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Matthias Koeppe
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src/sage/tests: sage -fixdoctests --only-tags
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src/sage/tests/article_heuberger_krenn_kropf_fsm-in-sage.py

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# sage.doctest: needs sage.graphs
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# sage.doctest: needs sage.graphs sage.modules
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r"""
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This file contains doctests of the article ::
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Sage example in fsm-in-sage.tex, line 1091::
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sage: var('y') # optional - sage.symbolic
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sage: var('y') # needs sage.symbolic
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y
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sage: def am_entry(trans):
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....: return y^add(trans.word_out) / 2
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sage: A = W.adjacency_matrix(entry=am_entry) # optional - sage.symbolic
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sage: A = W.adjacency_matrix(entry=am_entry) # needs sage.symbolic
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Sage example in fsm-in-sage.tex, line 1097::
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Sage example in fsm-in-sage.tex, line 1099::
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sage: latex(A) # optional - sage.symbolic
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sage: latex(A) # needs sage.symbolic
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\left(\begin{array}{ccccccccc}
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\frac{1}{2} & \frac{1}{2} \, y^{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
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0 & 0 & \frac{1}{2} & \frac{1}{2} & 0 & 0 & 0 & 0 & 0 \\
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Sage example in fsm-in-sage.tex, line 1109::
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sage: A1mI = (A.subs(y=1) - A.parent().identity_matrix()) # optional - sage.symbolic
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sage: (pi_not_normalized,) = A1mI.left_kernel().basis() # optional - sage.symbolic
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sage: pi = pi_not_normalized / pi_not_normalized.norm(p=1) # optional - sage.symbolic
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sage: A1mI = (A.subs(y=1) - A.parent().identity_matrix()) # needs sage.symbolic
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sage: (pi_not_normalized,) = A1mI.left_kernel().basis() # needs sage.symbolic
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sage: pi = pi_not_normalized / pi_not_normalized.norm(p=1) # needs sage.symbolic
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Sage example in fsm-in-sage.tex, line 1110::
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sage: str(pi) # optional - sage.symbolic
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sage: str(pi) # needs sage.symbolic
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'(1/9, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9)'
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Sage example in fsm-in-sage.tex, line 1117::
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sage: expected_output = derivative(A, y).subs(y=1) * vector(len(W.states())*[1]) # optional - sage.symbolic
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sage: expected_output = derivative(A, y).subs(y=1) * vector(len(W.states())*[1]) # needs sage.symbolic
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Sage example in fsm-in-sage.tex, line 1118::
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sage: latex(expected_output) # optional - sage.symbolic
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sage: latex(expected_output) # needs sage.symbolic
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\left(1,\,0,\,0,\,0,\,\frac{1}{2},\,1,\,1,\,\frac{1}{2},\,1\right)
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Sage example in fsm-in-sage.tex, line 1126::
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sage: pi * expected_output # optional - sage.symbolic
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sage: pi * expected_output # needs sage.symbolic
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5/9
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Sage example in fsm-in-sage.tex, line 1127::
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sage: latex(pi * expected_output) # optional - sage.symbolic
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sage: latex(pi * expected_output) # needs sage.symbolic
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\frac{5}{9}
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Sage example in fsm-in-sage.tex, line 1129::
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sage: latex(pi * expected_output) # optional - sage.symbolic
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sage: latex(pi * expected_output) # needs sage.symbolic
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\frac{5}{9}
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Sage example in fsm-in-sage.tex, line 1145::
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sage: var('k') # optional - sage.symbolic
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sage: var('k') # needs sage.symbolic
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k
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sage: moments = W.asymptotic_moments(k) # optional - sage.symbolic
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sage: moments = W.asymptotic_moments(k) # needs sage.symbolic
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Sage example in fsm-in-sage.tex, line 1155::
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sage: latex(moments['expectation']) # optional - sage.symbolic
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sage: latex(moments['expectation']) # needs sage.symbolic
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\frac{5}{9} \, k + \mathcal{O}\left(1\right)
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Sage example in fsm-in-sage.tex, line 1162::
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sage: latex(moments['variance']) # optional - sage.symbolic
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sage: latex(moments['variance']) # needs sage.symbolic
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\frac{44}{243} \, k + \mathcal{O}\left(1\right)
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Sage example in fsm-in-sage.tex, line 1192::
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sage: expectation_binary = Id.asymptotic_moments(k)['expectation'] # optional - sage.symbolic
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sage: expectation_binary = Id.asymptotic_moments(k)['expectation'] # needs sage.symbolic
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Sage example in fsm-in-sage.tex, line 1195::
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sage: latex(expectation_binary) # optional - sage.symbolic
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sage: latex(expectation_binary) # needs sage.symbolic
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\frac{1}{2} \, k + \mathcal{O}\left(1\right)
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Sage example in fsm-in-sage.tex, line 1202::
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sage: expectation_NAF = Weight(NAF).asymptotic_moments(k)['expectation'] # optional - sage.symbolic
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sage: expectation_NAF = Weight(NAF).asymptotic_moments(k)['expectation'] # needs sage.symbolic
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Sage example in fsm-in-sage.tex, line 1205::
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sage: latex(expectation_NAF) # optional - sage.symbolic
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sage: latex(expectation_NAF) # needs sage.symbolic
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\frac{1}{3} \, k + \mathcal{O}\left(1\right)
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Sage example in fsm-in-sage.tex, line 1211::
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sage: Abs = transducers.abs([-1, 0, 1]) # optional - sage.symbolic
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sage: Abs = transducers.abs([-1, 0, 1]) # needs sage.symbolic
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Sage example in fsm-in-sage.tex, line 1216::
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sage: latex(moments['expectation']) # optional - sage.symbolic
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sage: latex(moments['expectation']) # needs sage.symbolic
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\frac{5}{9} \, k + \mathcal{O}\left(1\right)
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"""

src/sage/tests/book_schilling_zabrocki_kschur_primer.py

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Sage example in ./kschurnotes/notes-mike-anne.tex, line 4055::
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sage: t = var('t') # optional - sage.symbolic
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sage: for mu in Partitions(5): # optional - sage.symbolic
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sage: t = var('t') # needs sage.symbolic
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sage: for mu in Partitions(5): # needs sage.symbolic
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....: print("{} {}".format(mu, sum(t^T.spin() for T in StrongTableaux(3,[4,1,1],mu))))
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[5] 0
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[4, 1] t

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