Python PolynomialRing.valuation方法代码示例

# 需要导入模块: from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing [as 别名]
# 或者: from sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing import valuation [as 别名]
class Polynomial_padic_capped_relative_dense(Polynomial_generic_domain):
    def __init__(self, parent, x=None, check=True, is_gen=False, construct = False, absprec = infinity, relprec = infinity):
        """
        TESTS:
            sage: K = Qp(13,7)
            sage: R.<t> = K[]
            sage: R([K(13), K(1)])
            (1 + O(13^7))*t + (13 + O(13^8))
            sage: T.<t> = ZZ[]
            sage: R(t + 2)
            (1 + O(13^7))*t + (2 + O(13^7))
        """
        Polynomial.__init__(self, parent, is_gen=is_gen)
        parentbr = parent.base_ring()
        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
        if construct:
            (self._poly, self._valbase, self._relprecs, self._normalized, self._valaddeds, self._list) = x #the last two of these may be None
            return
        elif is_gen:
            self._poly = PolynomialRing(ZZ, parent.variable_name()).gen()
            self._valbase = 0
            self._valaddeds = [infinity, 0]
            self._relprecs = [infinity, parentbr.precision_cap()]
            self._normalized = True
            self._list = None
            return

        #First we list the types that are turned into Polynomials
        if isinstance(x, ZZX):
            x = Polynomial_integer_dense(PolynomialRing(ZZ, parent.variable_name()), x, construct = True)
        elif isinstance(x, fraction_field_element.FractionFieldElement) and \
               x.denominator() == 1:
            #Currently we ignore precision information in the denominator.  This should be changed eventually
            x = x.numerator()

        #We now coerce various types into lists of coefficients.  There are fast pathways for some types of polynomials
        if isinstance(x, Polynomial):
            if x.parent() is self.parent():
                if not absprec is infinity or not relprec is infinity:
                    x._normalize()
                self._poly = x._poly
                self._valbase = x._valbase
                self._valaddeds = x._valaddeds
                self._relprecs = x._relprecs
                self._normalized = x._normalized
                self._list = x._list
                if not absprec is infinity or not relprec is infinity:
                    self._adjust_prec_info(absprec, relprec)
                return
            elif x.base_ring() is ZZ:
                self._poly = x
                self._valbase = Integer(0)
                p = parentbr.prime()
                self._relprecs = [c.valuation(p) + parentbr.precision_cap() for c in x.list()]
                self._comp_valaddeds()
                self._normalized = len(self._valaddeds) == 0 or (min(self._valaddeds) == 0)
                self._list = None
                if not absprec is infinity or not relprec is infinity:
                    self._adjust_prec_info(absprec, relprec)
                return
            else:
                x = [parentbr(a) for a in x.list()]
                check = False
        elif isinstance(x, dict):
            zero = parentbr.zero_element()
            n = max(x.keys())
            v = [zero for _ in xrange(n + 1)]
            for i, z in x.iteritems():
                v[i] = z
            x = v
        elif isinstance(x, pari_gen):
            x = [parentbr(w) for w in x.list()]
            check = False
        #The default behavior if we haven't already figured out what the type is is to assume it coerces into the base_ring as a constant polynomial
        elif not isinstance(x, list):
            x = [x] # constant polynomial

        # In contrast to other polynomials, the zero element is not distinguished
        # by having its list empty. Instead, it has list [0]
        if not x:
            x = [parentbr.zero_element()]
        if check:
            x = [parentbr(z) for z in x]

        # Remove this -- for p-adics this is terrible, since it kills any non exact zero.
        #if len(x) == 1 and not x[0]:
        #    x = []

        self._list = x
        self._valaddeds = [a.valuation() for a in x]
        self._valbase = sage.rings.padics.misc.min(self._valaddeds)
        if self._valbase is infinity:
            self._valaddeds = []
            self._relprecs = []
            self._poly = PolynomialRing(ZZ, parent.variable_name())()
            self._normalized = True
            if not absprec is infinity or not relprec is infinity:
                self._adjust_prec_info(absprec, relprec)
        else:
            self._valaddeds = [c - self._valbase for c in self._valaddeds]
#.........这里部分代码省略.........

# 需要导入模块: from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing [as 别名]
# 或者: from sage.rings.polynomial.polynomial_ring_constructor.PolynomialRing import valuation [as 别名]
class Polynomial_padic_capped_relative_dense(Polynomial_generic_domain, Polynomial_padic):
    def __init__(self, parent, x=None, check=True, is_gen=False, construct = False, absprec = infinity, relprec = infinity):
        """
        TESTS::

            sage: K = Qp(13,7)
            sage: R.<t> = K[]
            sage: R([K(13), K(1)])
            (1 + O(13^7))*t + (13 + O(13^8))
            sage: T.<t> = ZZ[]
            sage: R(t + 2)
            (1 + O(13^7))*t + (2 + O(13^7))

        Check that :trac:`13620` has been fixed::

            sage: f = R.zero()
            sage: R(f.dict())
            0

        """
        Polynomial.__init__(self, parent, is_gen=is_gen)
        parentbr = parent.base_ring()
        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
        if construct:
            (self._poly, self._valbase, self._relprecs, self._normalized, self._valaddeds, self._list) = x #the last two of these may be None
            return
        elif is_gen:
            self._poly = PolynomialRing(ZZ, parent.variable_name()).gen()
            self._valbase = 0
            self._valaddeds = [infinity, 0]
            self._relprecs = [infinity, parentbr.precision_cap()]
            self._normalized = True
            self._list = None
            return

        #First we list the types that are turned into Polynomials
        if isinstance(x, ZZX):
            x = Polynomial_integer_dense(PolynomialRing(ZZ, parent.variable_name()), x, construct = True)
        elif isinstance(x, fraction_field_element.FractionFieldElement) and \
               x.denominator() == 1:
            #Currently we ignore precision information in the denominator.  This should be changed eventually
            x = x.numerator()

        #We now coerce various types into lists of coefficients.  There are fast pathways for some types of polynomials
        if isinstance(x, Polynomial):
            if x.parent() is self.parent():
                if not absprec is infinity or not relprec is infinity:
                    x._normalize()
                self._poly = x._poly
                self._valbase = x._valbase
                self._valaddeds = x._valaddeds
                self._relprecs = x._relprecs
                self._normalized = x._normalized
                self._list = x._list
                if not absprec is infinity or not relprec is infinity:
                    self._adjust_prec_info(absprec, relprec)
                return
            elif x.base_ring() is ZZ:
                self._poly = x
                self._valbase = Integer(0)
                p = parentbr.prime()
                self._relprecs = [c.valuation(p) + parentbr.precision_cap() for c in x.list()]
                self._comp_valaddeds()
                self._normalized = len(self._valaddeds) == 0 or (min(self._valaddeds) == 0)
                self._list = None
                if not absprec is infinity or not relprec is infinity:
                    self._adjust_prec_info(absprec, relprec)
                return
            else:
                x = [parentbr(a) for a in x.list()]
                check = False
        elif isinstance(x, dict):
            zero = parentbr.zero()
            n = max(x.keys()) if x else 0
            v = [zero for _ in xrange(n + 1)]
            for i, z in x.iteritems():
                v[i] = z
            x = v
        elif isinstance(x, pari_gen):
            x = [parentbr(w) for w in x.list()]
            check = False
        #The default behavior if we haven't already figured out what the type is is to assume it coerces into the base_ring as a constant polynomial
        elif not isinstance(x, list):
            x = [x] # constant polynomial

        # In contrast to other polynomials, the zero element is not distinguished
        # by having its list empty. Instead, it has list [0]
        if not x:
            x = [parentbr.zero()]
        if check:
            x = [parentbr(z) for z in x]

        # Remove this -- for p-adics this is terrible, since it kills any non exact zero.
        #if len(x) == 1 and not x[0]:
        #    x = []

        self._list = x
        self._valaddeds = [a.valuation() for a in x]
        self._valbase = sage.rings.padics.misc.min(self._valaddeds)
        if self._valbase is infinity:
#.........这里部分代码省略.........