Skip to content
This repository has been archived by the owner on Jan 30, 2023. It is now read-only.

Commit

Permalink
improve repr, fix doctests
Browse files Browse the repository at this point in the history
  • Loading branch information
@mantepse
mantepse committed Aug 5, 2021
1 parent 362a99e commit 2d5285b
Show file tree
Hide file tree
Showing 2 changed files with 160 additions and 86 deletions.
218 changes: 146 additions & 72 deletions src/sage/rings/lazy_laurent_series.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1080,19 +1080,19 @@ def _lmul_(self, scalar):
sage: 2*g
2/2^z
sage: -1*g
-1/2^z
-1/(2^z)
sage: 0*g
0
sage: M = L(lambda n: n); M
1 + 2/2^z + 3/3^z + 4/4^z + 5/5^z + 6/6^z + 7/7^z + ...
1 + 2/2^z + 3/3^z + 4/4^z + 5/5^z + 6/6^z + 7/7^z + O(1/(8^z))
sage: M * 3
3 + 6/2^z + 9/3^z + 12/4^z + 15/5^z + 18/6^z + 21/7^z + ...
3 + 6/2^z + 9/3^z + 12/4^z + 15/5^z + 18/6^z + 21/7^z + O(1/(8^z))
sage: L = LazyDirichletSeriesRing(ZZ, "z", sparse=True)
sage: M = L(lambda n: n); M
1 + 2/2^z + 3/3^z + 4/4^z + 5/5^z + 6/6^z + 7/7^z + ...
1 + 2/2^z + 3/3^z + 4/4^z + 5/5^z + 6/6^z + 7/7^z + O(1/(8^z))
sage: M * 3
3 + 6/2^z + 9/3^z + 12/4^z + 15/5^z + 18/6^z + 21/7^z + ...
3 + 6/2^z + 9/3^z + 12/4^z + 15/5^z + 18/6^z + 21/7^z + O(1/(8^z))
sage: 1 * M is M
True
Expand Down Expand Up @@ -1233,17 +1233,20 @@ def _mul_(self, other):
sage: L.<x, y, z> = LazyTaylorSeriesRing(ZZ)
sage: (1 - x)*(1 - y)
1 + -x - y + x*y
1 + (-x-y) + x*y
sage: (1 - x)*(1 - y)*(1 - z)
1 + -x - y - z + x*y + x*z + y*z + -x*y*z
1 + (-x-y-z) + (x*y+x*z+y*z) + (-x*y*z)
"""
P = self.parent()
left = self._coeff_stream
right = other._coeff_stream
if isinstance(left, CoefficientStream_zero) or isinstance(right, CoefficientStream_zero):
return P.zero()

if isinstance(left, CoefficientStream_exact) and left._initial_coefficients == (P._coeff_ring.one(),) and left.valuation() == 0:
return other # self == 1
if isinstance(right, CoefficientStream_exact) and right._initial_coefficients == (P._coeff_ring.one(),) and right.valuation() == 0:
return self
# the product is exact if and only if both of the factors are
# exact, and one has eventually 0 coefficients:
# (p + a x^d/(1-x))(q + b x^e/(1-x))
Expand All @@ -1260,10 +1263,7 @@ def _mul_(self, other):
v = left.valuation() + right.valuation()
coeff_stream = CoefficientStream_exact(initial_coefficients, P._sparse, valuation=v)
return P.element_class(P, coeff_stream)
if isinstance(left, CoefficientStream_exact) and left._initial_coefficients == (P._coeff_ring.one(),) and left.valuation() == 0:
return other # self == 1
if isinstance(right, CoefficientStream_exact) and right._initial_coefficients == (P._coeff_ring.one(),) and right.valuation() == 0:
return self

return P.element_class(P, CoefficientStream_cauchy_product(left, right))

def __invert__(self):
Expand Down Expand Up @@ -2031,24 +2031,18 @@ class LazyTaylorSeries(LazySequencesModuleElement, LazyCauchyProductSeries):
EXAMPLES::
sage: L.<z> = LazyTaylorSeriesRing(ZZ)
sage: L(lambda i: i, valuation=3, constant=(-1, 6))
3*z^3 + 4*z^4 + 5*z^5 + -z^6 + -z^7 + -z^8 + ...
sage: L(lambda i: i, valuation=3, constant=-1, degree=6)
3*z^3 + 4*z^4 + 5*z^5 + -z^6 + -z^7 + -z^8 + ...
::
sage: f = 1 / (1 - z - z^2); f
1 + z + 2*z^2 + 3*z^3 + 5*z^4 + 8*z^5 + 13*z^6 + ...
sage: f.coefficient(100)
573147844013817084101
sage: L.<x, y> = LazyTaylorSeriesRing(ZZ)
sage: f = 1 / (1 - x^2 + y^3); f
1 + x^2 + (-y^3) + x^4 + (-2*x^2*y^3) + (x^6+y^6) + O(x,y)^7
sage: P.<x, y> = PowerSeriesRing(ZZ, default_prec=101)
sage: g = 1 / (1 - x^2 + y^3); f[100] - g[100]
0
Lazy Taylor series is picklable::
sage: g = loads(dumps(f))
sage: g
1 + z + 2*z^2 + 3*z^3 + 5*z^4 + 8*z^5 + 13*z^6 + ...
1 + x^2 + (-y^3) + x^4 + (-2*x^2*y^3) + (x^6+y^6) + O(x,y)^7
sage: g == f
True
"""
Expand All @@ -2066,7 +2060,7 @@ def change_ring(self, ring):
sage: s = 2 + z
sage: t = s.change_ring(QQ)
sage: t^-1
1/2 + -1/4*z + 1/8*z^2 + -1/16*z^3 + 1/32*z^4 + -1/64*z^5 + 1/128*z^6 + ...
1/2 - 1/4*z + 1/8*z^2 - 1/16*z^3 + 1/32*z^4 - 1/64*z^5 + 1/128*z^6 + O(z^7)
sage: t.parent()
Lazy Taylor Series Ring in z over Rational Field
Expand All @@ -2082,15 +2076,14 @@ def _format_series(self, formatter, format_strings=False):
TESTS::
sage: L.<x, y> = LazyTaylorSeriesRing(QQ)
sage: f = 1 / (2 - x^2 - y)
sage: f._format_series(ascii_art, True)
sage: f = 1 / (2 - x^2 + y)
sage: f._format_series(repr)
'1/2 + (-1/4*y) + (1/4*x^2+1/8*y^2) + (-1/4*x^2*y-1/16*y^3) + (1/8*x^4+3/16*x^2*y^2+1/32*y^4) + (-3/16*x^4*y-1/8*x^2*y^3-1/64*y^5) + (1/16*x^6+3/16*x^4*y^2+5/64*x^2*y^4+1/128*y^6) + O(x,y)^7'
sage: f = (2 - x^2 + y)
sage: f._format_series(repr)
'2 + y + (-x^2)'
"""
if format_strings:
strformat = formatter
else:
strformat = lambda x: x

P = self.parent()
cs = self._coeff_stream
v = cs._approximate_valuation
Expand All @@ -2102,13 +2095,48 @@ def _format_series(self, formatter, format_strings=False):
else:
m = v + P.options.display_length

# atomic_repr = P._coeff_ring._repr_option('element_is_atomic')
atomic_repr = P._coeff_ring._repr_option('element_is_atomic')
mons = [P.monomial(self[i], i) for i in range(v, m) if self[i]]
if not isinstance(cs, CoefficientStream_exact) or cs._constant:
if P._coeff_ring is P.base_ring():
bigO = ["O(%s)" % P.monomial(1, m)]
else:
bigO = ["O(%s)^%s" % (', '.join(str(g) for g in P._names), m)]
else:
bigO = []

from sage.misc.latex import latex
from sage.typeset.unicode_art import unicode_art
from sage.typeset.ascii_art import ascii_art
from sage.misc.repr import repr_lincomb
from sage.typeset.symbols import ascii_left_parenthesis, ascii_right_parenthesis
from sage.typeset.symbols import unicode_left_parenthesis, unicode_right_parenthesis
if formatter == repr:
poly = repr_lincomb([(1, m) for m in mons + bigO], strip_one=True)
elif formatter == latex:
poly = repr_lincomb([(1, m) for m in mons + bigO], is_latex=True, strip_one=True)
elif formatter == ascii_art:
if atomic_repr:
poly = ascii_art(*(mons + bigO), sep = " + ")
else:
def parenthesize(m):
a = ascii_art(m)
h = a.height()
return ascii_art(ascii_left_parenthesis.character_art(h),
a, ascii_right_parenthesis.character_art(h))
poly = ascii_art(*([parenthesize(m) for m in mons] + bigO), sep = " + ")
elif formatter == unicode_art:
if atomic_repr:
poly = unicode_art(*(mons + bigO), sep = " + ")
else:
def parenthesize(m):
a = unicode_art(m)
h = a.height()
return unicode_art(unicode_left_parenthesis.character_art(h),
a, unicode_right_parenthesis.character_art(h))
poly = unicode_art(*([parenthesize(m) for m in mons] + bigO), sep = " + ")

poly = [formatter(P.monomial(self[i], i)) for i in range(v, m) if self[i]]
poly = " + ".join(poly)
if isinstance(cs, CoefficientStream_exact) and not cs._constant:
return poly
return poly + strformat(" + O({})".format(formatter(P.monomial(1, m))))
return poly


class LazyDirichletSeries(LazySequencesModuleElement):
Expand Down Expand Up @@ -2149,16 +2177,16 @@ def _mul_(self, other):
sage: L = LazyDirichletSeriesRing(ZZ, "z")
sage: g = L(constant=1); g
1 + 1/(2^z) + 1/(3^z) + ...
1 + 1/(2^z) + 1/(3^z) + O(1/(4^z))
sage: g*g
1 + 2/2^z + 2/3^z + 3/4^z + 2/5^z + 4/6^z + 2/7^z + ...
1 + 2/2^z + 2/3^z + 3/4^z + 2/5^z + 4/6^z + 2/7^z + O(1/(8^z))
sage: [number_of_divisors(n) for n in range(1, 8)]
[1, 2, 2, 3, 2, 4, 2]
sage: mu = L(moebius); mu
1 + -1/2^z + -1/3^z + -1/5^z + 1/(6^z) + -1/7^z + ...
1 - 1/(2^z) - 1/(3^z) - 1/(5^z) + 1/(6^z) - 1/(7^z) + O(1/(8^z))
sage: g*mu
1 + ...
1 + O(1/(8^z))
sage: L.one() * mu is mu
True
sage: mu * L.one() is mu
Expand All @@ -2167,6 +2195,15 @@ def _mul_(self, other):
P = self.parent()
left = self._coeff_stream
right = other._coeff_stream
if (isinstance(left, CoefficientStream_exact)
and left._initial_coefficients == (P._coeff_ring.one(),)
and left.valuation() == 1):
return other # self == 1
if (isinstance(right, CoefficientStream_exact)
and right._initial_coefficients == (P._coeff_ring.one(),)
and right.valuation() == 1):
return self

coeff = CoefficientStream_dirichlet_convolution(left, right)
return P.element_class(P, coeff)

Expand All @@ -2178,10 +2215,10 @@ def __invert__(self):
sage: L = LazyDirichletSeriesRing(ZZ, "z", sparse=False)
sage: ~L(constant=1) - L(moebius)
0
O(1/(8^z))
sage: L = LazyDirichletSeriesRing(ZZ, "z", sparse=True)
sage: ~L(constant=1) - L(moebius)
0
O(1/(8^z))
"""
P = self.parent()
Expand Down Expand Up @@ -2220,38 +2257,75 @@ def __pow__(self, n):

return generic_power(self, n)

def _repr_(self):
def _format_series(self, formatter, format_strings=False):
"""
Return the string representation of this Dirichlet series.
Return nonzero ``self`` formatted by ``formatter``.
TESTS::
sage: L = LazyDirichletSeriesRing(ZZ, "z")
"""
if isinstance(self._coeff_stream, CoefficientStream_zero):
return '0'
if isinstance(self._coeff_stream, CoefficientStream_uninitialized) and self._coeff_stream._target is None:
return 'Uninitialized Lazy Dirichlet Series'
sage: L = LazyDirichletSeriesRing(QQ, "s")
sage: f = L(constant=1)
sage: f._format_series(repr)
'1 + 1/(2^s) + 1/(3^s) + O(1/(4^s))'
sage: L([1,-1,1])._format_series(repr)
'1 - 1/(2^s) + 1/(3^s)'
atomic_repr = self.base_ring()._repr_option('element_is_atomic')
X = self.parent().variable_name()
v = self._coeff_stream._approximate_valuation
sage: L([1,-1,1])._format_series(ascii_art)
-s -s
1 + -2 + 3
"""
P = self.parent()
cs = self._coeff_stream
v = cs._approximate_valuation
if isinstance(cs, CoefficientStream_exact):
if not cs._constant:
m = cs._degree
else:
m = cs._degree + P.options.constant_length
else:
m = v + P.options.display_length

if not isinstance(self._coeff_stream, CoefficientStream_exact):
m = v + 7 # long enough
atomic_repr = P._coeff_ring._repr_option('element_is_atomic')
mons = [P.monomial(self[i], i) for i in range(v, m) if self[i]]
if not isinstance(cs, CoefficientStream_exact) or cs._constant:
if P._coeff_ring is P.base_ring():
bigO = ["O(%s)" % P.monomial(1, m)]
else:
bigO = ["O(%s)^%s" % (', '.join(str(g) for g in P._names), m)]
else:
m = self._coeff_stream._degree + 3

# Use the symbolic ring printing
from sage.calculus.var import var
from sage.symbolic.ring import SR
variable = var(self.parent().variable_name())
ret = " + ".join([repr(SR(self._coeff_stream[i])*i**(-variable))
for i in range(v, m) if self._coeff_stream[i]])
if not ret:
return "0"
# TODO: Better handling when ret == 0 but we have not checked up to the constant term
bigO = []

if isinstance(self._coeff_stream, CoefficientStream_exact) and not self._coeff_stream._constant:
return ret
return ret + ' + ...'
from sage.misc.latex import latex
from sage.typeset.unicode_art import unicode_art
from sage.typeset.ascii_art import ascii_art
from sage.misc.repr import repr_lincomb
from sage.typeset.symbols import ascii_left_parenthesis, ascii_right_parenthesis
from sage.typeset.symbols import unicode_left_parenthesis, unicode_right_parenthesis
if formatter == repr:
poly = repr_lincomb([(1, m) for m in mons + bigO], strip_one=True)
elif formatter == latex:
poly = repr_lincomb([(1, m) for m in mons + bigO], is_latex=True, strip_one=True)
elif formatter == ascii_art:
if atomic_repr:
poly = ascii_art(*(mons + bigO), sep = " + ")
else:
def parenthesize(m):
a = ascii_art(m)
h = a.height()
return ascii_art(ascii_left_parenthesis.character_art(h),
a, ascii_right_parenthesis.character_art(h))
poly = ascii_art(*([parenthesize(m) for m in mons] + bigO), sep = " + ")
elif formatter == unicode_art:
if atomic_repr:
poly = unicode_art(*(mons + bigO), sep = " + ")
else:
def parenthesize(m):
a = unicode_art(m)
h = a.height()
return unicode_art(unicode_left_parenthesis.character_art(h),
a, unicode_right_parenthesis.character_art(h))
poly = unicode_art(*([parenthesize(m) for m in mons] + bigO), sep = " + ")

return poly
Loading

0 comments on commit 2d5285b

Please sign in to comment.