Example to call euclideanGroebner:
a1:DMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1)
a2:DMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1)
a3:DMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2)
an:=[a1,a2,a3]
euclideanGroebner(an)
This will return the weak euclidean Groebner basis set. All reductions are total reductions.
You can get more information by providing a second argument. To get the reduced critical pairs do:
euclideanGroebner(an,"redcrit")
You can get other information by calling:
euclideanGroebner(an,"info")
which returns:
ci => Leading monomial for critpair calculation
tci => Number of terms of polynomial i
cj => Leading monomial for critpair calculation
tcj => Number of terms of polynomial j
c => Leading monomial of critpair polynomial
tc => Number of terms of critpair polynomial
rc => Leading monomial of redcritpair polynomial
trc => Number of terms of redcritpair polynomial
tH => Number of polynomials in reduction list H
tD => Number of critpairs still to do
The three argument form returns all of the information:
euclideanGroebner(an,"info","redcrit")
The term ordering is determined by the polynomial type used.
Suggested types include
DistributedMultivariatePolynomial
HomogeneousDistributedMultivariatePolynomial
GeneralDistributedMultivariatePolynomial
See Also: