Package edu.jas.ps
Class UnivPowerSeries<C extends RingElem<C>>
- java.lang.Object
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- edu.jas.ps.UnivPowerSeries<C>
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- Type Parameters:
C
- ring element type
- All Implemented Interfaces:
AbelianGroupElem<UnivPowerSeries<C>>
,Element<UnivPowerSeries<C>>
,MonoidElem<UnivPowerSeries<C>>
,RingElem<UnivPowerSeries<C>>
,java.io.Serializable
,java.lang.Comparable<UnivPowerSeries<C>>
public class UnivPowerSeries<C extends RingElem<C>> extends java.lang.Object implements RingElem<UnivPowerSeries<C>>
Univariate power series implementation. Uses inner classes and lazy evaluated generating function for coefficients. All ring element methods use lazy evaluation except where noted otherwise. Eager evaluated methods aretoString()
,compareTo()
,equals()
,evaluate()
, or they use theorder()
method, likesignum()
,abs()
,divide()
,remainder()
andgcd()
.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description UnivPowerSeriesRing<C>
ring
Power series ring factory.
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Constructor Summary
Constructors Constructor Description UnivPowerSeries(UnivPowerSeriesRing<C> ring, Coefficients<C> lazyCoeffs)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description UnivPowerSeries<C>
abs()
Absolute value.GenPolynomial<C>
asPolynomial()
Get a GenPolynomial<C> from this.GenVector<C>
asVector()
Get a GenVector<C> from this.C
coefficient(int index)
Get coefficient.int
compareTo(UnivPowerSeries<C> ps)
Compare to.UnivPowerSeries<C>
copy()
Clone this power series.UnivPowerSeries<C>
differentiate()
Differentiate.UnivPowerSeries<C>
divide(UnivPowerSeries<C> ps)
Divide by another power series.UnivPowerSeries<C>[]
egcd(UnivPowerSeries<C> S)
Power series extended greatest common divisor.boolean
equals(java.lang.Object B)
Comparison with any other object.C
evaluate(C e)
Evaluate at given point.UnivPowerSeriesRing<C>
factory()
Get the corresponding element factory.UnivPowerSeries<C>
gcd(UnivPowerSeries<C> ps)
Power series greatest common divisor.int
hashCode()
Hash code for this polynomial.UnivPowerSeries<C>
integrate(C c)
Integrate with given constant.UnivPowerSeries<C>
inverse()
Inverse power series.boolean
isONE()
Is power series one.boolean
isUnit()
Is unit.boolean
isZERO()
Is power series zero.C
leadingCoefficient()
Leading base coefficient.UnivPowerSeries<C>
map(UnaryFunctor<? super C,C> f)
Map a unary function to this power series.UnivPowerSeries<C>
monic()
Monic.UnivPowerSeries<C>
multiply(C c)
Multiply by coefficient.UnivPowerSeries<C>
multiply(UnivPowerSeries<C> ps)
Multiply by another power series.UnivPowerSeries<C>
negate()
Negate.int
order()
Order.UnivPowerSeries<C>
prepend(C h)
Prepend a new leading coefficient.UnivPowerSeries<C>[]
quotientRemainder(UnivPowerSeries<C> S)
Quotient and remainder by division of this by S.UnivPowerSeries<C>
reductum()
Reductum.UnivPowerSeries<C>
remainder(UnivPowerSeries<C> ps)
Power series remainder.UnivPowerSeries<C>
select(Selector<? super C> sel)
Select coefficients.int
setTruncate(int t)
Set truncate.UnivPowerSeries<C>
shift(int k)
Shift coefficients.UnivPowerSeries<C>
shiftSelect(Selector<? super C> sel)
Shift select coefficients.int
signum()
Signum.UnivPowerSeries<C>
subtract(UnivPowerSeries<C> ps)
Subtraction of two power series.UnivPowerSeries<C>
sum(UnivPowerSeries<C> ps)
Sum of two power series.java.lang.String
toScript()
Get a scripting compatible string representation.java.lang.String
toScriptFactory()
Get a scripting compatible string representation of the factory.java.lang.String
toString()
String representation of power series.java.lang.String
toString(int truncate)
To String with given truncate.int
truncate()
Truncate.<C2 extends RingElem<C2>>
UnivPowerSeries<C>zip(BinaryFunctor<? super C,? super C2,C> f, UnivPowerSeries<C2> ps)
Map a binary function to this and another power series.-
Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
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Methods inherited from interface edu.jas.structure.MonoidElem
leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder
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Field Detail
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ring
public final UnivPowerSeriesRing<C extends RingElem<C>> ring
Power series ring factory.
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Constructor Detail
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UnivPowerSeries
public UnivPowerSeries(UnivPowerSeriesRing<C> ring, Coefficients<C> lazyCoeffs)
Constructor.- Parameters:
ring
- power series ring.lazyCoeffs
- generating function for coefficients.
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Method Detail
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factory
public UnivPowerSeriesRing<C> factory()
Get the corresponding element factory.
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copy
public UnivPowerSeries<C> copy()
Clone this power series.
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toString
public java.lang.String toString()
String representation of power series.- Overrides:
toString
in classjava.lang.Object
- See Also:
Object.toString()
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toString
public java.lang.String toString(int truncate)
To String with given truncate.- Returns:
- string representation of this to given truncate.
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toScript
public java.lang.String toScript()
Get a scripting compatible string representation.
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toScriptFactory
public java.lang.String toScriptFactory()
Get a scripting compatible string representation of the factory.- Specified by:
toScriptFactory
in interfaceElement<C extends RingElem<C>>
- Returns:
- script compatible representation for this ElemFactory.
- See Also:
Element.toScriptFactory()
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coefficient
public C coefficient(int index)
Get coefficient.- Parameters:
index
- number of requested coefficient.- Returns:
- coefficient at index.
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asPolynomial
public GenPolynomial<C> asPolynomial()
Get a GenPolynomial<C> from this.- Returns:
- a GenPolynomial<C> from this up to truncate parts.
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asVector
public GenVector<C> asVector()
Get a GenVector<C> from this.- Returns:
- a GenVector<C> from this up to truncate parts.
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leadingCoefficient
public C leadingCoefficient()
Leading base coefficient.- Returns:
- first coefficient.
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reductum
public UnivPowerSeries<C> reductum()
Reductum.- Returns:
- this - leading monomial.
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prepend
public UnivPowerSeries<C> prepend(C h)
Prepend a new leading coefficient.- Parameters:
h
- new coefficient.- Returns:
- new power series.
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shift
public UnivPowerSeries<C> shift(int k)
Shift coefficients.- Parameters:
k
- shift index.- Returns:
- new power series with coefficient(i) = old.coefficient(i-k).
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select
public UnivPowerSeries<C> select(Selector<? super C> sel)
Select coefficients.- Parameters:
sel
- selector functor.- Returns:
- new power series with selected coefficients.
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shiftSelect
public UnivPowerSeries<C> shiftSelect(Selector<? super C> sel)
Shift select coefficients. Not selected coefficients are removed from the result series.- Parameters:
sel
- selector functor.- Returns:
- new power series with shifted selected coefficients.
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map
public UnivPowerSeries<C> map(UnaryFunctor<? super C,C> f)
Map a unary function to this power series.- Parameters:
f
- evaluation functor.- Returns:
- new power series with coefficients f(this(i)).
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zip
public <C2 extends RingElem<C2>> UnivPowerSeries<C> zip(BinaryFunctor<? super C,? super C2,C> f, UnivPowerSeries<C2> ps)
Map a binary function to this and another power series.- Parameters:
f
- evaluation functor with coefficients f(this(i),other(i)).ps
- other power series.- Returns:
- new power series.
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sum
public UnivPowerSeries<C> sum(UnivPowerSeries<C> ps)
Sum of two power series.- Specified by:
sum
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Parameters:
ps
- other power series.- Returns:
- this + ps.
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subtract
public UnivPowerSeries<C> subtract(UnivPowerSeries<C> ps)
Subtraction of two power series.- Specified by:
subtract
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Parameters:
ps
- other power series.- Returns:
- this - ps.
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multiply
public UnivPowerSeries<C> multiply(C c)
Multiply by coefficient.- Parameters:
c
- coefficient.- Returns:
- this * c.
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monic
public UnivPowerSeries<C> monic()
Monic.- Returns:
- 1/orderCoeff() * this.
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negate
public UnivPowerSeries<C> negate()
Negate.- Specified by:
negate
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- - this.
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abs
public UnivPowerSeries<C> abs()
Absolute value.- Specified by:
abs
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- abs(this).
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order
public int order()
Order.- Returns:
- index of first non zero coefficient.
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truncate
public int truncate()
Truncate.- Returns:
- truncate index of power series.
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setTruncate
public int setTruncate(int t)
Set truncate.- Parameters:
t
- new truncate index.- Returns:
- old truncate index of power series.
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signum
public int signum()
Signum.- Specified by:
signum
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- sign of first non zero coefficient.
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compareTo
public int compareTo(UnivPowerSeries<C> ps)
Compare to. Note: compare only up to truncate.
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isZERO
public boolean isZERO()
Is power series zero. Note: compare only up to truncate.- Specified by:
isZERO
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- If this is 0 then true is returned, else false.
- See Also:
AbelianGroupElem.isZERO()
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isONE
public boolean isONE()
Is power series one. Note: compare only up to truncate.- Specified by:
isONE
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- If this is 1 then true is returned, else false.
- See Also:
MonoidElem.isONE()
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equals
public boolean equals(java.lang.Object B)
Comparison with any other object. Note: compare only up to truncate.
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hashCode
public int hashCode()
Hash code for this polynomial. Note: only up to truncate.
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isUnit
public boolean isUnit()
Is unit.- Specified by:
isUnit
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- true, if this power series is invertible, else false.
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multiply
public UnivPowerSeries<C> multiply(UnivPowerSeries<C> ps)
Multiply by another power series.- Specified by:
multiply
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- this * ps.
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inverse
public UnivPowerSeries<C> inverse()
Inverse power series.- Specified by:
inverse
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- ps with this * ps = 1.
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divide
public UnivPowerSeries<C> divide(UnivPowerSeries<C> ps)
Divide by another power series.- Specified by:
divide
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- this / ps.
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remainder
public UnivPowerSeries<C> remainder(UnivPowerSeries<C> ps)
Power series remainder.- Specified by:
remainder
in interfaceMonoidElem<C extends RingElem<C>>
- Parameters:
ps
- nonzero power series with invertible leading coefficient.- Returns:
- remainder with this = quotient * ps + remainder.
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quotientRemainder
public UnivPowerSeries<C>[] quotientRemainder(UnivPowerSeries<C> S)
Quotient and remainder by division of this by S.- Specified by:
quotientRemainder
in interfaceMonoidElem<C extends RingElem<C>>
- Parameters:
S
- a UnivPowerSeries- Returns:
- [this/S, this - (this/S)*S].
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differentiate
public UnivPowerSeries<C> differentiate()
Differentiate.- Returns:
- differentiate(this).
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integrate
public UnivPowerSeries<C> integrate(C c)
Integrate with given constant.- Parameters:
c
- integration constant.- Returns:
- integrate(this).
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gcd
public UnivPowerSeries<C> gcd(UnivPowerSeries<C> ps)
Power series greatest common divisor.
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egcd
public UnivPowerSeries<C>[] egcd(UnivPowerSeries<C> S)
Power series extended greatest common divisor. Note: not implemented.
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