Package edu.jas.fd
Class SolvableQuotient<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.fd.SolvableQuotient<C>
- All Implemented Interfaces:
AbelianGroupElem<SolvableQuotient<C>>
,Element<SolvableQuotient<C>>
,GcdRingElem<SolvableQuotient<C>>
,MonoidElem<SolvableQuotient<C>>
,QuotPair<GenPolynomial<C>>
,RingElem<SolvableQuotient<C>>
,Serializable
,Comparable<SolvableQuotient<C>>
public class SolvableQuotient<C extends GcdRingElem<C>>
extends Object
implements GcdRingElem<SolvableQuotient<C>>, QuotPair<GenPolynomial<C>>
SolvableQuotient, that is a (left) rational function, based on
GenSolvablePolynomial with RingElem interface. Objects of this class are
immutable.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final boolean
final GenSolvablePolynomial
<C> Denominator part of the element data structure.private static final org.apache.logging.log4j.Logger
final GenSolvablePolynomial
<C> Numerator part of the element data structure.final SolvableQuotientRing
<C> SolvableQuotient class factory data structure. -
Constructor Summary
ConstructorsModifierConstructorDescriptionThe constructor creates a SolvableQuotient object from a ring factory.The constructor creates a SolvableQuotient object from a ring factory and a numerator polynomial.The constructor creates a SolvableQuotient object from a ring factory and a numerator and denominator solvable polynomial.protected
SolvableQuotient
(SolvableQuotientRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d, boolean isred) The constructor creates a SolvableQuotient object from a ring factory and a numerator and denominator polynomial. -
Method Summary
Modifier and TypeMethodDescriptionabs()
SolvableQuotient absolute value.int
SolvableQuotient comparison.copy()
Clone this.Denominator.divide
(SolvableQuotient<C> S) SolvableQuotient division.egcd
(SolvableQuotient<C> b) Extended greatest common divisor.boolean
Comparison with any other object.factory()
Get the corresponding element factory.gcd
(SolvableQuotient<C> b) Greatest common divisor.int
hashCode()
Hash code for this element.inverse()
SolvableQuotient inverse.boolean
Is Qoutient a constant.boolean
isONE()
Is SolvableQuotient one.boolean
Test if SolvableQuotient right fraction.boolean
isUnit()
Is SolvableQuotient a unit.boolean
isZERO()
Is SolvableQuotient zero.monic()
SolvableQuotient monic.SolvableQuotient multiplication by coefficient.SolvableQuotient multiplication.SolvableQuotient multiplication by exponent.SolvableQuotient multiplication by GenSolvablePolynomial.negate()
SolvableQuotient negate.Numerator.Quotient and remainder by division of this by S.SolvableQuotient remainder.SolvableQuotient right fraction.int
signum()
SolvableQuotient signum.SolvableQuotient subtraction.sum
(SolvableQuotient<C> S) SolvableQuotient summation.toScript()
Get a scripting compatible string representation.Get a scripting compatible string representation of the factory.toString()
Get the String representation as RingElem.Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface edu.jas.structure.MonoidElem
leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug -
ring
SolvableQuotient class factory data structure. -
num
Numerator part of the element data structure. -
den
Denominator part of the element data structure.
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Constructor Details
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SolvableQuotient
The constructor creates a SolvableQuotient object from a ring factory.- Parameters:
r
- ring factory.
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SolvableQuotient
The constructor creates a SolvableQuotient object from a ring factory and a numerator polynomial. The denominator is assumed to be 1.- Parameters:
r
- ring factory.n
- numerator solvable polynomial.
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SolvableQuotient
public SolvableQuotient(SolvableQuotientRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d) The constructor creates a SolvableQuotient object from a ring factory and a numerator and denominator solvable polynomial.- Parameters:
r
- ring factory.n
- numerator polynomial.d
- denominator polynomial.
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SolvableQuotient
protected SolvableQuotient(SolvableQuotientRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d, boolean isred) The constructor creates a SolvableQuotient object from a ring factory and a numerator and denominator polynomial.- Parameters:
r
- ring factory.n
- numerator polynomial.d
- denominator polynomial.isred
- unused at the moment.
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Method Details
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factory
Get the corresponding element factory.- Specified by:
factory
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- factory for this Element.
- See Also:
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numerator
Numerator.- Specified by:
numerator
in interfaceQuotPair<C extends GcdRingElem<C>>
- See Also:
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denominator
Denominator.- Specified by:
denominator
in interfaceQuotPair<C extends GcdRingElem<C>>
- See Also:
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copy
Clone this.- Specified by:
copy
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- Creates and returns a copy of this Element.
- See Also:
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isZERO
public boolean isZERO()Is SolvableQuotient zero.- Specified by:
isZERO
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- If this is 0 then true is returned, else false.
- See Also:
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isONE
public boolean isONE()Is SolvableQuotient one.- Specified by:
isONE
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- If this is 1 then true is returned, else false.
- See Also:
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isUnit
public boolean isUnit()Is SolvableQuotient a unit.- Specified by:
isUnit
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- If this is a unit then true is returned, else false.
- See Also:
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isConstant
public boolean isConstant()Is Qoutient a constant.- Specified by:
isConstant
in interfaceQuotPair<C extends GcdRingElem<C>>
- Returns:
- true, if this has constant numerator and denominator, else false.
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toString
Get the String representation as RingElem. -
toScript
Get a scripting compatible string representation.- Specified by:
toScript
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- script compatible representation for this Element.
- See Also:
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toScriptFactory
Get a scripting compatible string representation of the factory.- Specified by:
toScriptFactory
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- script compatible representation for this ElemFactory.
- See Also:
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compareTo
SolvableQuotient comparison.- Specified by:
compareTo
in interfaceComparable<C extends GcdRingElem<C>>
- Specified by:
compareTo
in interfaceElement<C extends GcdRingElem<C>>
- Parameters:
b
- SolvableQuotient.- Returns:
- sign(this-b).
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equals
Comparison with any other object. -
hashCode
public int hashCode()Hash code for this element. -
rightFraction
SolvableQuotient right fraction. Note: It is not possible to distinguish right from left fractions in the current implementation. So it is not possible to compute with right fractions.- Returns:
- SolvableQuotient(a,b), where den-1 num = a b -1
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isRightFraction
Test if SolvableQuotient right fraction. Note: It is not possible to distinguish right from left fractions in the current implementation. So it is not possible to compute with right fractions.- Parameters:
s
- = SolvableQuotient(a,b)- Returns:
- true if s is a right fraction of this, i.e. den-1 num = a b-1
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abs
SolvableQuotient absolute value.- Specified by:
abs
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- the absolute value of this.
- See Also:
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sum
SolvableQuotient summation.- Specified by:
sum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- SolvableQuotient.- Returns:
- this+S.
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negate
SolvableQuotient negate.- Specified by:
negate
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- -this.
- See Also:
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signum
public int signum()SolvableQuotient signum.- Specified by:
signum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- signum(this).
- See Also:
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subtract
SolvableQuotient subtraction.- Specified by:
subtract
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- SolvableQuotient.- Returns:
- this-S.
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divide
SolvableQuotient division.- Specified by:
divide
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- SolvableQuotient.- Returns:
- this/S.
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inverse
SolvableQuotient inverse.- Specified by:
inverse
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- S with S = 1/this.
- See Also:
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remainder
SolvableQuotient remainder.- Specified by:
remainder
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- SolvableQuotient.- Returns:
- this - (this/S)*S.
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quotientRemainder
Quotient and remainder by division of this by S.- Specified by:
quotientRemainder
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- a SolvableQuotient- Returns:
- [this/S, this - (this/S)*S].
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multiply
SolvableQuotient multiplication.- Specified by:
multiply
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- SolvableQuotient.- Returns:
- this*S.
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multiply
SolvableQuotient multiplication by GenSolvablePolynomial.- Parameters:
b
- GenSolvablePolynomial. - Returns:
- this*b.
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multiply
SolvableQuotient multiplication by coefficient.- Parameters:
b
- coefficient.- Returns:
- this*b.
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multiply
SolvableQuotient multiplication by exponent.- Parameters:
e
- exponent vector.- Returns:
- this*b.
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monic
SolvableQuotient monic.- Returns:
- this with monic value part.
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gcd
Greatest common divisor.- Specified by:
gcd
in interfaceRingElem<C extends GcdRingElem<C>>
- Parameters:
b
- other element.- Returns:
- gcd(this,b).
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egcd
Extended greatest common divisor.- Specified by:
egcd
in interfaceRingElem<C extends GcdRingElem<C>>
- Parameters:
b
- other element.- Returns:
- [ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).
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