Local
edu.jas.poly

Class Local<C extends RingElem<C>>

• Constructor Summary

Constructors
Constructor and Description
`Local(LocalRing<C> r)`
The constructor creates a Local object from a ring factory.
`Local(LocalRing<C> r, C n)`
The constructor creates a Local object from a ring factory and a numerator element.
`Local(LocalRing<C> r, C n, C d)`
The constructor creates a Local object from a ring factory and a numerator and denominator element.
• Method Summary

Methods
Modifier and TypeMethod and Description
`Local<C>``abs()`
Local absolute value.
`int``compareTo(Local<C> b)`
Local comparison.
`Local<C>``copy()`
Clone this.
`C``denominator()`
Denominator.
`Local<C>``divide(Local<C> S)`
Local division.
`Local<C>[]``egcd(Local<C> b)`
Extended greatest common divisor.
`boolean``equals(Object b)`
Comparison with any other object.
`LocalRing<C>``factory()`
Get the corresponding element factory.
`Local<C>``gcd(Local<C> b)`
Greatest common divisor.
`int``hashCode()`
Hash code for this local.
`Local<C>``inverse()`
Local inverse.
`boolean``isConstant()`
Is Local a constant.
`boolean``isONE()`
Is Local one.
`boolean``isUnit()`
Is Local unit.
`boolean``isZERO()`
Is Local zero.
`Local<C>``multiply(Local<C> S)`
Local multiplication.
`Local<C>``negate()`
Local negate.
`C``numerator()`
Numerator.
`Local<C>[]``quotientRemainder(Local<C> S)`
Quotient and remainder by division of this by S.
`Local<C>``remainder(Local<C> S)`
Local remainder.
`int``signum()`
Local signum.
`Local<C>``subtract(Local<C> S)`
Local subtraction.
`Local<C>``sum(Local<C> S)`
Local summation.
`String``toScript()`
Get a scripting compatible string representation.
`String``toScriptFactory()`
Get a scripting compatible string representation of the factory.
`String``toString()`
Get the String representation as RingElem.
• Methods inherited from class java.lang.Object

`getClass, notify, notifyAll, wait, wait, wait`
• Constructor Detail

• Local

`public Local(LocalRing<C> r)`
The constructor creates a Local object from a ring factory.
Parameters:
`r` - ring factory.
• Local

`public Local(LocalRing<C> r,     C n)`
The constructor creates a Local object from a ring factory and a numerator element. The denominator is assumed to be 1.
Parameters:
`r` - ring factory.
`n` - numerator.
• Local

`public Local(LocalRing<C> r,     C n,     C d)`
The constructor creates a Local object from a ring factory and a numerator and denominator element.
Parameters:
`r` - ring factory.
`n` - numerator.
`d` - denominator.
• Method Detail

• factory

`public LocalRing<C> factory()`
Get the corresponding element factory.
Specified by:
`factory` in interface `Element<Local<C extends RingElem<C>>>`
Returns:
factory for this Element.
`Element.factory()`
• numerator

`public C numerator()`
Numerator.
Specified by:
`numerator` in interface `QuotPair<C extends RingElem<C>>`
`QuotPair.numerator()`
• denominator

`public C denominator()`
Denominator.
Specified by:
`denominator` in interface `QuotPair<C extends RingElem<C>>`
`QuotPair.denominator()`
• isConstant

`public boolean isConstant()`
Is Local a constant. Not implemented.
Specified by:
`isConstant` in interface `QuotPair<C extends RingElem<C>>`
Throws:
`UnsupportedOperationException.`
• copy

`public Local<C> copy()`
Clone this.
Specified by:
`copy` in interface `Element<Local<C extends RingElem<C>>>`
Returns:
Creates and returns a copy of this Element.
`Object.clone()`
• isZERO

`public boolean isZERO()`
Is Local zero.
Specified by:
`isZERO` in interface `AbelianGroupElem<Local<C extends RingElem<C>>>`
Returns:
If this is 0 then true is returned, else false.
`AbelianGroupElem.isZERO()`
• isONE

`public boolean isONE()`
Is Local one.
Specified by:
`isONE` in interface `MonoidElem<Local<C extends RingElem<C>>>`
Returns:
If this is 1 then true is returned, else false.
`MonoidElem.isONE()`
• isUnit

`public boolean isUnit()`
Is Local unit.
Specified by:
`isUnit` in interface `MonoidElem<Local<C extends RingElem<C>>>`
Returns:
If this is a unit then true is returned, else false.
`MonoidElem.isUnit()`
• toString

`public String toString()`
Get the String representation as RingElem.
Overrides:
`toString` in class `Object`
`Object.toString()`
• toScript

`public String toScript()`
Get a scripting compatible string representation.
Specified by:
`toScript` in interface `Element<Local<C extends RingElem<C>>>`
Returns:
script compatible representation for this Element.
`Element.toScript()`
• toScriptFactory

`public String toScriptFactory()`
Get a scripting compatible string representation of the factory.
Specified by:
`toScriptFactory` in interface `Element<Local<C extends RingElem<C>>>`
Returns:
script compatible representation for this ElemFactory.
`Element.toScriptFactory()`
• compareTo

`public int compareTo(Local<C> b)`
Local comparison.
Specified by:
`compareTo` in interface `Element<Local<C extends RingElem<C>>>`
Specified by:
`compareTo` in interface `Comparable<Local<C extends RingElem<C>>>`
Parameters:
`b` - Local.
Returns:
sign(this-b).
• equals

`public boolean equals(Object b)`
Comparison with any other object.
Specified by:
`equals` in interface `Element<Local<C extends RingElem<C>>>`
Overrides:
`equals` in class `Object`
Returns:
true if this is equal to b, else false.
`Object.equals(java.lang.Object)`
• hashCode

`public int hashCode()`
Hash code for this local.
Specified by:
`hashCode` in interface `Element<Local<C extends RingElem<C>>>`
Overrides:
`hashCode` in class `Object`
Returns:
the hashCode.
`Object.hashCode()`
• abs

`public Local<C> abs()`
Local absolute value.
Specified by:
`abs` in interface `AbelianGroupElem<Local<C extends RingElem<C>>>`
Returns:
the absolute value of this.
`AbelianGroupElem.abs()`
• sum

`public Local<C> sum(Local<C> S)`
Local summation.
Specified by:
`sum` in interface `AbelianGroupElem<Local<C extends RingElem<C>>>`
Parameters:
`S` - Local.
Returns:
this+S.
• negate

`public Local<C> negate()`
Local negate.
Specified by:
`negate` in interface `AbelianGroupElem<Local<C extends RingElem<C>>>`
Returns:
-this.
`AbelianGroupElem.negate()`
• signum

`public int signum()`
Local signum.
Specified by:
`signum` in interface `AbelianGroupElem<Local<C extends RingElem<C>>>`
Returns:
signum(this).
`AbelianGroupElem.signum()`
• subtract

`public Local<C> subtract(Local<C> S)`
Local subtraction.
Specified by:
`subtract` in interface `AbelianGroupElem<Local<C extends RingElem<C>>>`
Parameters:
`S` - Local.
Returns:
this-S.
• divide

`public Local<C> divide(Local<C> S)`
Local division.
Specified by:
`divide` in interface `MonoidElem<Local<C extends RingElem<C>>>`
Parameters:
`S` - Local.
Returns:
this/S.
• inverse

`public Local<C> inverse()`
Local inverse.
Specified by:
`inverse` in interface `MonoidElem<Local<C extends RingElem<C>>>`
Returns:
S with S = 1/this if defined.
`MonoidElem.inverse()`
• remainder

`public Local<C> remainder(Local<C> S)`
Local remainder.
Specified by:
`remainder` in interface `MonoidElem<Local<C extends RingElem<C>>>`
Parameters:
`S` - Local.
Returns:
this - (this/S)*S.
• quotientRemainder

`public Local<C>[] quotientRemainder(Local<C> S)`
Quotient and remainder by division of this by S.
Parameters:
`S` - a Local
Returns:
[this/S, this - (this/S)*S].
• multiply

`public Local<C> multiply(Local<C> S)`
Local multiplication.
Specified by:
`multiply` in interface `MonoidElem<Local<C extends RingElem<C>>>`
Parameters:
`S` - Local.
Returns:
this*S.
• gcd

`public Local<C> gcd(Local<C> b)`
Greatest common divisor. Note: Not implemented, throws UnsupportedOperationException.
Specified by:
`gcd` in interface `RingElem<Local<C extends RingElem<C>>>`
Parameters:
`b` - other element.
Returns:
gcd(this,b).
• egcd

`public Local<C>[] egcd(Local<C> b)`
Extended greatest common divisor. Note: Not implemented, throws UnsupportedOperationException.
Specified by:
`egcd` in interface `RingElem<Local<C extends RingElem<C>>>`
Parameters:
`b` - other element.
Returns:
[ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).

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