ed448goldilocks/_aux/idealized.sage

class Unique(object):
    def __init__(self,name):
        self.name = name
    
    def __str__(self):
        return self.name
    
    def __repr__(self):
        return "Unique(\"%s\")" % self.name

class Idealized(object):
    UNION = ["UNION"]
    
    def __init__(self, R, idealMap = 0, vars = {}):
        self.varnames = vars
        if not isinstance(idealMap,dict):
            idealMap = {()*R:idealMap}
        self.idealMap = idealMap
        self.R = R
        self._sqrt = None
        self._isqrt = None
    
    @staticmethod
    def uvar(x):
        return Idealized.var(Unique(x))
    
    @staticmethod
    def var(x):
        name = str(x)
        R = PolynomialRing(QQ,[name])
        rx = R.gens()[0]
        return Idealized(R,rx,{x:(name,rx)})
    
    @staticmethod
    def vars(xs):
        return tuple((Idealized.var(x) for x in xs))
    
    @staticmethod
    def uvars(xs):
        return tuple((Idealized.uvar(x) for x in xs))
    
    def __str__(self):
        def rep(I,x):
            x = str(x)
            gs = I.gens()
            gs = [g for g in gs if g != 0]
            if len(gs) == 0: return x
            else: