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4.12.3 poly operations
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+ addition
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- negation or subtraction
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* multiplication
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/ division by a polynomial, ignoring the rest
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^,** power by an integer
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<,<=,>,>=,==,<> comparison (w.r.t. monomial ordering)
- poly_expression
[intvec_expression] the monomial at the indicated place 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 |