
    that -
    
    Returns:
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - internalFormString
```
public java.lang.String internalFormString(boolean symbolsAsFactoryMethod,
                                           int depth)
```
    Description copied from class: ExprImpl
    
    Return the internal Java form of this expression.
    
    Specified by:
    
    internalFormString in interface IExpr
    
    Overrides:
    
    internalFormString in class ExprImpl
    
    Parameters:
    
    symbolsAsFactoryMethod - if true use the F.symbol() method, otherwise print the symbol name.
    
    depth - the recursion depth of this call. 0 indicates "recurse without a limit".
  - internalScalaString
```
public java.lang.String internalScalaString(boolean symbolsAsFactoryMethod,
                                            int depth)
```
    Description copied from class: ExprImpl
    
    Return the internal Scala form of this expression.
    
    Specified by:
    
    internalScalaString in interface IExpr
    
    Overrides:
    
    internalScalaString in class ExprImpl
    
    Parameters:
    
    symbolsAsFactoryMethod - if true use the F.symbol() method, otherwise print the symbol name.
    
    depth - the recursion depth of this call. 0 indicates "recurse without a limit".
  - internalJavaString
```
public java.lang.String internalJavaString(boolean symbolsAsFactoryMethod,
                                           int depth,
                                           boolean useOperators)
```
    Description copied from class: ExprImpl
    
    Return the internal Java form of this expression.
    
    Specified by:
    
    internalJavaString in interface IExpr
    
    Overrides:
    
    internalJavaString in class ExprImpl
    
    Parameters:
    
    symbolsAsFactoryMethod - if true use the F.symbol() method, otherwise print the symbol name.
    
    depth - the recursion depth of this call. 0 indicates "recurse without a limit".
    
    useOperators - use operators instead of function names for representation of Plus, Times, Power,...
  - complexSign
```
public int complexSign()
```
    Description copied from interface: INumber
    
    Gets the signum value of a complex number
    
    Specified by:
    
    complexSign in interface INumber
    
    Returns:
    
    0 for this == 0; +1 for real(this) > 0 or ( real(this)==0 && imaginary(this) > 0 ); -1 for real(this) < 0 || ( real(this) == 0 && imaginary(this) < 0 )
  compareTo public int compareTo(org.apache.commons.math4.complex.Complex that) compareTo public int compareTo(IExpr expr) Compares this expression with the specified expression for order. Returns a negative integer, zero, or a positive integer as this expression is canonical less than, equal to, or greater than the specified expression. Specified by: compareTo in interface edu.jas.structure.Element<IExpr> Specified by: compareTo in interface java.lang.Comparable<IExpr> Specified by: compareTo in interface IExpr Overrides: compareTo in class ExprImpl Returns: 0 if this is equal to b, -1 if this is less then b, else +1. head public ISymbol head() Description copied from class: ExprImpl If this object is an instance of IAST get the first element (offset 0) of the IAST list (i.e. get(0) ). Specified by: head in interface IExpr Specified by: head in class ExprImpl Returns: the head of the expression, which must not be null. complexValue public org.apache.commons.math4.complex.Complex complexValue() getCMComplex public org.apache.commons.math4.complex.Complex getCMComplex() accept public <T> T accept(IVisitor<T> visitor) Accept a visitor with return type T Specified by: accept in interface IExpr accept public boolean accept(IVisitorBoolean visitor) Accept a visitor with return type boolean Specified by: accept in interface IExpr accept public int accept(IVisitorInt visitor) Accept a visitor with return type int Specified by: accept in interface IExpr Returns: accept public long accept(IVisitorLong visitor) Accept a visitor with return type long Specified by: accept in interface IExpr Returns: equalsInt public boolean equalsInt(int i) Description copied from interface: INumber Check if this number equals the given int number? Specified by: equalsInt in interface INumber Parameters: i - the integer number Returns: getIm public ISignedNumber getIm() Returns the imaginary part of a complex number Specified by: getIm in interface INumber Returns: real part getRe public ISignedNumber getRe() Returns the real part of a complex number Specified by: getRe in interface INumber Returns: real part ceilFraction public INumber ceilFraction() throws java.lang.ArithmeticException Description copied from interface: INumber Returns the smallest (closest to negative infinity) IInteger value that is not less than this and is equal to a mathematical integer. This method raises ArithmeticException if a numeric value cannot be represented by an long type. Specified by: ceilFraction in interface INumber Returns: the smallest (closest to negative infinity) IInteger value that is not less than this and is equal to a mathematical integer. Throws: java.lang.ArithmeticException floorFraction public INumber floorFraction() throws java.lang.ArithmeticException Description copied from interface: INumber Returns the largest (closest to positive infinity) IInteger value that is not greater than this and is equal to a mathematical integer. This method raises ArithmeticException if a numeric value cannot be represented by an long type. Specified by: floorFraction in interface INumber Returns: the largest (closest to positive infinity) IInteger value that is not greater than this and is equal to a mathematical integer. Throws: java.lang.ArithmeticException

Class ComplexNum

Field Summary

Fields inherited from interface org.matheclipse.core.interfaces.IExpr

Method Summary

Methods inherited from class org.matheclipse.core.expression.ExprImpl

Methods inherited from class java.lang.Object

Methods inherited from interface org.matheclipse.core.interfaces.IExpr

Methods inherited from interface edu.jas.structure.RingElem

Methods inherited from interface edu.jas.structure.AbelianGroupElem

Methods inherited from interface edu.jas.structure.MonoidElem

Methods inherited from interface edu.jas.structure.Element

Field Detail

I

NaN

ONE

ZERO

Method Detail

newInstance

valueOf

valueOf

valueOf

valueOf

getImaginaryPart

getRealPart

isZero

hierarchy

add

add

apcomplexValue

apcomplexNumValue

complexNumValue

multiply

pow

add

conjugate

divide

divide

equals

evaluate

isSame

dabs

dabs

eabs

compareAbsValueToOne

getImaginary

getReal

hashCode

isInfinite

isNaN

multiply

negate

opposite

plus

inverse

subtract

subtract

times

toString

internalFormString

internalScalaString

internalJavaString

complexSign

compareTo

compareTo

head

complexValue

getCMComplex

accept

accept

accept

accept

equalsInt

getIm

getRe

ceilFraction

floorFraction