def zero(self):
'''Zero element of this ring.
'''
if self.isFactory():
return RingElem( self.elem.getZERO() );
else:
return RingElem( self.elem.ring.getZERO() );
def one(self):
'''One element of this ring.
'''
if self.isFactory():
return RingElem( self.elem.getONE() );
else:
return RingElem( self.elem.ring.getONE() );
def element(self,polystr):
'''Create an element from a string.
'''
I = Ideal(self, "( " + polystr + " )");
list = I.pset.list;
if len(list) > 0:
return RingElem( list[0] );
def CC(re=BigRational(),im=BigRational()):
'''Create JAS BigComplex as ring element.
'''
if isinstance(re,PyTuple) or isinstance(re,PyList):
if isinstance(re[0],PyTuple) or isinstance(re[0],PyList):
if len(re) > 1:
im = QQ( re[1] );
re = QQ( re[0] );
else:
re = QQ(re);
# re = makeJasArith( re );
if isinstance(im,PyTuple) or isinstance(im,PyList):
im = QQ( im );
# im = makeJasArith( im );
if isinstance(re,RingElem):
re = re.elem;
if isinstance(im,RingElem):
im = im.elem;
if im.isZERO():
if re.isZERO():
c = BigComplex();
else:
c = BigComplex(re);
else:
c = BigComplex(re,im);
return RingElem(c);
def random(self,k=5,l=7,d=3,q=0.3):
'''Get a random polynomial.
'''
r = self.ring.random(k,l,d,q);
if self.ring.coFac.isField():
r = r.monic();
return RingElem( r );
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 differentiate(self):
'''Differentiate a power series.
'''
try:
e = self.elem.differentiate();
except:
e = None;
return RingElem( e );
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 coerce(self,other):
'''Coerce other to self.
'''
#print "self type(%s) = %s" % (self,type(self));
#print "other type(%s) = %s" % (other,type(other));
if isinstance(other,RingElem):
if self.isPolynomial() and not other.isPolynomial():
o = self.ring.parse( str(other) );
return RingElem( o );
return other;
#print "--1";
if isinstance(other,PyTuple) or isinstance(other,PyList):
# assume BigRational or BigComplex
# assume self will be compatible with them. todo: check this
o = makeJasArith(other);
return RingElem(o);
#print "--2";
# test if self.elem is a factory itself
if self.isFactory():
if isinstance(other,PyInteger) or isinstance(other,PyLong):
o = self.elem.fromInteger(other);
else:
if isinstance(other,PyFloat): # ?? what to do ??
o = self.elem.fromInteger( int(other) );
else:
print "unknown other type(%s) = %s" % (other,type(other));
o = other;
return RingElem(o);
#print "--3";
# self.elem has a ring factory
if isinstance(other,PyInteger) or isinstance(other,PyLong):
o = self.elem.ring.fromInteger(other);
else:
if isinstance(other,PyFloat): # ?? what to do ??
o = self.elem.ring.fromInteger( int(other) );
else:
print "unknown other type(%s) = %s" % (other,type(other));
o = other;
#print "--4";
return RingElem(o);
def DD(d=0):
'''Create JAS BigDecimal as ring element.
'''
if isinstance(d,RingElem):
d = d.elem;
if isinstance(d,PyFloat):
d = str(d);
#print "d type(%s) = %s" % (d,type(d));
if d == 0:
r = BigDecimal();
else:
r = BigDecimal(d);
return RingElem(r);
def gcd(self,a,b):
'''Compute the greatest common divisor of a and b.
'''
if isinstance(a,RingElem):
a = a.elem;
else:
a = self.element( str(a) );
a = a.elem;
if isinstance(b,RingElem):
b = b.elem;
else:
b = self.element( str(b) );
b = b.elem;
return RingElem( self.engine.gcd(a,b) );
def integrate(self,a):
'''Integrate a power series with constant a.
'''
#print "self type(%s) = %s" % (self,type(self));
#print "a type(%s) = %s" % (a,type(a));
x = None;
if isinstance(a,RingElem):
x = a.elem;
if isinstance(a,PyTuple) or isinstance(a,PyList):
# assume BigRational or BigComplex
# assume self will be compatible with them. todo: check this
x = makeJasArith(a);
try:
e = self.elem.integrate(x);
except:
e = None;
return RingElem( e );
def RF(d,n=1):
'''Create JAS rational function Quotient as ring element.
'''
if isinstance(d,PyTuple) or isinstance(d,PyList):
if n != 1:
print "%s ignored" % n;
if len(d) > 1:
n = d[1];
d = d[0];
if isinstance(d,RingElem):
d = d.elem;
if isinstance(n,RingElem):
n = n.elem;
qr = QuotientRing(d.ring);
if n == 1:
r = Quotient(qr,d);
else:
r = Quotient(qr,d,n);
return RingElem(r);
def __pow__(self,other):
'''Power of this to other.
'''
#print "self type(%s) = %s" % (self,type(self));
#print "pow other type(%s) = %s" % (other,type(other));
if isinstance(other,PyInteger):
n = other;
else:
if isinstance(other,RingElem):
n = other.elem;
if isinstance(n,BigRational): # does not work
n = n.numerator().intValue();
if isinstance(n,BigInteger): # does not work
n = n.intValue();
if self.isFactory():
p = Power(self.elem).power( self.elem, n );
else:
p = Power(self.elem.ring).power( self.elem, n );
return RingElem( p );
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 QQ(d=0,n=1):
'''Create JAS BigRational as ring element.
'''
if isinstance(d,PyTuple) or isinstance(d,PyList):
if n != 1:
print "%s ignored" % n;
if len(d) > 1:
n = d[1];
d = d[0];
if isinstance(d,RingElem):
d = d.elem;
if isinstance(n,RingElem):
n = n.elem;
if n == 1:
if d == 0:
r = BigRational();
else:
r = BigRational(d);
else:
r = BigRational(d,n);
return RingElem(r);
def gens(self):
'''Get list of generators of the polynomial ring.
'''
L = self.ring.univariateList();
c = self.ring.coFac;
nv = None;
try:
nv = c.nvar;
except:
pass
#print "type(coFac) = ", type(self.ring.coFac);
#if isinstance(c,GenPolynomial): # does not work
if nv:
Lp = c.univariateList();
#Ls = [ GenPolynomial(self.ring,l) for l in Lp ];
i = 0;
for l in Lp:
L.add( i, GenPolynomial(self.ring,l) );
i += 1;
N = [ RingElem(e) for e in L ];
return N;
def tan(self):
'''Get the tangens power series.
'''
return RingElem( self.ring.getTAN() );
def cos(self):
'''Get the cosinus power series.
'''
return RingElem( self.ring.getCOS() );
def sin(self):
'''Get the sinus power series.
'''
return RingElem( self.ring.getSIN() );
def exp(self):
'''Get the exponential power series.
'''
return RingElem( self.ring.getEXP() );
def random(self,n):
'''Get a random power series.
'''
return RingElem( self.ring.random(n) );
def zero(self):
'''Get the zero of the power series ring.
'''
return RingElem( self.ring.getZERO() );
def one(self):
'''Get the one of the power series ring.
'''
return RingElem( self.ring.getONE() );
def gens(self):
'''Get the generator of the power series ring.
'''
return RingElem( self.ring.getONE().shift(1) );
def zero(self):
'''Get the zero of the solvable polynomial ring.
'''
return RingElem( self.ring.getZERO() );
def one(self):
'''Get the one of the solvable polynomial ring.
'''
return RingElem( self.ring.getONE() );
def __sub__(self,other):
'''Subtract two ring elements.
'''
[s,o] = coercePair(self,other);
return RingElem( s.elem.subtract( o.elem ) );
def __div__(self,other):
'''Divide two ring elements.
'''
[s,o] = coercePair(self,other);
return RingElem( s.elem.divide( o.elem ) );
def __mod__(self,other):
'''Modular remainder of two ring elements.
'''
[s,o] = coercePair(self,other);
return RingElem( s.elem.remainder( o.elem ) );