4.16.3 poly operations

+

addition

-

negation or subtraction

*

multiplication

/, div

division by a polynomial, ignoring the remainder (only implemented for polynomials over QQ, ZZ/p and field extensions of them)
(See also quotient, division, reduce)

%, mod

the remainder from the division by a polynomial (only implemented for polynomials over QQ, ZZ/p and field extensions of them)
(See also quotient, division, reduce)

^, **

power by a positive integer

<, <=, >, >=, ==, <>

comparators (considering leading monomials w.r.t. monomial ordering)

poly_expression [ intvec_expression ]

the sum of monomials at the indicated places w.r.t. the monomial ordering

Example:

ring R=0,(x,y),dp; poly f = x3y2 + 2x2y2 + xy - x + y + 1; f; ==> x3y2+2x2y2+xy-x+y+1 f + x5 + 2; ==> x5+x3y2+2x2y2+xy-x+y+3 f * x2; ==> x5y2+2x4y2+x3y-x3+x2y+x2 (x+y)/x; ==> 1 f/3x2; ==> 1/3xy2+2/3y2 x5 > f; ==> 1 x<=y; ==> 0 x>y; ==> 1 ring r=0,(x,y),ds; poly f = fetch(R,f); f; ==> 1-x+y+xy+2x2y2+x3y2 x5 > f; ==> 0 f[2..4]; ==> -x+y+xy size(f); ==> 6 f[size(f)+1]; f[-1]; // monomials out of range are 0 ==> 0 ==> 0 intvec v = 6,1,3; f[v]; // the polynom built from the 1st, 3rd and 6th monomial of f ==> 1+y+x3y2