Python ZZ.is_prime方法代码示例

# 需要导入模块: from sage.all import ZZ [as 别名]
# 或者: from sage.all.ZZ import is_prime [as 别名]
 def includes_composite(s):
     s = s.replace(' ','').replace('..','-')
     for interval in s.split(','):
         if '-' in interval[1:]:
             ix = interval.index('-',1)
             a,b = int(interval[:ix]), int(interval[ix+1:])
             if b == a:
                 if a != 1 and not a.is_prime():
                     return True
             if b > a and b > 3:
                 return True
         else:
             a = ZZ(interval)
             if a != 1 and not a.is_prime():
                 return True

# 需要导入模块: from sage.all import ZZ [as 别名]
# 或者: from sage.all.ZZ import is_prime [as 别名]
 def includes_composite(s):
     s = s.replace(" ", "").replace("..", "-")
     for interval in s.split(","):
         if "-" in interval[1:]:
             ix = interval.index("-", 1)
             a, b = int(interval[:ix]), int(interval[ix + 1 :])
             if b == a:
                 if a != 1 and not a.is_prime():
                     return True
             if b > a and b > 3:
                 return True
         else:
             a = ZZ(interval)
             if a != 1 and not a.is_prime():
                 return True

# 需要导入模块: from sage.all import ZZ [as 别名]
# 或者: from sage.all.ZZ import is_prime [as 别名]
def find_curve(P, DB, NE, prec, sign_ap = None, magma = None, return_all = False, initial_data = None, ramification_at_infinity = None, **kwargs):
    r'''
    EXAMPLES:

    First example::

    sage: from darmonpoints.findcurve import find_curve
    sage: find_curve(5,6,30,20) # long time # optional - magma
    # B = F<i,j,k>, with i^2 = -1 and j^2 = 3
    ...
    '(1, 0, 1, -289, 1862)'

    A second example, now over a real quadratic::

    sage: from darmonpoints.findcurve import find_curve
    sage: F.<r> = QuadraticField(5)
    sage: P = F.ideal(3/2*r + 1/2)
    sage: D = F.ideal(3)
    sage: find_curve(P,D,P*D,30,ramification_at_infinity = F.real_places()[:1]) # long time # optional - magma
    ...

    Now over a cubic of mixed signature::

    sage: from darmonpoints.findcurve import find_curve
    sage: F.<r> = NumberField(x^3 -3)
    sage: P = F.ideal(r-2)
    sage: D = F.ideal(r-1)
    sage: find_curve(P,D,P*D,30) # long time # optional - magma
    ...

    '''
    config = ConfigParser.ConfigParser()
    config.read('config.ini')
    param_dict = config_section_map(config, 'General')
    param_dict.update(config_section_map(config, 'FindCurve'))
    param_dict.update(kwargs)
    param = Bunch(**param_dict)

    # Get general parameters
    outfile = param.get('outfile')
    use_ps_dists = param.get('use_ps_dists',False)
    use_shapiro = param.get('use_shapiro',True)
    use_sage_db = param.get('use_sage_db',False)
    magma_seed = param.get('magma_seed',1515316)
    parallelize = param.get('parallelize',False)
    Up_method = param.get('up_method','naive')
    use_magma = param.get('use_magma',True)
    progress_bar = param.get('progress_bar',True)
    sign_at_infinity = param.get('sign_at_infinity',ZZ(1))

    # Get find_curve specific parameters
    grouptype = param.get('grouptype')
    hecke_bound = param.get('hecke_bound',3)
    timeout = param.get('timeout',0)
    check_conductor = param.get('check_conductor',True)

    if initial_data is None:
        page_path = os.path.dirname(__file__) + '/KleinianGroups-1.0/klngpspec'
        if magma is None:
            from sage.interfaces.magma import Magma
            quit_when_done = True
            magma = Magma()
        else:
            quit_when_done = False
        if magma_seed is not None:
            magma.eval('SetSeed(%s)'%magma_seed)
        magma.attach_spec(page_path)
        magma.eval('Page_initialized := true')
    else:
        quit_when_done = False

    sys.setrecursionlimit(10**6)

    # global qE, Linv, G, Coh, phiE, xgen, xi1, xi2, Phi

    try:
        F = P.ring()
        Fdisc = F.discriminant()
        if not (P*DB).divides(NE):
            raise ValueError,'Conductor (NE) should be divisible by P*DB'
        p = ZZ(P.norm()).abs()

    except AttributeError:
        F = QQ
        P = ZZ(P)
        p = ZZ(P)
        Fdisc = ZZ(1)
        if NE % (P*DB) != 0:
            raise ValueError,'Conductor (NE) should be divisible by P*DB'

    Ncartan = kwargs.get('Ncartan',None)
    Np = NE / (P * DB)
    if Ncartan is not None:
        Np = Np / Ncartan**2
    if use_ps_dists is None:
        use_ps_dists = False # More efficient our own implementation

    if not p.is_prime():
        raise ValueError,'P (= %s) should be a prime, of inertia degree 1'%P

#.........这里部分代码省略.........