from sympy import QQ, S
from sympy.polys.agca.modules import FreeModule, ModuleOrder,
FreeModulePolyRing
from sympy.polys import CoercionFailed, QQ, lex, grlex, ilex, ZZ
from sympy.abc import x, y, z
from sympy.utilities.pytest import raises
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
R = QQ.o
ring r = 0,(x,y,z),dp
module MD =
[1,x2+y,x*y-y*z,0,0],[0,x*z-y,z-x,0,0],[0,0,0,x2+y,x*y-y*z],[1,0,0,x*z-y,z-x];
module MK = syz(MD);
matrix MM = MK;
print(MM);
module N =[x2+y,x*z-y],[x*y-y*z,z-x];
quotient(N,freemodule(nrows(MK)));
from sympy import QQ
from sympy.abc import x
QQ.old_poly
ring r = 0,(x,y,z),dp
module MD =
[1,x2+y,x*y-y*z,0,0],[0,x*z-y,z-x,0,0],[0,0,0,x2+y,x*y-y*z],[1,0,0,x*z-y,z-x];
module MK = syz(MD);
matrix MM = MK;
print(MM);
module N =[x2+y,x*z-y],[x*y-y*z,z-x];
quotient(N,freemodule(nrows(MK)));
from sympy import QQ
from sympy.abc import x
QQ.old_poly
any IDE have intelligence sense for sympy
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from __future__ import division
from sympy import *
from sympy.abc import x, y
from sympy import QQ
QQ[x].free_module(2).submodule([1, 0], [1, 1]).syzygy_module()
when run above code, it return QQ is not defined
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