/**/ Use R ::= QQ[x,y,z];
/**/ F := x^2*y +x*y^2 +y^2;
/**/ L := [x*y-1, y^2-1];
/**/ DivAlg(F, L);
Record[Quotients := [x +y, 1], Remainder := x +y +1]
/**/ D := It;
/**/ D.Quotients;
[x +y, 1]
/**/ D.Remainder;
x +y + 1
/**/ ScalarProduct(D.Quotients, L) + D.Remainder = F;
true
/**/ V := Vector(x^2+y^2+z^2, xyz); --***OBSOLETE MANUAL: WORK IN PROGRESS***
/**/ L := [Vector(x,y), Vector(y,z), Vector(z,x)];
/**/ DivAlg(V, L);
Record[Quotients := [0, -z^2, yz], Remainder := Vector(x^2 + y^2 + z^2, z^3)]
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