shh.csparse
Class SparseEltEuc

Object
  SparseElt
      SparseEltEuc

Direct Known Subclasses:

SparseEltField, SparseEltZ

public abstract class SparseEltEuc

extends SparseElt

A class of SparseElts should implement this interface if its underlying integral domain D is a Euclidean domain.

Author:

Mark McConnell

Field Summary

Fields inherited from class SparseElt

INDEX_SORTER, NEG_ONE, ONE, ZERO

Constructor Summary

SparseEltEuc()

Method Summary

abstract Number	eucNorm() Returns the Euclidean norm.
abstract Comparator	getEucNormComparator() Returns a Comparator C that compares by Euclidean norm.
abstract SparseEltEuc	negClosestQuotient(SparseEltEuc y) Negative of the closest quotient: returns q such that q * y + this is as small as possible for eucNorm().

Methods inherited from class SparseElt

add, bitLength, copy, divides, equals, getIndex, getNegOne, getOne, getPrintValue, getZero, hashCode, isEqualValue, isNegOne, isOne, isZero, multiply, multiply, negate, subtract, toString

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

SparseEltEuc

public SparseEltEuc()

Method Detail

eucNorm

public abstract Number eucNorm()

Returns the Euclidean norm. An implementing class may return BigInteger, Integer, etc., as long as it's consistent.

getEucNormComparator

public abstract Comparator getEucNormComparator()

Returns a Comparator C that compares by Euclidean norm. C.compare(a,b) should give the same results as a.eucNorm().compareTo(b.eucNorm()), where compareTo is the usual <, but C.compare might be more efficient.

negClosestQuotient

public abstract SparseEltEuc negClosestQuotient(SparseEltEuc y)

Negative of the closest quotient: returns q such that q * y + this is as small as possible for eucNorm(). In other words, returns -this/y rounded off to the nearest element of D. The index is that of this.

Throws:

ArithmeticException - If y is zero.