def __init__(self,ringstr="",truncate=None,ring=None,cofac=None,name="z"):
'''Ring constructor.
'''
if ring == None:
if len(ringstr) > 0:
sr = StringReader( ringstr );
tok = GenPolynomialTokenizer(sr);
pset = tok.nextPolynomialSet();
ring = pset.ring;
vname = ring.vars;
name = vname[0];
cofac = ring.coFac;
if isinstance(cofac,RingElem):
cofac = cofac.elem;
if truncate == None:
self.ring = UnivPowerSeriesRing(cofac,name);
else:
self.ring = UnivPowerSeriesRing(cofac,truncate,name);
else:
self.ring = ring;
class SeriesRing:
'''Represents a JAS power series ring: UnivPowerSeriesRing.
Methods for power series arithmetic.
'''
def __init__(self,ringstr="",truncate=None,ring=None,cofac=None,name="z"):
'''Ring constructor.
'''
if ring == None:
if len(ringstr) > 0:
sr = StringReader( ringstr );
tok = GenPolynomialTokenizer(sr);
pset = tok.nextPolynomialSet();
ring = pset.ring;
vname = ring.vars;
name = vname[0];
cofac = ring.coFac;
if isinstance(cofac,RingElem):
cofac = cofac.elem;
if truncate == None:
self.ring = UnivPowerSeriesRing(cofac,name);
else:
self.ring = UnivPowerSeriesRing(cofac,truncate,name);
else:
self.ring = ring;
def __str__(self):
'''Create a string representation.
'''
return str(self.ring);
def gens(self):
'''Get the generator of the power series ring.
'''
return RingElem( self.ring.getONE().shift(1) );
def one(self):
'''Get the one of the power series ring.
'''
return RingElem( self.ring.getONE() );
def zero(self):
'''Get the zero of the power series ring.
'''
return RingElem( self.ring.getZERO() );
def random(self,n):
'''Get a random power series.
'''
return RingElem( self.ring.random(n) );
def exp(self):
'''Get the exponential power series.
'''
return RingElem( self.ring.getEXP() );
def sin(self):
'''Get the sinus power series.
'''
return RingElem( self.ring.getSIN() );
def cos(self):
'''Get the cosinus power series.
'''
return RingElem( self.ring.getCOS() );
def tan(self):
'''Get the tangens power series.
'''
return RingElem( self.ring.getTAN() );
def create(self,ifunc=None,jfunc=None,clazz=None):
'''Create a power series with given generating function.
ifunc(int i) must return a value which is used in RingFactory.fromInteger().
jfunc(int i) must return a value of type ring.coFac.
clazz must implement the Coefficients abstract class.
'''
class coeff( Coefficients ):
def __init__(self,cofac):
self.coFac = cofac;
def generate(self,i):
if jfunc == None:
return self.coFac.fromInteger( ifunc(i) );
else:
return jfunc(i);
if clazz == None:
ps = UnivPowerSeries( self.ring, coeff(self.ring.coFac) );
else:
ps = UnivPowerSeries( self.ring, clazz );
return RingElem( ps );
def fixPoint(self,psmap):
'''Create a power series as fixed point of the given mapping.
psmap must implement the PowerSeriesMap interface.
'''
ps = self.ring.fixPoint( psmap );
return RingElem( ps );
def gcd(self,a,b):
'''Compute the greatest common divisor of a and b.
'''
if isinstance(a,RingElem):
a = a.elem;
if isinstance(b,RingElem):
b = b.elem;
return RingElem( a.gcd(b) );
def from(self,a):
'''Convert a GenPolynomial to a power series.
'''
if isinstance(a,RingElem):
a = a.elem;
return RingElem( self.ring.fromPolynomial(a) );
