i tried to take this into consideration
giving the following code
P.<x,y,z> = PolynomialRing(QQ,order='neglex')
I = Ideal(x^5 + y^4 +z^3, x^3 + y^2 + z^2 -1)
print I
gb=I.groebner_basis()
rgb=Ideal(gb).interreduced_basis()
bgr=Ideal(rgb)
ir=Ideal(f.Im() for f in bgr)
print 'with revlex order'
print rgb
print ir
R.<x,y,z> = PolynomialRing(QQ,order='lex')
J = Ideal(x^5 + y^4 +z^3, x^3 + y^2 + z^2 -1)
gc=J.groebner_basis()
rgc=Ideal(gc).interreduced_basis()
cri=Ideal(rgc)
irc=Ideal(f.Im() for f in cri)
print 'with lexographic order'
print rgc
print irc
this gives output
Ideal (z^3 + y^4 + x^5, -1 + z^2 + y^2 + x^3) of Multivariate
Polynomial Ring in x, y, z over Rational Field
Traceback (most recent call last):
File "A1Q3.py", line 10, in <module>
ir=Ideal(f.Im() for f in bgr)
TypeError: 'MPolynomialIdeal' object is not iterable
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