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sage.arith.misc: fixes error in binomial for p-adic numbers with negative valuation #35823

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merged 10 commits into from
Dec 26, 2023
Merged

sage.arith.misc: fixes error in binomial for p-adic numbers with negative valuation #35823

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0953412
Fixed error in binomial function for p-adic numbers with negative val…
Jun 22, 2023
eec0d9b
Updated EXAMPLES and TESTS.
Jun 24, 2023
c1807ad
Fixed codestyle PEP8 errors
Jun 24, 2023
23d770f
Merge branch 'develop' into binomial
knospe Aug 2, 2023
adb2e06
Merge branch 'develop' into binomial
knospe Aug 10, 2023
65c3e72
Merge branch 'develop' into binomial
fchapoton Sep 13, 2023
d776f63
Resolved merge conflict by incorporating an upstream comment.
Oct 29, 2023
087a33b
Merge branch 'binomial' of github.com:knospe/sage into binomial
Oct 29, 2023
487237f
Merge branch 'sagemath:develop' into binomial
knospe Dec 15, 2023
7bada4e
Merge branch 'sagemath:develop' into binomial
knospe Dec 19, 2023
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29 changes: 28 additions & 1 deletion src/sage/arith/misc.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3696,6 +3696,12 @@ def binomial(x, m, **kwds):
0
sage: binomial(RealField()('2.5'), 2) # needs sage.rings.real_mpfr
1.87500000000000
sage: binomial(Zp(5)(99),50)
3 + 4*5^3 + 2*5^4 + 4*5^5 + 4*5^6 + 4*5^7 + 4*5^8 + 5^9 + 2*5^10 + 3*5^11 +
4*5^12 + 4*5^13 + 2*5^14 + 3*5^15 + 3*5^16 + 4*5^17 + 4*5^18 + 2*5^19 + O(5^20)
sage: binomial(Qp(3)(2/3),2)
2*3^-2 + 2*3^-1 + 2 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + 2*3^5 + 2*3^6 + 2*3^7 +
2*3^8 + 2*3^9 + 2*3^10 + 2*3^11 + 2*3^12 + 2*3^13 + 2*3^14 + 2*3^15 + 2*3^16 + 2*3^17 + O(3^18)
sage: n = var('n'); binomial(n, 2) # needs sage.symbolic
1/2*(n - 1)*n
sage: n = var('n'); binomial(n, n) # needs sage.symbolic
Expand Down Expand Up @@ -3792,6 +3798,27 @@ def binomial(x, m, **kwds):
sage: binomial(n,2) # needs sage.symbolic
1/2*(n - 1)*n

Test p-adic numbers::

sage: binomial(Qp(3)(-1/2),4) # p-adic number with valuation >= 0
1 + 3 + 2*3^2 + 3^3 + 2*3^4 + 3^6 + 3^7 + 3^8 + 3^11 + 2*3^14 + 2*3^16 + 2*3^17 + 2*3^19 + O(3^20)

Check that :trac:`35811` is fixed::

sage: binomial(Qp(3)(1/3),4) # p-adic number with negative valuation
2*3^-5 + 2*3^-4 + 3^-3 + 2*3^-2 + 2*3^-1 + 2 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + 2*3^5 +
2*3^6 + 2*3^7 + 2*3^8 + 2*3^9 + 2*3^10 + 2*3^11 + 2*3^12 + 2*3^13 + 2*3^14 + O(3^15)

sage: binomial(Qp(3)(1/3),10).parent()
3-adic Field with capped relative precision 20

sage: F.<w>=Qq(9); binomial(w,4) # p-adic extension field
(w + 2)*3^-1 + (w + 1) + (2*w + 1)*3 + 2*w*3^2 + (2*w + 2)*3^3 + 2*w*3^4 + (2*w + 2)*3^5 +
2*w*3^6 + (2*w + 2)*3^7 + 2*w*3^8 + (2*w + 2)*3^9 + 2*w*3^10 + (2*w + 2)*3^11 + 2*w*3^12 +
(2*w + 2)*3^13 + 2*w*3^14 + (2*w + 2)*3^15 + 2*w*3^16 + (2*w + 2)*3^17 + 2*w*3^18 + O(3^19)
sage: F.<w>=Qq(9); binomial(w,10).parent()
3-adic Unramified Extension Field in w defined by x^2 + 2*x + 2

Invalid inputs::

sage: x = polygen(ZZ)
Expand Down Expand Up @@ -3872,7 +3899,7 @@ def binomial(x, m, **kwds):
# case 2: conversion to integers
try:
x = ZZ(x)
except TypeError:
except (TypeError, ValueError):
pass
else:
# Check invertibility of factorial(m) in P
Expand Down