This CD holds a collection of basic modular arithmetic for polynomials over fields.
The data structures for polynomials can be arithmetic expressions, for
instance using the ring1.expression symbol, or DMP as
in the CD polyd1.
This symbol is a unary function, whose argument should be a polynomial f.
When applied to f, it represents a complete list of irreducible factors of f.
Example:
The following expression represents the list [X+1,X+1] of rational polynomials.
This symbol represents the binary division operator on univariate polynomials
over fields. That is,
for univariate polynomials a and b, quotient(a,b) denotes the polynomial q such that a=b*q+r, with degree(r)
less than degree(b).
Commented Mathematical property (CMP):
For all a,b with a,b univariate polynomials over a field F we have
a = b * quotient(a,b) + remainder(a,b) and degree(remainder(a,b)) is less than degree(b).
The symbol represents a binary function, whose arguments should be univariate
polynomials in the same polynomial ring whose coefficient ring is a field.
When applied to a and b, it represents the polynomial remainder after division
of a by b.
For univariate polynomials a and b, remainder(a,b) denotes r such that a=b*q+r, with degree(r) less
than degree(b).
See remainder for a formal statement of this property.