An object of type POLY in CoCoA represents a polynomial. To fix
terminology: a polynomial is a sum of terms; each term is the product
of a coefficient and power-product, a power-product being a product of
powers of indeterminates. (In English it is standard to use 'monomial'
to mean a power-product, however, in other languages, such as Italian,
monomial connotes a power product multiplied by a scalar. In the
interest of world peace, we will use the term power-product in those
cases where confusion may arise.)
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The following are CoCoA polynomials:
Use R ::= Q[x,y,z];
F := 3xyz + xy^2;
F;
xy^2 + 3xyz
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Use R ::= Q[x[1..5]];
Sum([x[N]^2 | N In 1..5]);
x[1]^2 + x[2]^2 + x[3]^2 + x[4]^2 + x[5]^2
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CoCoA always keeps polynomials ordered with respect to the
term-orderings of their corresponding rings..
The following algebraic operations on polynomials are supported:
F^N, +F, -F, F*G, F/G if G divides F, F+G, F-G,
where F, G are polynomials and N is an integer. The result may be a
rational function.
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