A geobucket is a polynomial represented in a C++ vector of buckets:
a bucket
contains a polynomial (and some other info)
This construction is useful for
adding many short polynomials to a long one
(in particular the reduction process) because it lowers the number of calls
of cmp
between PPMonoidElem
s.
geobucket(const SparsePolyRing&)
;
IsZero(g)
-- true iff g
is the zero polynomial
Let gbk
be a geobucket
, f
a RefRingElem
(see RingElem
)
CoeffRing(gbk)
-- the ring
of coefficients of the ring of gbk
PPM(gbk)
-- the PPMonoid
of the ring of gbk
LC(gbk)
-- the leading coeff of gbk
; it is an element of CoeffRing(gbk)
content(gbk)
-- the gcd of all coefficients in gbk
; it is an element of CoeffRing(gbk)
RemoveBigContent(gbk)
-- if gbk
has a big content, gbk
is divided by it
AddClear(f, gbk)
-- assign the polynomial value of gbk
to f
,
and set 0 to gbk
MoveLM(f, gbk)
;
ReductionStep(gbk, f, RedLen)
;
ReductionStepGCD(gbk, f, FScale, RedLen)
;
operator<<(std::ostream&, gbk)
PrintLengths(std::ostream&, gbk)
-- just for debugging
operator<<(std::ostream&, const geobucket&)
myAddClear(f, len)
myDeleteLM(void)
myPushBackZeroBucket(MaxLen)
myBucketIndex(len)
-- the index for the bucket
with length len
myAddMul(monom, g, std::gLen, SkipLMFlag)
-- *this += monom*g
myDivByCoeff(coeff)
-- content MUST be divisible by coeff
myMulByCoeff(coeff)
myCascadeFrom(std::size_t i)
mySize(void)
mySetLM()
-- Sets the LM of *this
in the 0-th bucket
and set IhaveLM
to true;
*this
will be normalized
After calling gbk.mySetLM()
the leading monomial of gbk
is in
gbk.myBuckets[0]
(and then gbk
is zero iff gbk.myBuckets[0]=0
)
gbk.myBuckets[i]
contains at most gbk_minlen * gbk_factor^i
summands
myPolyRing
-- the SparsePolyRing gbk lives in
IhaveLM
-- true if certified that LM(gbk) = LM(gbk[0])
myBuckets
-- the bucket vector
This class is to be used only by geobucket
s.
A bucket
represents a polynomial as a product of a polynomial and
a coefficient, two RingElem
respectivey in a SparsePolyRing
P
and CoeffRing(P)
.
The coeffient factor is used for fast multiplication of a geobucket by a coefficient and it comes useful in the reduction process over a field of fraction of a GCD ring.
We normalize the bucket
(i.e. multiply the polynomial by the
coefficient) only when it is necessary: e.g. to compute a reference to
the LC of the bucket.
All methods are private (to be used only by geobucket
s, friend)
Methods on buckets (weak exception guarantee)
myNormalize(void)
-- myPoly *=myCoeff; myCoeff 1
myAddClear(RefRingElem f, int FLen)
-- *this += f; f = 0; *this normalized
myAddClear(bucket& b)
-- *this += b; b = 0; *this normalized
myMul(ConstRefRingElem coeff)
-- *this *= coeff
myDiv(ConstRefRingElem coeff)
-- *this /= coeff; assumes *this divisible by coeff
IsZero(const bucket&)
--
content(const bucket& b)
--
poly(bucket& b)
-- normalize b and return a reference to the polynomial
Dirty method and function for efficiency (b1 and b2 will be normalized))
myIsZeroAddLCs(const SparsePolyRing&, bucket& b1, bucket& b2)
--
b1 += LM(b2); b2 -= LM(b2);
return LC(b1)+LC(b2)==0
;
it assumes LPP(b1) == LPP(b2)
MoveLM(const SparsePolyRing&, bucket& b1, bucket& b2)
--
b1 += LM(b2); b2 -= LM(b2);
it assumes LPP(b1)<LPP(b2)
myPoly
-- the polynomial (a RingElem
in P
)
myCoeff
-- the coefficient factor (a RingElem
in CoeffRing(P)
)
myMaxLen
-- the maximal length allowed for the polynomial of this bucket
myApproxLen
-- an upper bound for the current length of the polynomial of this bucket
2004
myDivMaskImplPtr
for computing LPPwMask
:
LPP with DivMask if this pointer is 0 LPPwMask returns an error
(through CoCoA_ASSERT
?)