Examples
User documentation
In CoCoALib factorization
is a template class for representing
(partial) factorizations. Conceptually it comprises a list of factors
and their multiplicities, and an extra remaining factor (which may be,
for instance, an unfactorized part, or an invertible element).
The class itself imposes few conditions: the factors in the list
cannot be invertible or zero-divisors, and their multiplicities are
all positive. The remaining factor is a non-zero-divisor. The exact
characteristics of the factors depend on the function which generated
the factorization
. Naturally, the vectors returned by
myFactors
and myMultiplicities
will be of the same length.
In particular, an empty factorization is permitted (i.e. with empty
lists of factors and multiplicities).
See also: the functions factor
, SqFreeFactor
, ContentFreeFactor
(in section factor
),
and the functions factor
(in section NumTheory
)
Constructor
factorization(RemFactor)
specifies an initial remaining factor, the factor/multiplicity lists are emptyfactorization(facs, mults, RemFactor)
specifies initial values for the 3 components
Accessors
Let FactorInfo
be of type factorization<T>
. These are the accessor functions:
FactorInfo.myFactors()
all the factors as astd::vector<T>
(read-only)FactorInfo.myMultiplicities()
all the multiplicities as astd::vector<long>
(read-only)FactorInfo.myRemainingFactor()
the remaining factor (read-only)
For better readability of code using factorization
we recommend using const ref
aliases for the lists of factors and multiplicities; for instance
const factorization<RingElem> FactorInfo = factor(f); const vector<RingElem>& facs = FactorInfo.myFactors(); const vector<long>& mults = FactorInfo.myMultiplicities(); ... // code using the arrays "facs" and "mults"
Operations
Let FactorInfo
be of type factorization<T>
. These are the operations available:
FactorInfo.myAppend(fac, mult)
appends a new factor with its multiplicityFactorInfo.myNewRemainingFactor(RemFactor)
setsRemFactor
as the remaining factor
Maintainer documentation
Being template code it's all in the header file. It's mostly fairly straightfoward.
The main point to note is that ourCheckNotZeroDiv
and ourCheckNotUnit
need to be written by hand for each instantiation -- this is enforced by the
absence of a default template impl. Note that the impls for DUPFp
are
defined in the file DUPFp.H
.
The fn ourCheckCompatibility
is needed for RingElem
but not for other
types (so the default impl is empty). It simply checks that all the factors
belong to the same ring (equiv. that they belong to ring of myRemainingFactorValue
).
In CoCoALib there are just 4 instantiations of this template:
factorization<BigInt>
for the fnsfactor
andSmoothFactor
inNumTheory
factorization<RingElem>
for the fnsfactor
andSqFreeFactor
andContentFreeFactor
inPolyRing
(actuallyTmpFactor
)factorization<long>
factorization<DUPFp>
Bugs, shortcomings and other ideas
It would be safer to have pairs of factor-and-multiplicity rather than two separate vectors whose length must be the same. However it may be less convenient for the user.
Maybe add fn to get length of a factorization
? (same as length of myFactors()
)
Maybe add fn to get ring of a factorization<RingElem>
?
Maybe add fn to change the multiplicity of a factor?
Bruns questioned the necessity of the restriction that factors be non-zero-divisiors and non-units. JAA prefers to apply these restrictions for the time being, because it will be easier to relax the restrictions later than it would be to tighten them (might break some existing code).
Bruns/Soeger asked whether requiring all factors to be in the same ring is necessary (esp. once CoCoA allows arithmetic between different rings). They cite the example of factors in ZZ[x] and remaining factor in QQ.
Main changes
2014
- March: fields are now private: new accessor fns; new append fn, and new fn to update rem factor
2012
- October: chose "myMultiplicities" rather than "myExponents" as the field name.
- April: first version of doc (v0.9950)