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4.15.3 poly operations
+
- addition
-
- negation or subtraction
*
- multiplication
/
- division by a polynomial, non divisible terms yield 0
^, **
- 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
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