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Here is sample code (only an example, not my real use case):

class Rationals:

def __init__(self,nom,denom):
    if (denom==0):
        print("Error")
        print(quit)
        quit() 
    else:
        divisor=ggT(nom,denom)
        if (divisor!=0):
            self.nom=nom/divisor
            self.denom=denom/divisor
        else:
            self.nom=nom
            self.denom=denom

def __add__(self,element2):
    result=Rationals()
    result.denom=self.denom*element2.denom
    result.nom=self.denom*element.nom+self.nom*element.denom
    divisor=ggT(result.nom,result.denom)
    result.nom=result.nom/divisor
    result.denom=result.denom/divisor
    return result

def __mul__(self,element2):
    result=Rationals()
    result.nom=self.nom*element2.nom
    result.denom=self.denom*element2.denom
    divisor=ggT(result.nom,result.denom)
    result.nom=result.nom/divisor
    result.denom=result.denom/divisor
    return result

Now if I type in RR = PolynomialRing(Rationals,'y') I get an error:

TypeError Traceback (most recent call last) <ipython-input-112-6f1923f0a0bd> in <module> ----> 1 RR = PolynomialRing(Rationals,'y')

/usr/lib/python3/dist-packages/sage/rings/polynomial/polynomial_ring_constructor.py in PolynomialRing(base_ring, args, *kwds) 553 """ 554 if not ring.is_Ring(base_ring): --> 555 raise TypeError("base_ring {!r} must be a ring".format(base_ring)) 556 557 n = -1 # Unknown number of variables

TypeError: base_ring <class '__main__.rationals'=""> must be a ring

Note that this is only an example, not my real use case. Of course, I could use QQ in sagemath, but I consider a more complex ring which does not exist in sagemath.

How do I tell sage that I am confident that my domain is actually a ring?

Here is sample code (only an example, not my real use case):

class Rationals:

def __init__(self,nom,denom):
    if (denom==0):
        print("Error")
        print(quit)
        quit() 
    else:
        divisor=gcd(nom,denom)
        if (divisor!=0):
            self.nom=nom/divisor
            self.denom=denom/divisor
        else:
            self.nom=nom
            self.denom=denom

def __add__(self,element2):
    denom=self.denom*element2.denom
    nom=self.denom*element2.nom+self.nom*element2.denom
    divisor=gcd(nom,denom)
    nom=nom/divisor
    denom=denom/divisor
    return Rationals(nom,denom)

def __mul__(self,element2):
    nom=self.nom*element2.nom
    denom=self.denom*element2.denom
    divisor=gcd(nom,denom)
    nom=nom/divisor
    denom=denom/divisor
    return Rationals(nom,denom)

Now if I type in RR = PolynomialRing(Rationals,'y') I get an error:

TypeError Traceback (most recent call last) <ipython-input-112-6f1923f0a0bd> in <module> ----> 1 RR = PolynomialRing(Rationals,'y')

/usr/lib/python3/dist-packages/sage/rings/polynomial/polynomial_ring_constructor.py in PolynomialRing(base_ring, args, *kwds) 553 """ 554 if not ring.is_Ring(base_ring): --> 555 raise TypeError("base_ring {!r} must be a ring".format(base_ring)) 556 557 n = -1 # Unknown number of variables

TypeError: base_ring <class '__main__.rationals'=""> must be a ring

Note that this is only an example, not my real use case. Of course, I could use QQ in sagemath, but I consider a more complex ring which does not exist in sagemath.

How do I tell sage that I am confident that my domain is actually a ring?