
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+xyx+y+1
f + x5 + 2;
==> x5+x3y2+2x2y2+xyx+y+3
f * x2;
==> x5y2+2x4y2+x3yx3+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;
==> 1x+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

