Package sage :: Package rings :: Module sparse_poly :: Class Polynomial_rational
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Type Polynomial_rational

object --+    
         |    
Polynomial --+
             |
            Polynomial_rational


Polynomial_rational():

Create the zero polynomial over the rational numbers.
Method Summary
  __init__(...)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
  __add__(x, y)
x.__add__(y) <==> x+y
  __delitem__(x, y)
x.__delitem__(y) <==> del x[y]
  __mul__(x, y)
x.__mul__(y) <==> x*y
  __new__(T, S, ...)
T.__new__(S, ...) -> a new object with type S, a subtype of T
  __radd__(x, y)
x.__radd__(y) <==> y+x
  __repr__(x)
x.__repr__() <==> repr(x)
  __rmul__(x, y)
x.__rmul__(y) <==> y*x
  __setitem__(x, i, y)
x.__setitem__(i, y) <==> x[i]=y
  copy(...)
  list(...)
    Inherited from Polynomial
  __call__(x, ...)
x.__call__(...) <==> x(...)
  __cmp__(x, y)
x.__cmp__(y) <==> cmp(x,y)
  __div__(x, y)
x.__div__(y) <==> x/y
  __floordiv__(x, y)
x.__floordiv__(y) <==> x//y
  __getitem__(x, y)
x.__getitem__(y) <==> x[y]
  __getslice__(x, i, j)
Use of negative indices is not supported.
  __hash__(x)
x.__hash__() <==> hash(x)
  __int__(x)
x.__int__() <==> int(x)
  __long__(x)
x.__long__() <==> long(x)
  __mod__(x, y)
x.__mod__(y) <==> x%y
  __neg__(x)
x.__neg__() <==> -x
  __pos__(x)
x.__pos__() <==> +x
  __pow__(x, y, z)
x.__pow__(y[, z]) <==> pow(x, y[, z])
  __rdiv__(x, y)
x.__rdiv__(y) <==> y/x
  __rfloordiv__(x, y)
x.__rfloordiv__(y) <==> y//x
  __rmod__(x, y)
x.__rmod__(y) <==> y%x
  __rpow__(y, x, z)
y.__rpow__(x[, z]) <==> pow(x, y[, z])
  __rsub__(x, y)
x.__rsub__(y) <==> y-x
  __sub__(x, y)
x.__sub__(y) <==> x-y
  base_ring(...)
  degree(...)
  derivative(...)
  factor(...)
  gcd(...)
  is_irreducible(...)
  is_zero(...)
  leading_coefficient(...)
  randomize(...)
  resultant(...)
  reverse(...)
  valuation(...)
  variable(...)
  xgcd(...)
    Inherited from object
  __delattr__(...)
x.__delattr__('name') <==> del x.name
  __getattribute__(...)
x.__getattribute__('name') <==> x.name
  __reduce__(...)
helper for pickle
  __reduce_ex__(...)
helper for pickle
  __setattr__(...)
x.__setattr__('name', value) <==> x.name = value
  __str__(x)
x.__str__() <==> str(x)

Method Details

__init__(...)
(Constructor)

x.__init__(...) initializes x; see x.__class__.__doc__ for signature
Overrides:
sage.rings.sparse_poly.Polynomial.__init__

__add__(x, y)
(Addition operator)

x.__add__(y) <==> x+y
Returns:
x+y
Overrides:
sage.rings.sparse_poly.Polynomial.__add__

__delitem__(x, y)
(Index deletion operator)

x.__delitem__(y) <==> del x[y]
Returns:
del x[y]
Overrides:
sage.rings.sparse_poly.Polynomial.__delitem__

__mul__(x, y)

x.__mul__(y) <==> x*y
Returns:
x*y
Overrides:
sage.rings.sparse_poly.Polynomial.__mul__

__new__(T, S, ...)

T.__new__(S, ...) -> a new object with type S, a subtype of T
Returns:
a new object with type S, a subtype of T
Overrides:
sage.rings.sparse_poly.Polynomial.__new__

__radd__(x, y)
(Right-side addition operator)

x.__radd__(y) <==> y+x
Returns:
y+x
Overrides:
sage.rings.sparse_poly.Polynomial.__radd__

__repr__(x)
(Representation operator)

x.__repr__() <==> repr(x)
Returns:
repr(x)
Overrides:
sage.rings.sparse_poly.Polynomial.__repr__

__rmul__(x, y)

x.__rmul__(y) <==> y*x
Returns:
y*x
Overrides:
sage.rings.sparse_poly.Polynomial.__rmul__

__setitem__(x, i, y)
(Index assignment operator)

x.__setitem__(i, y) <==> x[i]=y
Returns:
x[i]=y
Overrides:
sage.rings.sparse_poly.Polynomial.__setitem__

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