The **Basic Polynomial Algebra Subprograms** (BPAS) library provides
support for arithmetic operations
with polynomials on modern computer architectures,
in particular hardware accelerators.
Typical operations are polynomial multiplication, multi-point
evaluation and interpolation, real root isolation for both
univariate and multivariate systems.
Its code is written in C++ with
CilkPlus extension targeting multi-core processors.
Polymorphic integration code features exact integration (as a formal sum) and symbolic-numeric integration of both dense and sparse representations of rational functions.
### Exposed BPAS ring classes

Integer
RationalNumber
ComplexRationalNumber
Fraction
SmartFraction
SmallPrimeField
BigPrimeField
GeneralizedFermatPrimeField

DenseUnivariateIntegerPolynomial (also named as DUZP)
DenseUnivariateRationalPolynomial (also named as DUQP)
SparseUnivariatePolynomial<Ring>, taking any BPAS ring as the coefficient type
UnivariateRationalFunction<UnivariatePolynomialOverField, Field>
SmallPrimeFieldDistributedDenseMultivariateModularPolynomial (also named as SFDDMMP)
DistributedDenseMultivariateModularPolynomial<Field>
SparseMultivariateRationalPolynomial (also named as SMQP)
SparseMultivariatePolynomial<Ring>, taking any BPAS ring as the coefficient type
### Exposed BPAS triangular set classes

RationalRegularChain
RegularChain<Ring>, taking any BPAS ring
TriangularSet<Ring>, taking any BPAS ring

- Polynomial multiplication and matrix multiplication are at the core of many algorithms in symbolic computation.
- Algebraic complexity is often estimated in terms of multiplication time. At the software level, this reduction to multiplication is also common (Magma, NTL, FLINT, ...).
- BPAS design follows the principle
*reducing everything to multiplication*.

It appears you don't have a PDF plugin for this browser. No biggie... you can click here to download the PDF file.

If you have questions or bug reports, please contact bpas <at> scl <dot> csd <dot> uwo <dot> ca.

ORCCA Lab, Department of Computer Science, The University of Western Ontario, London, Ontario, Canada N6A 5B7