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groebner::spoly -- the S-polynomial of two polynomials

Introduction

groebner::spoly(p1, p2) computes the S-polynomial of the polynomials p1 and p2.

Call(s)

groebner::spoly(p1, p2 <, order>)

Parameters

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.

Returns

a polynomial of the same type as the input polynomials. If polynomial expressions are used as input, then a polynomial expression is returned.

Related Functions

poly

Details

Example 1

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:

Background

Changes




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