Trac #32367: Replace Lazy Power Series in species directory

In this ticket we finalize the implementation of lazy series, and
replace the old lazy series framework.

URL: https://trac.sagemath.org/32367
Reported by: gh-tejasvicsr1
Ticket author(s): Tejasvi Chebrolu, Martin Rubey, Travis Scrimshaw
Reviewer(s): Martin Rubey, Travis Scrimshaw

src/doc/en/reference/combinat/module_list.rst

@@ -339,11 +339,8 @@ Comprehensive Module List
     sage/combinat/species/permutation_species
     sage/combinat/species/product_species
     sage/combinat/species/recursive_species
-    sage/combinat/species/series
-    sage/combinat/species/series_order
     sage/combinat/species/set_species
     sage/combinat/species/species
-    sage/combinat/species/stream
     sage/combinat/species/structure
     sage/combinat/species/subset_species
     sage/combinat/species/sum_species

src/sage/categories/highest_weight_crystals.py

@@ -322,14 +322,9 @@ def q_dimension(self, q=None, prec=None, use_product=False):
                 1 + q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 7*q^6
                  + 9*q^7 + 13*q^8 + 16*q^9 + O(q^10)
                 sage: qdim = C.q_dimension(); qdim
-                1 + q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 7*q^6
-                 + 9*q^7 + 13*q^8 + 16*q^9 + 22*q^10 + O(x^11)
-                sage: qdim.compute_coefficients(15)
-                sage: qdim
-                1 + q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 7*q^6
-                 + 9*q^7 + 13*q^8 + 16*q^9 + 22*q^10 + 27*q^11
-                 + 36*q^12 + 44*q^13 + 57*q^14 + 70*q^15 + O(x^16)
-
+                1 + q + 2*q^2 + 2*q^3 + 4*q^4 + 5*q^5 + 7*q^6 + O(q^7)
+                sage: qdim[:16]
+                [1, 1, 2, 2, 4, 5, 7, 9, 13, 16, 22, 27, 36, 44, 57, 70]
             """
             from sage.rings.integer_ring import ZZ
             WLR = self.weight_lattice_realization()
@@ -375,22 +370,21 @@ def iter_by_deg(gens):
             elif prec is None:
                 # If we're here, we may not be a finite crystal.
                 # In fact, we're probably infinite.
-                from sage.combinat.species.series import LazyPowerSeriesRing
+                from sage.rings.lazy_series_ring import LazyPowerSeriesRing
                 if q is None:
                     P = LazyPowerSeriesRing(ZZ, names='q')
                 else:
                     P = q.parent()
                 if not isinstance(P, LazyPowerSeriesRing):
                     raise TypeError("the parent of q must be a lazy power series ring")
                 ret = P(iter_by_deg(mg))
-                ret.compute_coefficients(10)
                 return ret
 
             from sage.rings.power_series_ring import PowerSeriesRing, PowerSeriesRing_generic
             if q is None:
                 q = PowerSeriesRing(ZZ, 'q', default_prec=prec).gen(0)
             P = q.parent()
-            ret = P.sum(c * q**deg for deg,c in enumerate(iter_by_deg(mg)))
+            ret = P.sum(c * q**deg for deg, c in enumerate(iter_by_deg(mg)))
             if ret.degree() == max_deg and isinstance(P, PowerSeriesRing_generic):
                 ret = P(ret, prec)
             return ret

src/sage/categories/sets_with_grading.py

@@ -212,11 +212,21 @@ def generating_series(self):
                 Non negative integers
                 sage: N.generating_series()
                 1/(-z + 1)
+
+                sage: Permutations().generating_series()
+                1 + z + 2*z^2 + 6*z^3 + 24*z^4 + 120*z^5 + 720*z^6 + O(z^7)
+
+             .. TODO::
+
+                 - Very likely, this should always return a lazy power series.
             """
-            from sage.combinat.species.series import LazyPowerSeriesRing
+            from sage.sets.non_negative_integers import NonNegativeIntegers
+            from sage.rings.lazy_series_ring import LazyPowerSeriesRing
             from sage.rings.integer_ring import ZZ
-            R = LazyPowerSeriesRing(ZZ)
-            R(self.graded_component(grade).cardinality() for grade in self.grading_set())
+            if isinstance(self.grading_set(), NonNegativeIntegers):
+                R = LazyPowerSeriesRing(ZZ, names="z")
+                return R(lambda n: self.graded_component(n).cardinality())
+            raise NotImplementedError
 
         # TODO:
         #   * asymptotic behavior: we need an object for asymptotic behavior and

src/sage/combinat/species/all.py

@@ -11,14 +11,6 @@
 - :ref:`section-examples-catalan`
 - :ref:`section-generic-species`
 
-Lazy Power Series
------------------
-
-- :ref:`sage.combinat.species.stream`
-- :ref:`sage.combinat.species.series_order`
-- :ref:`sage.combinat.species.series`
-- :ref:`sage.combinat.species.generating_series`
-
 Basic Species
 -------------
 
@@ -52,6 +44,8 @@
 from sage.misc.namespace_package import install_doc
 install_doc(__package__, __doc__)
 
-from .series import LazyPowerSeriesRing
-from .recursive_species import CombinatorialSpecies
-from . import library as species
+from sage.misc.lazy_import import lazy_import
+lazy_import("sage.combinat.species.recursive_species", "CombinatorialSpecies")
+lazy_import("sage.combinat.species", "library", as_="species")
+del lazy_import
+

src/sage/combinat/species/characteristic_species.py

@@ -109,15 +109,15 @@ def __init__(self, n, min=None, max=None, weight=None):
             [1]
             sage: X.structures([1,2]).list()
             []
-            sage: X.generating_series().coefficients(4)
+            sage: X.generating_series()[0:4]
             [0, 1, 0, 0]
-            sage: X.isotype_generating_series().coefficients(4)
+            sage: X.isotype_generating_series()[0:4]
             [0, 1, 0, 0]
-            sage: X.cycle_index_series().coefficients(4)
+            sage: X.cycle_index_series()[0:4]
             [0, p[1], 0, 0]
 
             sage: F = species.CharacteristicSpecies(3)
-            sage: c = F.generating_series().coefficients(4)
+            sage: c = F.generating_series()[0:4]
             sage: F._check()
             True
             sage: F == loads(dumps(F))
@@ -163,7 +163,7 @@ def _gs_term(self, base_ring):
         EXAMPLES::
 
             sage: F = species.CharacteristicSpecies(2)
-            sage: F.generating_series().coefficients(5)
+            sage: F.generating_series()[0:5]
             [0, 0, 1/2, 0, 0]
             sage: F.generating_series().count(2)
             1
@@ -187,7 +187,7 @@ def _itgs_term(self, base_ring):
         EXAMPLES::
 
             sage: F = species.CharacteristicSpecies(2)
-            sage: F.isotype_generating_series().coefficients(5)
+            sage: F.isotype_generating_series()[0:5]
             [0, 0, 1, 0, 0]
 
         Here we test out weighting each structure by q.
@@ -196,7 +196,7 @@ def _itgs_term(self, base_ring):
 
             sage: R.<q> = ZZ[]
             sage: Fq = species.CharacteristicSpecies(2, weight=q)
-            sage: Fq.isotype_generating_series().coefficients(5)
+            sage: Fq.isotype_generating_series()[0:5]
             [0, 0, q, 0, 0]
         """
         return base_ring(self._weight)
@@ -207,7 +207,7 @@ def _cis_term(self, base_ring):
 
             sage: F = species.CharacteristicSpecies(2)
             sage: g = F.cycle_index_series()
-            sage: g.coefficients(5)
+            sage: g[0:5]
             [0, 0, 1/2*p[1, 1] + 1/2*p[2], 0, 0]
         """
         cis = SetSpecies(weight=self._weight).cycle_index_series(base_ring)
@@ -248,11 +248,11 @@ def __init__(self, min=None, max=None, weight=None):
             [{}]
             sage: X.structures([1,2]).list()
             []
-            sage: X.generating_series().coefficients(4)
+            sage: X.generating_series()[0:4]
             [1, 0, 0, 0]
-            sage: X.isotype_generating_series().coefficients(4)
+            sage: X.isotype_generating_series()[0:4]
             [1, 0, 0, 0]
-            sage: X.cycle_index_series().coefficients(4)
+            sage: X.cycle_index_series()[0:4]
             [p[], 0, 0, 0]
 
         TESTS::
@@ -290,11 +290,11 @@ def __init__(self, min=None, max=None, weight=None):
             [1]
             sage: X.structures([1,2]).list()
             []
-            sage: X.generating_series().coefficients(4)
+            sage: X.generating_series()[0:4]
             [0, 1, 0, 0]
-            sage: X.isotype_generating_series().coefficients(4)
+            sage: X.isotype_generating_series()[0:4]
             [0, 1, 0, 0]
-            sage: X.cycle_index_series().coefficients(4)
+            sage: X.cycle_index_series()[0:4]
             [0, p[1], 0, 0]
 
         TESTS::

src/sage/combinat/species/composition_species.py

@@ -62,7 +62,7 @@ def transport(self, perm):
         f, gs = self._list
         pi = self._partition.transport(perm)
         f = f.change_labels(pi._list)
-        g = [g.change_labels(part) for g, part in zip(gs, pi)]  # BUG HERE ?
+        _ = [g.change_labels(part) for g, part in zip(gs, pi)]  # TODO: BUG HERE ?
         return self.__class__(self, self._labels, pi, f, gs)
 
     def change_labels(self, labels):
@@ -105,7 +105,7 @@ def __init__(self, F, G, min=None, max=None, weight=None):
             sage: E = species.SetSpecies()
             sage: C = species.CycleSpecies()
             sage: S = E(C)
-            sage: S.generating_series().coefficients(5)
+            sage: S.generating_series()[:5]
             [1, 1, 1, 1, 1]
             sage: E(C) is S
             True
@@ -114,7 +114,7 @@ def __init__(self, F, G, min=None, max=None, weight=None):
 
             sage: E = species.SetSpecies(); C = species.CycleSpecies()
             sage: L = E(C)
-            sage: c = L.generating_series().coefficients(3)
+            sage: c = L.generating_series()[:3]
             sage: L._check() #False due to isomorphism types not being implemented
             False
             sage: L == loads(dumps(L))
@@ -193,7 +193,7 @@ def _gs(self, series_ring, base_ring):
 
             sage: E = species.SetSpecies(); C = species.CycleSpecies()
             sage: L = E(C)
-            sage: L.generating_series().coefficients(5)
+            sage: L.generating_series()[:5]
             [1, 1, 1, 1, 1]
         """
         return self._F.generating_series(base_ring)(self._G.generating_series(base_ring))
@@ -204,7 +204,7 @@ def _itgs(self, series_ring, base_ring):
 
             sage: E = species.SetSpecies(); C = species.CycleSpecies()
             sage: L = E(C)
-            sage: L.isotype_generating_series().coefficients(10)
+            sage: L.isotype_generating_series()[:10]
             [1, 1, 2, 3, 5, 7, 11, 15, 22, 30]
         """
         cis = self.cycle_index_series(base_ring)
@@ -216,7 +216,7 @@ def _cis(self, series_ring, base_ring):
 
             sage: E = species.SetSpecies(); C = species.CycleSpecies()
             sage: L = E(C)
-            sage: L.cycle_index_series().coefficients(5)
+            sage: L.cycle_index_series()[:5]
             [p[],
              p[1],
              p[1, 1] + p[2],
@@ -233,7 +233,7 @@ def _cis(self, series_ring, base_ring):
             sage: E = species.SetSpecies()
             sage: C = species.CycleSpecies(weight=t)
             sage: S = E(C)
-            sage: S.isotype_generating_series().coefficients(5) #indirect
+            sage: S.isotype_generating_series()[:5] #indirect
             [1, t, t^2 + t, t^3 + t^2 + t, t^4 + t^3 + 2*t^2 + t]
 
         We do the same thing with set partitions weighted by the number of
@@ -245,17 +245,11 @@ def _cis(self, series_ring, base_ring):
             sage: E = species.SetSpecies()
             sage: E_t = species.SetSpecies(min=1,weight=t)
             sage: Par = E(E_t)
-            sage: Par.isotype_generating_series().coefficients(5)
+            sage: Par.isotype_generating_series()[:5]
             [1, t, t^2 + t, t^3 + t^2 + t, t^4 + t^3 + 2*t^2 + t]
         """
         f_cis = self._F.cycle_index_series(base_ring)
         g_cis = self._G.cycle_index_series(base_ring)
-
-        #If G is a weighted species, then we can't use the default
-        #algorithm for the composition of the cycle index series
-        #since we must raise the weighting to the power.
-        if self._G.is_weighted():
-            return f_cis.weighted_composition(self._G)
         return f_cis(g_cis)
 
     def weight_ring(self):

src/sage/combinat/species/cycle_species.py

@@ -14,9 +14,7 @@
 
 from .species import GenericCombinatorialSpecies
 from .structure import GenericSpeciesStructure
-from .generating_series import _integers_from
 from sage.structure.unique_representation import UniqueRepresentation
-from sage.rings.integer_ring import ZZ
 from sage.arith.all import divisors, euler_phi
 from sage.combinat.species.misc import accept_size
 
@@ -142,7 +140,7 @@ def __init__(self, min=None, max=None, weight=None):
             True
 
             sage: P = species.CycleSpecies()
-            sage: c = P.generating_series().coefficients(3)
+            sage: c = P.generating_series()[:3]
             sage: P._check()
             True
             sage: P == loads(dumps(P))
@@ -177,7 +175,7 @@ def _isotypes(self, structure_class, labels):
         if len(labels) != 0:
             yield structure_class(self, labels, range(1, len(labels)+1))
 
-    def _gs_iterator(self, base_ring):
+    def _gs_callable(self, base_ring, n):
         r"""
         The generating series for cyclic permutations is
         `-\log(1-x) = \sum_{n=1}^\infty x^n/n`.
@@ -186,20 +184,19 @@ def _gs_iterator(self, base_ring):
 
             sage: P = species.CycleSpecies()
             sage: g = P.generating_series()
-            sage: g.coefficients(10)
+            sage: g[0:10]
             [0, 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9]
 
         TESTS::
 
             sage: P = species.CycleSpecies()
             sage: g = P.generating_series(RR)
-            sage: g.coefficients(3)
+            sage: g[0:3]
             [0.000000000000000, 1.00000000000000, 0.500000000000000]
         """
-        one = base_ring(1)
-        yield base_ring(0)
-        for n in _integers_from(ZZ(1)):
-            yield self._weight*one/n
+        if n:
+            return self._weight * base_ring.one() / n
+        return base_ring.zero()
 
     def _order(self):
         """
@@ -213,7 +210,7 @@ def _order(self):
         """
         return 1
 
-    def _itgs_list(self, base_ring):
+    def _itgs_list(self, base_ring, n):
         """
         The isomorphism type generating series for cyclic permutations is
         given by `x/(1-x)`.
@@ -222,19 +219,21 @@ def _itgs_list(self, base_ring):
 
             sage: P = species.CycleSpecies()
             sage: g = P.isotype_generating_series()
-            sage: g.coefficients(5)
+            sage: g[0:5]
             [0, 1, 1, 1, 1]
 
         TESTS::
 
             sage: P = species.CycleSpecies()
             sage: g = P.isotype_generating_series(RR)
-            sage: g.coefficients(3)
+            sage: g[0:3]
             [0.000000000000000, 1.00000000000000, 1.00000000000000]
         """
-        return [base_ring(0), self._weight*base_ring(1)]
+        if n:
+            return self._weight * base_ring.one()
+        return base_ring.zero()
 
-    def _cis_iterator(self, base_ring):
+    def _cis_callable(self, base_ring, n):
         r"""
         The cycle index series of the species of cyclic permutations is
         given by
@@ -256,7 +255,7 @@ def _cis_iterator(self, base_ring):
 
             sage: P = species.CycleSpecies()
             sage: cis = P.cycle_index_series()
-            sage: cis.coefficients(7)
+            sage: cis[0:7]
             [0,
              p[1],
              1/2*p[1, 1] + 1/2*p[2],
@@ -268,15 +267,15 @@ def _cis_iterator(self, base_ring):
         from sage.combinat.sf.sf import SymmetricFunctions
         p = SymmetricFunctions(base_ring).power()
 
-        zero = base_ring(0)
+        zero = base_ring.zero()
 
-        yield zero
-        for n in _integers_from(1):
-            res = zero
-            for k in divisors(n):
-                res += euler_phi(k)*p([k])**(n//k)
-            res /= n
-            yield self._weight*res
+        if not n:
+            return zero
+        res = zero
+        for k in divisors(n):
+            res += euler_phi(k)*p([k])**(n//k)
+        res /= n
+        return self._weight * res
 
 #Backward compatibility
 CycleSpecies_class = CycleSpecies