@@ -2240,13 +2240,12 @@ class LazyCompletionGradedAlgebra(LazySeriesRing):
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EXAMPLES::
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- sage: NCSF = NonCommutativeSymmetricFunctions(QQ) # needs sage.modules
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- sage: S = NCSF.Complete() # needs sage.modules
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- sage: L = S.formal_series_ring(); L # needs sage.modules
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+ sage: # needs sage.modules
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+ sage: NCSF = NonCommutativeSymmetricFunctions(QQ)
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+ sage: S = NCSF.Complete()
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+ sage: L = S.formal_series_ring(); L
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Lazy completion of Non-Commutative Symmetric Functions
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over the Rational Field in the Complete basis
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-
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- sage: # needs sage.modules
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sage: f = 1 / (1 - L(S[1])); f
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S[] + S[1] + (S[1,1]) + (S[1,1,1]) + (S[1,1,1,1]) + (S[1,1,1,1,1])
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+ (S[1,1,1,1,1,1]) + O^7
@@ -2275,23 +2274,23 @@ def __init__(self, basis, sparse=True, category=None):
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sage: LazySymmetricFunctions.options.halting_precision(6)
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- sage: s = SymmetricFunctions(QQ).s() # needs sage.modules
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- sage: L = LazySymmetricFunctions(s) # needs sage.modules
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- sage: TestSuite(L).run() # needs lrcalc_python sage.modules
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-
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- sage: p = SymmetricFunctions(GF(5)).p() # needs sage.modules
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- sage: L = LazySymmetricFunctions(p) # needs sage.modules
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- sage: TestSuite(L).run() # needs sage.modules
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+ sage: # needs sage.modules
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+ sage: s = SymmetricFunctions(QQ).s()
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+ sage: L = LazySymmetricFunctions(s)
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+ sage: TestSuite(L).run() # needs lrcalc_python
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+ sage: p = SymmetricFunctions(GF(5)).p()
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+ sage: L = LazySymmetricFunctions(p)
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+ sage: TestSuite(L).run()
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Reversion will only work when the base ring is a field::
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- sage: s = SymmetricFunctions(ZZ).s() # needs sage.modules
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- sage: L = LazySymmetricFunctions(s) # needs sage.modules
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- sage: TestSuite(L).run(skip=['_test_revert']) # needs lrcalc_python sage.modules
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-
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- sage: s = SymmetricFunctions(QQ["q"]).s() # needs sage.modules
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- sage: L = LazySymmetricFunctions(s) # needs sage.modules
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- sage: TestSuite(L).run(skip=['_test_revert']) # needs lrcalc_python sage.modules
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+ sage: # needs sage.modules
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+ sage: s = SymmetricFunctions(ZZ).s()
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+ sage: L = LazySymmetricFunctions(s)
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+ sage: TestSuite(L).run(skip=['_test_revert']) # needs lrcalc_python
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+ sage: s = SymmetricFunctions(QQ["q"]).s()
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+ sage: L = LazySymmetricFunctions(s)
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+ sage: TestSuite(L).run(skip=['_test_revert']) # needs lrcalc_python
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Options are remembered across doctests::
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@@ -2399,22 +2398,22 @@ def _element_constructor_(self, x=None, valuation=None, degree=None, constant=No
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EXAMPLES::
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- sage: # needs sage.modules sage.rings.finite_rings
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+ sage: # needs sage.modules
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sage: m = SymmetricFunctions(GF(2)).m()
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sage: L = LazySymmetricFunctions(m)
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sage: L(2)
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0
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sage: L(3)
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m[]
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- sage: m = SymmetricFunctions(ZZ).m() # needs sage.modules
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- sage: L = LazySymmetricFunctions(m) # needs sage.modules
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- sage: f = L(lambda i: m([i]), valuation=5, degree=10); f # needs sage.modules
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+ sage: # needs sage.modules
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+ sage: m = SymmetricFunctions(ZZ).m()
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+ sage: L = LazySymmetricFunctions(m)
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+ sage: f = L(lambda i: m([i]), valuation=5, degree=10); f
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m[5] + m[6] + m[7] + m[8] + m[9]
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-
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- sage: f.coefficient(6) # needs sage.modules
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+ sage: f.coefficient(6)
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m[6]
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- sage: f[20] # needs sage.modules
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+ sage: f[20]
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0
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Alternatively, ``x`` can be a list of elements of the base ring.
@@ -2442,22 +2441,20 @@ def _element_constructor_(self, x=None, valuation=None, degree=None, constant=No
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sage: L(lambda n: 0)
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O^7
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- sage: L(lambda n: tensor([h[n], e([])]) + tensor([h([]), e[n]]), degree=3) # needs sage.modules
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+ sage: # needs sage.modules
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+ sage: L(lambda n: tensor([h[n], e([])]) + tensor([h([]), e[n]]), degree=3)
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(2*h[]#e[]) + (h[]#e[1]+h[1]#e[]) + (h[]#e[2]+h[2]#e[])
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-
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- sage: L(lambda n: n)[3]; # needs sage.modules
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+ sage: L(lambda n: n)[3];
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Traceback (most recent call last):
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...
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ValueError: coefficient 3*h[] # e[] should be an element
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of homogeneous degree 3 but has degree 0
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-
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- sage: L([1, 2, 3]); # needs sage.modules
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+ sage: L([1, 2, 3]);
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Traceback (most recent call last):
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...
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ValueError: coefficient 2*h[] # e[] should be an element
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of homogeneous degree 1 but has degree 0
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-
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- sage: L(lambda n: n, degree=3); # needs sage.modules
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+ sage: L(lambda n: n, degree=3);
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Traceback (most recent call last):
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...
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ValueError: coefficient h[] # e[] should be an element
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