groebner::spoly
-- the
S-polynomial of two polynomialsgroebner::spoly
(p1, p2)
computes the
S-polynomial of the polynomials p1
and
p2
.
groebner::spoly(p1, p2 <, order>)
p1, p2 |
- | polynomials of the same type or polynomial expressions with rational coefficients |
order |
- | one of the identifiers DegInvLexOrder, DegreeOrder, and LexOrder, or a user-defined term ordering of type
Dom::MonomOrdering .
The default ordering is DegInvLexOrder. |
a polynomial of the same type as the input polynomials. If polynomial expressions are used as input, then a polynomial expression is returned.
groebner
package concerning the
polynomial types and the ordering apply.poly
and polynomial expressions!The polynomials
>> p1 := poly(x^2 - x + 2*y^2, [x, y]): p2 := poly(x + 2*y - 1, [x, y]):
generate the following S-polynomial with respect to lexicographical ordering:
>> groebner::spoly(p1, p2, LexOrder)
2 poly(- 2 x y + 2 y , [x, y])
>> delete p1, p2:
lcm(lterm(p[1]),lterm(p[2]))/lmonomial(p[1])*p[1] - lcm(lterm(p[1]),lterm(p[2]))/lmonomial(p[2])*p[2],where
lterm
and lmonomial
are used in the
same sense as the MuPAD functions of the same name. This formula
is constructed such that the leading terms of the two summands
cancel.Dom::MonomOrdering
are handled.
The special term orderings from the Gröbner package were moved
there.