PLURAL is a kernel extension of SINGULAR,
providing many algorithms for computations within certain noncommutative algebras
(see see G-algebras and Mathematical background (plural) for detailed information on algebras and algorithms).
PLURAL is compatible with SINGULAR, since it uses the
same data structures, sometimes interpreting them in a different way
and/or modifying them for its own purposes.
In spite of such a difference, one can always transfer
objects from commutative rings of SINGULAR
to noncommutative rings PLURAL and back.
With PLURAL, one can set up a noncommutative
-algebra with
a Poincaré-Birkhoff-Witt (PBW) basis, say,
(see G-algebras for step-by-step building instructions and also PLURAL libraries
for procedures for setting many important algebras easily).
Functionalities of PLURAL (enlisted in Functions (plural)) are accessible as soon as the basering becomes noncommutative (see ncalgebra).
One can perform various computations with polynomials and ideals in
and with
vectors and submodules of a free module
.
One can work also within factor-algebras of
-algebras (see qring (plural) type)
by two-sided ideals (see twostd).