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Matthias Koeppe
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sage.rings.padics: Update # needs
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src/sage/rings/padics/factory.py

Lines changed: 6 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -975,10 +975,10 @@ def Qq(q, prec=None, type='capped-rel', modulus=None, names=None,
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2. The modulus can also be given as a **symbolic expression**. ::
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sage: x = var('x') # optional - sage.symbolic
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sage: X.<a> = Qq(27, modulus = x^3 + 2*x + 1); X.modulus() # optional - sage.symbolic
978+
sage: x = var('x') # needs sage.symbolic
979+
sage: X.<a> = Qq(27, modulus = x^3 + 2*x + 1); X.modulus() # needs sage.symbolic
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(1 + O(3^20))*x^3 + O(3^20)*x^2 + (2 + O(3^20))*x + 1 + O(3^20)
981-
sage: X == R # optional - sage.symbolic
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sage: X == R # needs sage.symbolic
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True
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By default, the polynomial chosen is the standard lift of the
@@ -2225,10 +2225,10 @@ def Zq(q, prec=None, type='capped-rel', modulus=None, names=None,
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2. The modulus can also be given as a **symbolic expression**. ::
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sage: x = var('x') # optional - sage.symbolic
2229-
sage: X.<a> = Zq(27, modulus = x^3 + 2*x + 1); X.modulus() # optional - sage.symbolic
2228+
sage: x = var('x') # needs sage.symbolic
2229+
sage: X.<a> = Zq(27, modulus = x^3 + 2*x + 1); X.modulus() # needs sage.symbolic
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(1 + O(3^20))*x^3 + O(3^20)*x^2 + (2 + O(3^20))*x + 1 + O(3^20)
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sage: X == R # optional - sage.symbolic
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sage: X == R # needs sage.symbolic
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True
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By default, the polynomial chosen is the standard lift of the

src/sage/rings/padics/misc.py

Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -91,25 +91,25 @@ def gauss_sum(a, p, f, prec=20, factored=False, algorithm='pari', parent=None):
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In this example, we verify that `g_3(0) = -1`::
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sage: from sage.rings.padics.misc import gauss_sum
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sage: -gauss_sum(0, 3, 1) # optional - sage.rings.padics
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sage: -gauss_sum(0, 3, 1) # needs sage.rings.padics
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1 + O(pi^40)
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Next, we verify that `g_5(a) g_5(-a) = 5 (-1)^a`::
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sage: from sage.rings.padics.misc import gauss_sum
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sage: gauss_sum(2,5,1)^2 - 5 # optional - sage.rings.padics
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sage: gauss_sum(2,5,1)^2 - 5 # needs sage.rings.padics
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O(pi^84)
102-
sage: gauss_sum(1,5,1)*gauss_sum(3,5,1) + 5 # optional - sage.rings.padics
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sage: gauss_sum(1,5,1)*gauss_sum(3,5,1) + 5 # needs sage.rings.padics
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O(pi^84)
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Finally, we compute a non-trivial value::
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sage: from sage.rings.padics.misc import gauss_sum
108-
sage: gauss_sum(2,13,2) # optional - sage.rings.padics
108+
sage: gauss_sum(2,13,2) # needs sage.rings.padics
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6*pi^2 + 7*pi^14 + 11*pi^26 + 3*pi^62 + 6*pi^74 + 3*pi^86 + 5*pi^98 +
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pi^110 + 7*pi^134 + 9*pi^146 + 4*pi^158 + 6*pi^170 + 4*pi^194 +
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pi^206 + 6*pi^218 + 9*pi^230 + O(pi^242)
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sage: gauss_sum(2,13,2, prec=5, factored=True) # optional - sage.rings.padics
112+
sage: gauss_sum(2,13,2, prec=5, factored=True) # needs sage.rings.padics
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(2, 6 + 6*13 + 10*13^2 + O(13^5))
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.. SEEALSO::

src/sage/rings/padics/padic_base_generic.py

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -433,11 +433,11 @@ def plot(self, max_points=2500, **args):
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EXAMPLES::
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sage: Zp(3).plot() # optional - sage.plot
436+
sage: Zp(3).plot() # needs sage.plot
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Graphics object consisting of 1 graphics primitive
438-
sage: Zp(5).plot(max_points=625) # optional - sage.plot
438+
sage: Zp(5).plot(max_points=625) # needs sage.plot
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Graphics object consisting of 1 graphics primitive
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sage: Zp(23).plot(rgbcolor=(1,0,0)) # optional - sage.plot
440+
sage: Zp(23).plot(rgbcolor=(1,0,0)) # needs sage.plot
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Graphics object consisting of 1 graphics primitive
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"""
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if 'pointsize' not in args:

src/sage/rings/padics/padic_lattice_element.py

Lines changed: 5 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -17,10 +17,11 @@
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sage: R3 = QpLC(2)
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sage: R4 = QpLF(2)
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20-
sage: TestSuite(R1).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
21-
sage: TestSuite(R2).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
22-
sage: TestSuite(R3).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
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sage: TestSuite(R4).run(skip=['_test_teichmuller', '_test_matrix_smith']) # long time
20+
sage: # long time
21+
sage: TestSuite(R1).run(skip=['_test_teichmuller', '_test_matrix_smith'])
22+
sage: TestSuite(R2).run(skip=['_test_teichmuller', '_test_matrix_smith'])
23+
sage: TestSuite(R3).run(skip=['_test_teichmuller', '_test_matrix_smith'])
24+
sage: TestSuite(R4).run(skip=['_test_teichmuller', '_test_matrix_smith'])
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"""
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# ****************************************************************************

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