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Fix printing of Tate series #41194

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Fix printing of Tate series #41194

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29 changes: 19 additions & 10 deletions src/sage/rings/tate_algebra_element.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -1123,7 +1123,7 @@ cdef class TateAlgebraElement(CommutativeAlgebraElement):
sage: S.<x,y> = TateAlgebra(Qp(5), log_radii=(1,0))
sage: f = 5*x
sage: f.add_bigoh(1)
(5 + O(5^2))*x + O(5 * <x/5, y>)
(5 + O(5^2))*x + O(5 * <5*x, y>)
"""
self._is_normalized = True
if self._prec is Infinity:
Expand Down Expand Up @@ -1169,6 +1169,15 @@ cdef class TateAlgebraElement(CommutativeAlgebraElement):

sage: A(x + 2*x^2 + x^3, prec=5)
...00001*x^3 + ...00001*x + ...00010*x^2 + O(2^5 * <x, y>)

TESTS::

sage: S.<x> = TateAlgebra(R, log_radii=[-1])
sage: S(x, 5)
...0001*x + O(2^5 * <x/2>)
sage: S.<x> = TateAlgebra(R, log_radii=[1])
sage: S(x, 5)
...000001*x + O(2^5 * <2*x>)
"""
vars = self._parent.variable_names()
s = ""
Expand All @@ -1191,14 +1200,14 @@ cdef class TateAlgebraElement(CommutativeAlgebraElement):
for i in range(len(vars)):
if lr[i] == 0:
sv.append(vars[i])
elif lr[i] == -1:
sv.append("%s*%s" % (su, vars[i]))
elif lr[i] == 1:
sv.append("%s*%s" % (su, vars[i]))
elif lr[i] == -1:
sv.append("%s/%s" % (vars[i], su))
elif lr[i] < 0:
sv.append("%s^%s*%s" % (su, -lr[i], vars[i]))
elif lr[i] > 0:
sv.append("%s^%s*%s" % (su, lr[i], vars[i]))
else:
sv.append("%s/%s^%s" % (vars[i], su, lr[i]))
sv.append("%s/%s^%s" % (vars[i], su, -lr[i]))
sv = ", ".join(sv)
if self._prec == 0:
s += "O(<%s>)" % sv
Expand Down Expand Up @@ -2534,8 +2543,8 @@ cdef class TateAlgebraElement(CommutativeAlgebraElement):
However `\log(1+x)` converges on a smaller disk::

sage: f.restriction(-1).log()
...000000001*x + ...0000000.1*x^3 + ...111111*x^2 + ...
+ O(3^10 * <3*x, 3*y>)
...000000001*x + ...0000000.1*x^3 + ...11111111*x^2 + ...
+ O(3^10 * <x/3, y/3>)

TESTS::

Expand Down Expand Up @@ -2692,8 +2701,8 @@ cdef class TateAlgebraElement(CommutativeAlgebraElement):
However `\exp(x)` converges on a smaller disk::

sage: f.restriction(-1).exp()
...0000000001 + ...000000001*x + ...1111111.2*x^3 + ...111112*x^2
+ ... + O(3^10 * <3*x, 3*y>)
...0000000001 + ...000000001*x + ...1111111.2*x^3 + ...11111112*x^2
+ ... + O(3^10 * <x/3, y/3>)

TESTS::

Expand Down
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