|
|
D.2.9.4 pdivi2
Procedure from library redcgs.lib (see redcgs_lib).
- Usage:
- pdivi2(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 ideal of quotients, and m is the
factor by which f is to be multiplied.
- Note:
- Pseudodivision of a polynomial f by an ideal F in @R. Returns a
list (r,q,m) such that m*f=r+sum(q.G).
Example:
| | LIB "redcgs.lib";
ring R=(0,a,b,c),(x,y),dp;
setglobalrings();
poly f=(ab-ac)*xy+(ab)*x+(5c);
ideal F=ax+b,cy+a;
def r=pdivi2(f,F);
r;
==> [1]:
==> (ab2-abc-b2c+5c2)
==> [2]:
==> _[1]=(bc-c2)*y+(bc)
==> _[2]=(-b2+bc)
==> [3]:
==> (c)
r[3]*f-(r[2][1]*F[1]+r[2][2]*F[2])-r[1];
==> 0
|
|
