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Univariate polynomial rings may be defined over any ring R.
Let us denote the univariate polynomial
ring in indeterminate x over the coefficient ring R by P=R[x].
There are two kinds of polynomials in Magma:
univariate polynomials, represented as vectors of coefficients; and
multivariate polynomials represented in distributive form (linear
sums of coefficient-monomial pairs).
In this chapter we discuss univariate polynomials.
The vector representation enables fast arithmetic on univariate polynomials,
but it requires considerable amounts of memory for multivariate polynomials;
therefore, only univariate polynomial rings using the vector representation
can be created directly (but, if one insists, it is possible to create
univariate polynomial rings over univariate polynomial rings, etc.).
Multivariate polynomials can be stored efficiently in distributive form,
but the arithmetic operations on polynomials of one variable stored in
this way may be considerably slower.
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