Working more on __call__ for LazySymFunc.

src/sage/data_structures/stream.py

@@ -2195,3 +2195,4 @@ def is_nonzero(self):
  True
  """
  return self._series.is_nonzero()
+

src/sage/rings/lazy_series.py

@@ -722,9 +722,13 @@ def define(self, s):
  sage: L = LazySymmetricFunctions(m)
  sage: E = L(lambda n: s[n], valuation=0)
  sage: X = L(s[1])
- sage: A = L(None); A.define(X*E(A))
+ sage: A = L(None, valuation=1); A.define(X*E(A))
  sage: A
- m[1] + (2*m[1,1]+m[2]) + (9*m[1,1,1]+5*m[2,1]+2*m[3]) + (64*m[1,1,1,1]+34*m[2,1,1]+18*m[2,2]+13*m[3,1]+4*m[4]) + (625*m[1,1,1,1,1]+326*m[2,1,1,1]+171*m[2,2,1]+119*m[3,1,1]+63*m[3,2]+35*m[4,1]+9*m[5]) + (7776*m[1,1,1,1,1,1]+4016*m[2,1,1,1,1]+2078*m[2,2,1,1]+1077*m[2,2,2]+1433*m[3,1,1,1]+744*m[3,2,1]+268*m[3,3]+401*m[4,1,1]+209*m[4,2]+95*m[5,1]+20*m[6]) + O^7
+ m[1] + (2*m[1,1]+m[2]) + (9*m[1,1,1]+5*m[2,1]+2*m[3])
+ + (64*m[1,1,1,1]+34*m[2,1,1]+18*m[2,2]+13*m[3,1]+4*m[4])
+ + (625*m[1,1,1,1,1]+326*m[2,1,1,1]+171*m[2,2,1]+119*m[3,1,1]+63*m[3,2]+35*m[4,1]+9*m[5])
+ + (7776*m[1,1,1,1,1,1]+4016*m[2,1,1,1,1]+2078*m[2,2,1,1]+1077*m[2,2,2]+1433*m[3,1,1,1]+744*m[3,2,1]+268*m[3,3]+401*m[4,1,1]+209*m[4,2]+95*m[5,1]+20*m[6])
+ + O^7
 
  TESTS::
 
@@ -3170,11 +3174,12 @@ def polynomial(self, degree=None, name=None):
  """
  S = self.parent()
 
+ if isinstance(self._coeff_stream, Stream_zero):
+ from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+ return PolynomialRing(S.base_ring(), name=name).zero()
+
  if degree is None:
- if isinstance(self._coeff_stream, Stream_zero):
- from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
- return PolynomialRing(S.base_ring(), name=name).zero()
- elif isinstance(self._coeff_stream, Stream_exact) and not self._coeff_stream._constant:
+ if isinstance(self._coeff_stream, Stream_exact) and not self._coeff_stream._constant:
  m = self._coeff_stream._degree
  else:
  raise ValueError("not a polynomial")
@@ -3327,13 +3332,13 @@ def __call__(self, *g):
  if len(g) == 1:
  # we assume that the valuation of self[i](g) is at least i
  def coefficient(n):
- r = R(0)
+ r = R.zero()
  for i in range(n+1):
  r += self[i]*(g0 ** i)[n]
  return r
  else:
  def coefficient(n):
- r = R(0)
+ r = R.zero()
  for i in range(n+1):
  r += self[i](g)[n]
  return r
@@ -3456,11 +3461,11 @@ def polynomial(self, degree=None, names=None):
  if names is None:
  names = S.variable_names()
  R = PolynomialRing(S.base_ring(), names=names)
+ if isinstance(self._coeff_stream, Stream_zero):
+ return R.zero()
 
  if degree is None:
- if isinstance(self._coeff_stream, Stream_zero):
- return R.zero()
- elif (isinstance(self._coeff_stream, Stream_exact)
+ if (isinstance(self._coeff_stream, Stream_exact)
  and not self._coeff_stream._constant):
  m = self._coeff_stream._degree
  else:
@@ -3507,20 +3512,23 @@ def __call__(self, *args):
  sage: P.<q> = QQ[]
  sage: s = SymmetricFunctions(P).s()
  sage: L = LazySymmetricFunctions(s)
- sage: f = s[2]; g = s[3]
+ sage: f = s[2]
+ sage: g = s[3]
  sage: L(f)(L(g)) - L(f(g))
- O^7
+ 0
 
- sage: f = s[2] + s[2,1]; g = s[1] + s[2,2]
+ sage: f = s[2] + s[2,1]
+ sage: g = s[1] + s[2,2]
  sage: L(f)(L(g)) - L(f(g))
- O^7
+ 0
 
  sage: L(f)(g) - L(f(g))
- O^7
+ 0
 
- sage: f = s[2] + s[2,1]; g = s[1] + s[2,2]
+ sage: f = s[2] + s[2,1]
+ sage: g = s[1] + s[2,2]
  sage: L(f)(L(q*g)) - L(f(q*g))
- O^7
+ 0
 
  The Frobenius character of the permutation action on set
  partitions is a plethysm::
@@ -3533,21 +3541,63 @@ def __call__(self, *args):
  sage: [s(x) for x in P[:5]]
  [s[], s[1], 2*s[2], s[2, 1] + 3*s[3], 2*s[2, 2] + 2*s[3, 1] + 5*s[4]]
 
+ TESTS::
+
+ sage: s = SymmetricFunctions(QQ).s()
+ sage: S = LazySymmetricFunctions(s)
+ sage: f = 1 / (1 - S(s[2]))
+ sage: g = f(s[2]); g
+ s[] + (s[2,2]+s[4]) + O^7
+ sage: S(sum(f[i](s[2]) for i in range(5))).truncate(10) == g.truncate(10)
+ True
+ sage: f(0)
+ 1
+ sage: f(s(1))
+ Traceback (most recent call last):
+ ...
+ ValueError: can only compose with a positive valuation series
  """
  if len(args) != self.parent()._arity:
  raise ValueError("arity must be equal to the number of arguments provided")
  from sage.combinat.sf.sfa import is_SymmetricFunction
- if not all(isinstance(g, LazySymmetricFunction) or is_SymmetricFunction(g) for g in args):
+ if not all(isinstance(g, LazySymmetricFunction) or is_SymmetricFunction(g) or not g for g in args):
  raise ValueError("all arguments must be (possibly lazy) symmetric functions")
- from sage.misc.lazy_list import lazy_list
+
+ if isinstance(self._coeff_stream, Stream_zero):
+ return self
+
  if len(args) == 1:
  g = args[0]
  P = g.parent()
+
+ # Handle other types of 0s
+ if not isinstance(g, LazySymmetricFunction) and not g:
+ return P(self[0].leading_coefficient())
+
+ if isinstance(self._coeff_stream, Stream_exact) and not self._coeff_stream._constant:
+ f = self.symmetric_function()
+ if is_SymmetricFunction(g):
+ return f(g)
+ # g must be a LazySymmetricFunction
+ if isinstance(g._coeff_stream, Stream_exact) and not g._coeff_stream._constant:
+ gs = g.symmetric_function()
+ return P(f(gs))
+
  BR = P.base_ring()
  if isinstance(g, LazySymmetricFunction):
  R = P._laurent_poly_ring
  else:
- R = P
+ from sage.rings.lazy_series_ring import LazySymmetricFunctions
+ R = g.parent()
+ P = LazySymmetricFunctions(R)
+ g = P(g)
+
+ # self has (potentially) infinitely many terms
+ if g._coeff_stream._approximate_order == 0:
+ if g[0]:
+ raise ValueError("can only compose with a positive valuation series")
+ g._coeff_stream._approximate_order = 1
+
  p = R.realization_of().power()
  g_p = Stream_map_coefficients(g._coeff_stream, lambda c: c, p)
  try:
@@ -3574,6 +3624,7 @@ def stretched_coefficient(k, n):
  def g_coeff_stream(k):
  return Stream_function(lambda n: stretched_coefficient(k, n),
  R, P._sparse, 0)
+ from sage.misc.lazy_list import lazy_list
  stretched = lazy_list(lambda k: g_coeff_stream(k))
  f_p = Stream_map_coefficients(self._coeff_stream, lambda c: c, p)
  def coefficient(n):
@@ -3657,6 +3708,71 @@ def parenthesize(m):
 
  return poly
 
+ def symmetric_function(self, degree=None):
+ r"""
+ Return ``self`` as a symmetric function if ``self`` is actually so.
+
+ INPUT:
+
+ - ``degree`` -- ``None`` or an integer
+
+ OUTPUT:
+
+ If ``degree`` is not ``None``, the terms of the series of degree greater
+ than ``degree`` are truncated first. If ``degree`` is ``None`` and the
+ series is not a polynomial polynomial, a ``ValueError`` is raised.
+
+ EXAMPLES::
+
+ sage: s = SymmetricFunctions(QQ).s()
+ sage: S = LazySymmetricFunctions(s)
+ sage: elt = S(s[2])
+ sage: elt.symmetric_function()
+ s[2]
+
+ TESTS::
+
+ sage: s = SymmetricFunctions(QQ).s()
+ sage: S = LazySymmetricFunctions(s)
+ sage: elt = S(s[2])
+ sage: elt.symmetric_function()
+ s[2]
+ sage: f = 1 / (1 - elt)
+ sage: f
+ s[] + s[2] + (s[2,2]+s[3,1]+s[4]) + (s[2,2,2]+2*s[3,2,1]+s[3,3]+s[4,1,1]+3*s[4,2]+2*s[5,1]+s[6]) + O^7
+ sage: f.symmetric_function()
+ Traceback (most recent call last):
+ ...
+ ValueError: not a symmetric function
+
+ sage: f4 = f.truncate(5); f4
+ s[] + s[2] + (s[2,2]+s[3,1]+s[4])
+ sage: f4.symmetric_function()
+ s[] + s[2] + s[2, 2] + s[3, 1] + s[4]
+ sage: f4.symmetric_function() == f.symmetric_function(4)
+ True
+ sage: S.zero().symmetric_function()
+ 0
+ sage: f4.symmetric_function(0)
+ s[]
+ """
+ S = self.parent()
+ R = S._laurent_poly_ring
+
+ if isinstance(self._coeff_stream, Stream_zero):
+ return R.zero()
+
+ if degree is None:
+ if (isinstance(self._coeff_stream, Stream_exact)
+ and not self._coeff_stream._constant):
+ m = self._coeff_stream._degree
+ else:
+ raise ValueError("not a symmetric function")
+ else:
+ m = degree + 1
+
+ return R.sum(self[:m])
+
 class LazyDirichletSeries(LazyModuleElement):
  r"""
  A Dirichlet series where the coefficients are computed lazily.
@@ -3985,3 +4101,4 @@ def parenthesize(m):
  poly = formatter(*([parenthesize(mo) for mo in mons] + bigO), sep=" + ")
 
  return poly
+

src/sage/rings/lazy_series_ring.py

@@ -2057,3 +2057,4 @@ def _monomial(self, c, n):
  return '({})/{}^{}'.format(self.base_ring()(c), n, self.variable_name())
 
  options = LazyLaurentSeriesRing.options
+