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Dobrý den,

There is no direct way to do it. The question is what properties of the set do you want to use? Here is a simple class that more or less do what you wanted

from sage.misc.mrange import cantor_product

from sage.structure.parent import Parent
from sage.rings.qqbar import AA

class RealZZSubmodule(Parent):
    def __init__(self, elts):
        self._elts = [AA(x) for x in elts]
        Parent.__init__(self, category=(InfiniteEnumeratedSets(), Modules(ZZ)), facade=(AA,))

    def _repr_(self):
        return "ZZ-module generated by {}".format(self._elts)       

    def an_element(self):
        return self._elts[0]

    def _element_constructor_(self, arg):
        if isinstance(arg, (tuple,list)):
            assert len(arg) == len(self._elts)
            return sum(c*e for c,e in zip(arg, self._elts))
        elif arg in AA:
            raise NotImplementedError("please do it?")

    def __iter__(self):
        for i in cantor_product(ZZ, repeat=len(self._elts)):
            yield self(i)

With it you can do the following

sage: R = RealZZSubmodule([1,sqrt2])
sage: R.cardinality()
+Infinity
sage: R
ZZ-module generated by [1, 1.414213562373095?]
sage: it = iter(R)
sage: for _ in range(10):
....:     print next(it)
0
1
1.414213562373095?
-1
2.414213562373095?
-1.414213562373095?
2
0.4142135623730951?
-0.4142135623730951?
2.828427124746190?

In order to make it answers less trivial questions you need to implement more methods...

Dobrý den,

There is no direct way to do it. The question is what properties of the set do you want to use? Here is a simple class that more or less do what you wanted

from sage.misc.mrange import cantor_product

from sage.structure.parent import Parent
from sage.rings.qqbar import AA

class RealZZSubmodule(Parent):
    def __init__(self, elts):
        self._elts = [AA(x) for x in elts]
        Parent.__init__(self, category=(InfiniteEnumeratedSets(), Modules(ZZ)), facade=(AA,))

    def _repr_(self):
        return "ZZ-module generated by {}".format(self._elts)       

    def an_element(self):
        return self._elts[0]

    def _element_constructor_(self, arg):
        if isinstance(arg, (tuple,list)):
            assert len(arg) == len(self._elts)
            return sum(c*e for c,e in zip(arg, self._elts))
        elif arg in AA:
            raise NotImplementedError("please do it?")

    def __iter__(self):
        for i in cantor_product(ZZ, repeat=len(self._elts)):
            yield self(i)

With it you can do the following

sage: sqrt2 = AA(2).sqrt()
sage: R = RealZZSubmodule([1,sqrt2])
sage: R.cardinality()
+Infinity
sage: R
ZZ-module generated by [1, 1.414213562373095?]
sage: R((1,0))
1
sage: R((0,1))
1.414213562373095?
sage: R((8, -5))
0.9289321881345248?
sage: it = iter(R)
sage: for _ in range(10):
....:     print next(it)
0
1
1.414213562373095?
-1
2.414213562373095?
-1.414213562373095?
2
0.4142135623730951?
-0.4142135623730951?
2.828427124746190?

In order to make it answers less trivial questions you need to implement more methods...