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D.2.4.4 pdivi

Procedure from library grobcov.lib (see grobcov_lib).

Usage:
pdivi(f,F);
poly f: the polynomial to be divided
ideal F: the divisor ideal

Return:
A list (poly r, ideal q, poly m). r is the remainder of the pseudodivision, q is the set of quotients, and m is the coefficient factor by which f is to be multiplied.

Note:
pseudodivision of a poly f by an ideal F in @R. Returns a list (r,q,m) such that m*f=r+sum(q.G), and no lpp of a divisor divides a pp of r.

Example:
 
LIB "grobcov.lib";
ring R=(0,a,b,c),(x,y),dp;
"Divisor=";
==> Divisor=
poly f=(ab-ac)*xy+(ab)*x+(5c);
"Dividends=";
==> Dividends=
ideal F=ax+b,cy+a;
"(Remainder, quotients, factor)=";
==> (Remainder, quotients, factor)=
def r=pdivi(f,F);
r;
==> [1]:
==>    (ab2-abc-b2c+5c2)
==> [2]:
==>    _[1]=(bc-c2)*y+(bc)
==>    _[2]=(-b2+bc)
==> [3]:
==>    (c)
"Verifying the division: r[3]*f-(r[2][1]*F[1]+r[2][2]*F[2])-r[1] =";
==> Verifying the division: r[3]*f-(r[2][1]*F[1]+r[2][2]*F[2])-r[1] =
r[3]*f-(r[2][1]*F[1]+r[2][2]*F[2])-r[1];
==> 0


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