IntegerSym

java.lang.Object
- org.matheclipse.core.expression.ExprImpl
- - org.matheclipse.core.expression.AbstractIntegerSym
  - - org.matheclipse.core.expression.IntegerSym

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.Externalizable, java.io.Serializable, java.lang.Comparable<IExpr>, org.apache.commons.math4.FieldElement<IExpr>, IBigNumber, IExpr, IInteger, INumber, IRational, ISignedNumber
```
public class IntegerSym
extends AbstractIntegerSym
```
IInteger implementation which uses an internal int value

See Also:

AbstractIntegerSym, BigIntegerSym, Serialized Form

Field Summary
- Fields inherited from class org.matheclipse.core.expression.AbstractIntegerSym
  BI_MINUS_ONE
- Fields inherited from interface org.matheclipse.core.interfaces.IInteger
  PRIME_CERTAINTY
- Fields inherited from interface org.matheclipse.core.interfaces.IExpr
  ASTID, BLANKID, COMPLEXID, DOUBLECOMPLEXID, DOUBLEID, FRACTIONID, INTEGERID, METHODSYMBOLID, PATTERNID, STRINGID, SYMBOLID

Constructor Summary

Constructors
Constructor and Description
`IntegerSym()` do not use directly, needed for serialization/deserialization
`IntegerSym(int value)` do not use directly, needed for serialization/deserialization

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`IInteger`	`add(IInteger that)`
`IRational`	`add(IRational parm1)`
`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`	`compareInt(int value)`
`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
`IInteger`	`div(IInteger that)`
`IInteger[]`	`divideAndRemainder(IInteger that)` Returns an array of two IIntegers containing (this / that) followed by (this % that).
`ISignedNumber`	`divideBy(ISignedNumber that)` Divide `this` signed number by `that` signed number.
`IAST`	`divisors()` Return the divisors of this integer number.
`double`	`doubleValue()`
`IInteger`	`eabs()` Get the absolute value for a given number
`IExpr[]`	`egcd(IExpr that)` IntegerSym extended greatest common divisor.
`boolean`	`equals(java.lang.Object obj)` Test if this is equal to b.
`boolean`	`equalsFraction(int numerator, int denominator)` Check if this number equals the given fraction `numerator/denominator` number.
`boolean`	`equalsInt(int value)` Check if this number equals the given `int` number?
`IExpr`	`exponent(IInteger base)` Get the highest exponent of `base` that divides `this`
`IAST`	`factorInteger()` Return the factors paired with their exponents for integer and fractional numbers.
`IAST`	`factorize(IAST result)` Get all prime factors of this integer
`IInteger`	`gcd(IInteger that)` Returns the greatest common divisor of this large integer and the one specified.
`java.math.BigInteger`	`getBigDenominator()` Returns the denominator of this fraction.
`java.math.BigInteger`	`getBigNumerator()` Returns the numerator of this Rational.
`IInteger`	`getDenominator()` Returns the denominator of this fraction.
`org.apache.commons.math4.fraction.BigFraction`	`getFraction()` Returns this number as `BigFraction` number.
`ISignedNumber`	`getIm()` Returns the imaginary part of a complex number
`IInteger`	`getNumerator()` Returns the numerator of this fraction.
`ISignedNumber`	`getRe()` Returns the real part of a complex number
`int`	`hashCode()` Hashcode of this Element.
`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.
`int`	`intValue()` Converts this large integer to `int`; unlike `ISignedNumber.toInt()` this method raises no exception, if this integer cannot be represented by an `int` type.
`ISignedNumber`	`inverse()` Returns the multiplicative inverse of this object.
`boolean`	`isEven()`
`boolean`	`isGreaterThan(ISignedNumber obj)` Test if `this` signed number is greater `than` that signed number..
`boolean`	`isLargerThan(java.math.BigInteger that)`
`boolean`	`isLessThan(ISignedNumber obj)` Test if `this` signed number is less `than` that signed number..
`boolean`	`isMinusOne()` Test if this expression equals `-1` in symbolic or numeric mode.
`boolean`	`isNegative()` Test if this object is a negative signed number.
`boolean`	`isOdd()`
`boolean`	`isOne()` Test if this expression equals `1` in symbolic or numeric mode.
`boolean`	`isPositive()` Test if this object is a positive signed number.
`boolean`	`isProbablePrime()`
`boolean`	`isProbablePrime(int certainty)`
`boolean`	`isRationalValue(IRational value)` Test if this expression equals `value` in symbolic or numeric mode.
`boolean`	`isZero()` Test if this expression equals `0` in symbolic or numeric mode.
`long`	`longValue()`
`IInteger`	`mod(IInteger that)`
`IInteger`	`modInverse(IInteger that)`
`IInteger`	`modPow(IInteger exp, IInteger that)`
`IInteger`	`moebiusMu()`
`IInteger`	`multiply(IInteger that)` Multiply this integer with value
`IRational`	`multiply(IRational parm1)`
`IntegerSym`	`negate()` Negate this.
`INumber`	`normalize()` Return the normalized form of this number (i.e. if the denominator part equals one, return the numerator part as an integer number).
`IInteger`	`nthRoot(int n)` Returns the nth-root of this integer.
`IInteger[]`	`nthRootSplit(int n)` Split this integer into the nth-root (with prime factors less equal 1021) and the "rest-factor", so that `this== (nth-root)^n + rest`
`INumber`	`numericNumber()` Create a numeric number from this exact "symbolic" number.
`Num`	`numValue()` Get a Java double number wrapped into a `Num` object.
`IInteger`	`quotient(IInteger that)`
`void`	`readExternal(java.io.ObjectInput objectInput)`
`IExpr`	`remainder(IExpr that)` Remainder after division of this by S.
`IInteger`	`remainder(IInteger that)`
`IInteger`	`round()` Returns the closest `IInteger` to the argument.
`IInteger`	`shiftLeft(int n)`
`IInteger`	`shiftRight(int n)`
`int`	`sign()` Returns the signum function of this number (i.e., -1, 0 or 1 as the value of this number is negative, zero or positive).
`IInteger`	`sqrt()` Returns the integer square root of this integer.
`IInteger`	`subtract(IInteger that)`
`IRational`	`subtract(IRational parm1)`
`int`	`toInt()` Converts this number to `int`; unlike `#intValue` this method raises `ArithmeticException` if this number cannot be represented by an `int` type.
`long`	`toLong()` Converts this number to `long`; unlike `#longValue` this method raises `ArithmeticException` if this number cannot be represented by an `long` type.
`java.lang.String`	`toString()`
`void`	`writeExternal(java.io.ObjectOutput objectOutput)`

Methods inherited from class org.matheclipse.core.expression.AbstractIntegerSym
abs, accept, accept, accept, accept, apcomplexNumValue, apcomplexValue, apfloatNumValue, ceil, ceilFraction, divideBy, eulerPhi, evaluate, floor, floorFraction, gcd, getImaginary, getReal, head, hierarchy, internalFormString, isNumEqualInteger, isNumEqualRational, isNumIntValue, jacobiSymbol, jacobiSymbolF, jacobiSymbolG, lcm, lcm, multiply, opposite, plus, pow, primitiveRoots, subtractFrom, times, toByteArray, valueOf, valueOf, valueOf, valueOf

Methods inherited from class org.matheclipse.core.expression.ExprImpl
$div, $minus, $plus, $times, $up, and, apply, apply, asType, conjugate, copy, dec, divide, evalComplex, evalDouble, evalNumber, evalSignedNumber, factory, fullFormString, getAt, inc, leafCount, leaves, minus, mod, multiply, negative, optional, or, power, power, 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.INumber
conjugate

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, isModule, isNegativeInfinity, isNegativeResult, isNonNegativeResult, isNot, isNumber, isNumeric, isNumericFunction, isNumericMode, isONE, isOr, isOrderlessAST, isPattern, isPatternDefault, isPatternExpr, isPatternSequence, isPi, isPlus, isPlusTimesPower, isPolynomial, isPolynomial, isPolynomialOfMaxDegree, isPositiveResult, isPower, isPresent, isRational, isRationalResult, isRealResult, isRuleAST, isSame, 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.Element
copy, factory, toScript, toScriptFactory

- Constructor Detail
  - IntegerSym
```
public IntegerSym()
```
    do not use directly, needed for serialization/deserialization
  - IntegerSym
```
public IntegerSym(int value)
```
    do not use directly, needed for serialization/deserialization
- Method Detail
  - add
```
public IInteger add(IInteger that)
```
    Parameters:
    
    that -
    
    Returns:
  - add
```
public IRational add(IRational parm1)
```
  - 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
    Returns:
  - compareInt
```
public int compareInt(int value)
```
  - 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.
  - complexNumValue
```
public ComplexNum complexNumValue()
```
    Description copied from interface: INumber
    
    Get a ComplexNum number bject.
    
    Returns:
  - complexSign
```
public int complexSign()
```
    Description copied from interface: INumber
    
    Gets the signum value of a complex number
    
    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 )
  div public IInteger div(IInteger that) divideAndRemainder public IInteger[] divideAndRemainder(IInteger that) Returns an array of two IIntegers containing (this / that) followed by (this % that). Returns: divideBy public ISignedNumber divideBy(ISignedNumber that) Description copied from interface: ISignedNumber Divide this signed number by that signed number. Parameters: that - a signed number Returns: divisors public IAST divisors() Return the divisors of this integer number. divisors(24) ==> {1,2,3,4,6,8,12,24} doubleValue public double doubleValue() Returns: eabs public IInteger eabs() Get the absolute value for a given number Returns: egcd public IExpr[] egcd(IExpr that) IntegerSym extended greatest common divisor. Specified by: egcd in interface edu.jas.structure.RingElem<IExpr> Overrides: egcd in class ExprImpl Parameters: that - if that is of type IntegerSym calculate the extended GCD otherwise call super#egcd(IExpr); Returns: [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S). 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. equalsFraction public final boolean equalsFraction(int numerator, int denominator) Description copied from interface: IRational Check if this number equals the given fraction numerator/denominator number. GCD(numerator, /denominator) should be 1; Parameters: numerator - the numerator denominator - the denominator Returns: equalsInt public boolean equalsInt(int value) Description copied from interface: INumber Check if this number equals the given int number? Parameters: value - the integer number Returns: exponent public IExpr exponent(IInteger base) Get the highest exponent of base that divides this Parameters: base - an integer greater than 1 Returns: the exponent factorInteger public IAST factorInteger() Return the factors paired with their exponents for integer and fractional numbers. For factors of the denominator part of fractional numbers the exponents are negative. factorInteger(-4) ==> {{-1,1},{2,2}} factorize public IAST factorize(IAST result) Get all prime factors of this integer Returns: gcd public IInteger gcd(IInteger that) Returns the greatest common divisor of this large integer and the one specified. getBigDenominator public java.math.BigInteger getBigDenominator() Returns the denominator of this fraction. Returns: denominator getBigNumerator public java.math.BigInteger getBigNumerator() Returns the numerator of this Rational. Returns: numerator getDenominator public IInteger getDenominator() Returns the denominator of this fraction. Returns: denominator getFraction public org.apache.commons.math4.fraction.BigFraction getFraction() Returns this number as BigFraction number. Returns: this number s big fraction. getIm public ISignedNumber getIm() Returns the imaginary part of a complex number Returns: real part getNumerator public IInteger getNumerator() Returns the numerator of this fraction. Returns: denominator getRe public ISignedNumber getRe() Returns the real part of a complex number Returns: real part hashCode public final int hashCode() Hashcode of this Element. Specified by: hashCode in interface edu.jas.structure.Element<IExpr> Overrides: hashCode in class java.lang.Object Returns: the hashCode. 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,... 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". intValue public int intValue() Description copied from interface: IInteger Converts this large integer to int; unlike ISignedNumber.toInt() this method raises no exception, if this integer cannot be represented by an int type. Returns: the numeric value represented by this integer after conversion to type int. inverse public ISignedNumber 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 Specified by: inverse in interface ISignedNumber Specified by: inverse in class AbstractIntegerSym Returns: isEven public boolean isEven() isGreaterThan public boolean isGreaterThan(ISignedNumber obj) Description copied from interface: ISignedNumber Test if this signed number is greater than that signed number.. Returns: this > that isLargerThan public boolean isLargerThan(java.math.BigInteger that) Parameters: that - Returns: isLessThan public boolean isLessThan(ISignedNumber obj) Description copied from interface: ISignedNumber Test if this signed number is less than that signed number.. Returns: this < that isMinusOne public boolean isMinusOne() Description copied from interface: IExpr Test if this expression equals -1 in symbolic or numeric mode. isNegative public boolean isNegative() Test if this object is a negative signed number. For an IAST object the method checks, if it is a numeric constant. If the IAST object evaluates to a negative numeric expression this method returns true. Returns: true, if this < 0; false in all other case. isOdd public boolean isOdd() isOne public boolean isOne() Description copied from interface: IExpr Test if this expression equals 1 in symbolic or numeric mode. isPositive public boolean isPositive() Test if this object is a positive signed number. For an IAST object the method checks, if it is a numeric constant. If the IAST object evaluates to a positive numeric expression this method returns true. Returns: true, if this > 0; false in all other case. isProbablePrime public boolean isProbablePrime() isProbablePrime public boolean isProbablePrime(int certainty) isRationalValue public boolean isRationalValue(IRational value) Test if this expression equals value in symbolic or numeric mode. isZero public boolean isZero() Description copied from interface: IExpr Test if this expression equals 0 in symbolic or numeric mode. longValue public long longValue() Returns: mod public IInteger mod(IInteger that) modInverse public IInteger modInverse(IInteger that) modPow public IInteger modPow(IInteger exp, IInteger that) moebiusMu public IInteger moebiusMu() multiply public IInteger multiply(IInteger that) Description copied from interface: IInteger Multiply this integer with value Parameters: that - Returns: multiply public IRational multiply(IRational parm1) negate public IntegerSym 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> Specified by: negate in interface IInteger Specified by: negate in interface IRational Specified by: negate in interface ISignedNumber Specified by: negate in class AbstractIntegerSym Returns: - this. normalize public INumber normalize() Description copied from interface: IRational Return the normalized form of this number (i.e. if the denominator part equals one, return the numerator part as an integer number). Returns: nthRoot public IInteger nthRoot(int n) throws java.lang.ArithmeticException Returns the nth-root of this integer. Returns: k such as k^n <= this < (k + 1)^n Throws: java.lang.IllegalArgumentException - if this < 0 java.lang.ArithmeticException - if this integer is negative and n is even. nthRootSplit public IInteger[] nthRootSplit(int n) throws java.lang.ArithmeticException Split this integer into the nth-root (with prime factors less equal 1021) and the "rest-factor", so that this== (nth-root)^n + rest Returns: {nth-root, rest} Throws: java.lang.ArithmeticException numericNumber public final INumber numericNumber() Description copied from interface: IBigNumber Create a numeric number from this exact "symbolic" number. Returns: numValue public Num numValue() Description copied from interface: ISignedNumber Get a Java double number wrapped into a Num object. Returns: quotient public IInteger quotient(IInteger that) readExternal public void readExternal(java.io.ObjectInput objectInput) throws java.io.IOException, java.lang.ClassNotFoundException Throws: java.io.IOException java.lang.ClassNotFoundException remainder public IExpr remainder(IExpr that) Description copied from interface: edu.jas.structure.MonoidElem Remainder after division of this by S. Specified by: remainder in interface edu.jas.structure.MonoidElem<IExpr> Overrides: remainder in class ExprImpl Returns: this - (this / S) * S. remainder public IInteger remainder(IInteger that) round public IInteger round() Description copied from interface: ISignedNumber Returns the closest IInteger to the argument. The result is rounded to an integer by adding 1/2 and taking the floor of the result. This method raises ArithmeticException if a numeric value cannot be represented by an long type. Returns: the closest integer to the argument. shiftLeft public IInteger shiftLeft(int n) shiftRight public IInteger shiftRight(int n) sign public int sign() Description copied from interface: ISignedNumber Returns the signum function of this number (i.e., -1, 0 or 1 as the value of this number is negative, zero or positive). Returns: -1 if this is a negative number; 0 if this is a zero; -1 if this is a negative number; sqrt public IInteger sqrt() throws java.lang.ArithmeticException Returns the integer square root of this integer. Returns: k such as k^2 <= this < (k + 1)^2 Throws: java.lang.ArithmeticException - if this integer is negative. subtract public IInteger subtract(IInteger that) subtract public IRational subtract(IRational parm1) Specified by: subtract in interface IRational Overrides: subtract in class AbstractIntegerSym toInt public int toInt() throws java.lang.ArithmeticException Converts this number to int; unlike #intValue this method raises ArithmeticException if this number cannot be represented by an int type. Returns: the numeric value represented by this integer after conversion to type int. Throws: java.lang.ArithmeticException - if conversion to int is not possible. toLong public long toLong() throws java.lang.ArithmeticException Converts this number to long; unlike #longValue this method raises ArithmeticException if this number cannot be represented by an long type. Returns: the numeric value represented by this integer after conversion to type long. Throws: java.lang.ArithmeticException - if conversion to int is not possible. toString public java.lang.String toString() Overrides: toString in class java.lang.Object writeExternal public void writeExternal(java.io.ObjectOutput objectOutput) throws java.io.IOException Throws: java.io.IOException

Class IntegerSym

Field Summary

Fields inherited from class org.matheclipse.core.expression.AbstractIntegerSym

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

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

Constructor Summary

Method Summary

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

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

Methods inherited from class java.lang.Object

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

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

Methods inherited from interface edu.jas.structure.Element

Constructor Detail

IntegerSym

IntegerSym

Method Detail

add

add

compareAbsValueToOne

compareInt

compareTo

complexNumValue

complexSign

div

divideAndRemainder

divideBy

divisors

doubleValue

eabs

egcd

equals

equalsFraction

equalsInt

exponent

factorInteger

factorize

gcd

getBigDenominator

getBigNumerator

getDenominator

getFraction

getIm

getNumerator

getRe

hashCode

internalJavaString

internalScalaString

intValue

inverse

isEven

isGreaterThan

isLargerThan

isLessThan

isMinusOne

isNegative

isOdd

isOne

isPositive

isProbablePrime

isProbablePrime

isRationalValue

isZero

longValue

mod

modInverse

modPow

moebiusMu

multiply

multiply

negate

normalize

nthRoot

nthRootSplit

numericNumber

numValue

quotient

readExternal

remainder

remainder