def _coerce_impl(self, f):
"""
Return the canonical coercion of ``f`` into this multivariate power
series ring, if one is defined, or raise a TypeError.
The rings that canonically coerce to this multivariate power series
ring are:
- this ring itself
- a polynomial or power series ring in the same variables or a
subset of these variables (possibly empty), over any base
ring that canonically coerces into the base ring of this ring
EXAMPLES::
sage: R.<t,u,v> = PowerSeriesRing(QQ); R
Multivariate Power Series Ring in t, u, v over Rational Field
sage: S1.<t,v> = PolynomialRing(ZZ); S1
Multivariate Polynomial Ring in t, v over Integer Ring
sage: f1 = -t*v + 2*v^2 + v; f1
-t*v + 2*v^2 + v
sage: R(f1)
v - t*v + 2*v^2
sage: S2.<u,v> = PowerSeriesRing(ZZ); S2
Multivariate Power Series Ring in u, v over Integer Ring
sage: f2 = -2*v^2 + 5*u*v^2 + S2.O(6); f2
-2*v^2 + 5*u*v^2 + O(u, v)^6
sage: R(f2)
-2*v^2 + 5*u*v^2 + O(t, u, v)^6
sage: R2 = R.change_ring(GF(2))
sage: R2(f1)
v + t*v
sage: R2(f2)
u*v^2 + O(t, u, v)^6
TESTS::
sage: R.<t,u,v> = PowerSeriesRing(QQ)
sage: S1.<t,v> = PolynomialRing(ZZ)
sage: f1 = S1.random_element()
sage: g1 = R._coerce_impl(f1)
sage: f1.parent() == R
False
sage: g1.parent() == R
True
"""
P = f.parent()
if is_MPolynomialRing(P) or is_MPowerSeriesRing(P) \
or is_PolynomialRing(P) or is_PowerSeriesRing(P):
if set(P.variable_names()).issubset(set(self.variable_names())):
if self.has_coerce_map_from(P.base_ring()):
return self(f)
else:
return self._coerce_try(f, [self.base_ring()])
def _coerce_impl(self, f):
"""
Return the canonical coercion of ``f`` into this multivariate power
series ring, if one is defined, or raise a TypeError.
The rings that canonically coerce to this multivariate power series
ring are:
- this ring itself
- a polynomial or power series ring in the same variables or a
subset of these variables (possibly empty), over any base
ring that canonically coerces into the base ring of this ring
EXAMPLES::
sage: R.<t,u,v> = PowerSeriesRing(QQ); R
Multivariate Power Series Ring in t, u, v over Rational Field
sage: S1.<t,v> = PolynomialRing(ZZ); S1
Multivariate Polynomial Ring in t, v over Integer Ring
sage: f1 = -t*v + 2*v^2 + v; f1
-t*v + 2*v^2 + v
sage: R(f1)
v - t*v + 2*v^2
sage: S2.<u,v> = PowerSeriesRing(ZZ); S2
Multivariate Power Series Ring in u, v over Integer Ring
sage: f2 = -2*v^2 + 5*u*v^2 + S2.O(6); f2
-2*v^2 + 5*u*v^2 + O(u, v)^6
sage: R(f2)
-2*v^2 + 5*u*v^2 + O(t, u, v)^6
sage: R2 = R.change_ring(GF(2))
sage: R2(f1)
v + t*v
sage: R2(f2)
u*v^2 + O(t, u, v)^6
TESTS::
sage: R.<t,u,v> = PowerSeriesRing(QQ)
sage: S1.<t,v> = PolynomialRing(ZZ)
sage: f1 = S1.random_element()
sage: g1 = R._coerce_impl(f1)
sage: f1.parent() == R
False
sage: g1.parent() == R
True
"""
P = f.parent()
if is_MPolynomialRing(P) or is_MPowerSeriesRing(P) \
or is_PolynomialRing(P) or is_PowerSeriesRing(P):
if set(P.variable_names()).issubset(set(self.variable_names())):
if self.has_coerce_map_from(P.base_ring()):
return self(f)
else:
return self._coerce_try(f,[self.base_ring()])
def _coerce_map_from_(self, P):
"""
The rings that canonically coerce to this multivariate power series
ring are:
- this ring itself
- a polynomial or power series ring in the same variables or a
subset of these variables (possibly empty), over any base
ring that canonically coerces into this ring
- any ring that coerces into the foreground polynomial ring of this ring
TESTS::
sage: M = PowerSeriesRing(ZZ,3,'x,y,z');
sage: M._coerce_map_from_(M)
True
sage: M._coerce_map_from_(M.remove_var(x))
True
sage: M._coerce_map_from_(PowerSeriesRing(ZZ,x))
True
sage: M._coerce_map_from_(PolynomialRing(ZZ,'x,z'))
True
sage: M._coerce_map_from_(PolynomialRing(ZZ,0,''))
True
sage: M._coerce_map_from_(ZZ)
True
sage: M._coerce_map_from_(Zmod(13))
False
sage: M._coerce_map_from_(PolynomialRing(ZZ,2,'x,t'))
False
sage: M._coerce_map_from_(PolynomialRing(Zmod(11),2,'x,y'))
False
sage: P = PolynomialRing(ZZ,3,'z')
sage: H = PowerSeriesRing(P,4,'f'); H
Multivariate Power Series Ring in f0, f1, f2, f3 over Multivariate Polynomial Ring in z0, z1, z2 over Integer Ring
sage: H._coerce_map_from_(P)
True
sage: H._coerce_map_from_(P.remove_var(P.gen(1)))
True
sage: H._coerce_map_from_(PolynomialRing(ZZ,'z2,f0'))
True
"""
if is_MPolynomialRing(P) or is_MPowerSeriesRing(P) \
or is_PolynomialRing(P) or is_PowerSeriesRing(P):
if set(P.variable_names()).issubset(set(self.variable_names())):
if self.has_coerce_map_from(P.base_ring()):
return True
return self._poly_ring().has_coerce_map_from(P)
def _coerce_map_from_(self, P):
"""
The rings that canonically coerce to this multivariate power series
ring are:
- this ring itself
- a polynomial or power series ring in the same variables or a
subset of these variables (possibly empty), over any base
ring that canonically coerces into this ring
- any ring that coerces into the foreground polynomial ring of this ring
TESTS::
sage: M = PowerSeriesRing(ZZ,3,'x,y,z');
sage: M._coerce_map_from_(M)
True
sage: M._coerce_map_from_(M.remove_var(x))
True
sage: M._coerce_map_from_(PowerSeriesRing(ZZ,x))
True
sage: M._coerce_map_from_(PolynomialRing(ZZ,'x,z'))
True
sage: M._coerce_map_from_(PolynomialRing(ZZ,0,''))
True
sage: M._coerce_map_from_(ZZ)
True
sage: M._coerce_map_from_(Zmod(13))
False
sage: M._coerce_map_from_(PolynomialRing(ZZ,2,'x,t'))
False
sage: M._coerce_map_from_(PolynomialRing(Zmod(11),2,'x,y'))
False
sage: P = PolynomialRing(ZZ,3,'z')
sage: H = PowerSeriesRing(P,4,'f'); H
Multivariate Power Series Ring in f0, f1, f2, f3 over Multivariate Polynomial Ring in z0, z1, z2 over Integer Ring
sage: H._coerce_map_from_(P)
True
sage: H._coerce_map_from_(P.remove_var(P.gen(1)))
True
sage: H._coerce_map_from_(PolynomialRing(ZZ,'z2,f0'))
True
"""
if is_MPolynomialRing(P) or is_MPowerSeriesRing(P) \
or is_PolynomialRing(P) or is_PowerSeriesRing(P):
if set(P.variable_names()).issubset(set(self.variable_names())):
if self.has_coerce_map_from(P.base_ring()):
return True
return self._poly_ring().has_coerce_map_from(P)
def __init__(self, parent, x=0, prec=infinity, is_gen=False, check=False):
"""
input x can be an MPowerSeries, or an element of
- the background univariate power series ring
- the foreground polynomial ring
- a ring that coerces to one of the above two
TESTS::
sage: S.<s,t> = PowerSeriesRing(ZZ)
sage: f = s + 4*t + 3*s*t
sage: f in S
True
sage: f = f.add_bigoh(4); f
s + 4*t + 3*s*t + O(s, t)^4
sage: g = 1 + s + t - s*t + S.O(5); g
1 + s + t - s*t + O(s, t)^5
sage: B.<s, t> = PowerSeriesRing(QQ)
sage: C.<z> = PowerSeriesRing(QQ)
sage: B(z)
Traceback (most recent call last):
...
TypeError: Cannot coerce input to polynomial ring.
sage: D.<s> = PowerSeriesRing(QQ)
sage: s.parent() is D
True
sage: B(s) in B
True
sage: d = D.random_element(20)
sage: b = B(d) # test coercion from univariate power series ring
sage: b in B
True
"""
PowerSeries.__init__(self, parent, prec, is_gen=is_gen)
self._PowerSeries__is_gen = is_gen
try:
prec = min(prec, x.prec()) # use precision of input, if defined
except AttributeError:
pass
# set the correct background value, depending on what type of input x is
try:
xparent = x.parent() # 'int' types have no parent
except AttributeError:
xparent = None
# test whether x coerces to background univariate
# power series ring of parent
from sage.rings.multi_power_series_ring import is_MPowerSeriesRing
if is_PowerSeriesRing(xparent) or is_MPowerSeriesRing(xparent):
# x is either a multivariate or univariate power series
#
# test whether x coerces directly to designated parent
if is_MPowerSeries(x):
try:
self._bg_value = parent._bg_ps_ring(x._bg_value)
except TypeError:
raise TypeError("Unable to coerce into background ring.")
# test whether x coerces to background univariate
# power series ring of parent
elif xparent == parent._bg_ps_ring():
self._bg_value = x
elif parent._bg_ps_ring().has_coerce_map_from(xparent):
# previous test may fail if precision or term orderings of
# base rings do not match
self._bg_value = parent._bg_ps_ring(x)
else:
# x is a univariate power series, but not from the
# background power series ring
#
# convert x to a polynomial and send to background
# ring of parent
x = x.polynomial()
self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
# test whether x coerces to underlying polynomial ring of parent
elif is_PolynomialRing(xparent):
self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
else:
try:
x = parent._poly_ring(x)
#self._value = x
self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
except (TypeError, AttributeError):
raise TypeError("Input does not coerce to any of the expected rings.")
self._go_to_fg = parent._send_to_fg
self._prec = self._bg_value.prec()
# self._parent is used a lot by the class PowerSeries
self._parent = self.parent()
def __init__(self, parent, x=0, prec=infinity, is_gen=False, check=False):
"""
input x can be an MPowerSeries, or an element of
- the background univariate power series ring
- the foreground polynomial ring
- a ring that coerces to one of the above two
TESTS::
sage: S.<s,t> = PowerSeriesRing(ZZ)
sage: f = s + 4*t + 3*s*t
sage: f in S
True
sage: f = f.add_bigoh(4); f
s + 4*t + 3*s*t + O(s, t)^4
sage: g = 1 + s + t - s*t + S.O(5); g
1 + s + t - s*t + O(s, t)^5
sage: B.<s, t> = PowerSeriesRing(QQ)
sage: C.<z> = PowerSeriesRing(QQ)
sage: B(z)
Traceback (most recent call last):
...
TypeError: Cannot coerce input to polynomial ring.
sage: D.<s> = PowerSeriesRing(QQ)
sage: s.parent() is D
True
sage: B(s) in B
True
sage: d = D.random_element(20)
sage: b = B(d) # test coercion from univariate power series ring
sage: b in B
True
"""
PowerSeries.__init__(self, parent, prec, is_gen=is_gen)
self._PowerSeries__is_gen = is_gen
try:
prec = min(prec, x.prec()) # use precision of input, if defined
except AttributeError:
pass
# set the correct background value, depending on what type of input x is
try:
xparent = x.parent() # 'int' types have no parent
except AttributeError:
xparent = None
# test whether x coerces to background univariate
# power series ring of parent
from sage.rings.multi_power_series_ring import is_MPowerSeriesRing
if is_PowerSeriesRing(xparent) or is_MPowerSeriesRing(xparent):
# x is either a multivariate or univariate power series
#
# test whether x coerces directly to designated parent
if is_MPowerSeries(x):
try:
self._bg_value = parent._bg_ps_ring(x._bg_value)
except TypeError:
raise TypeError("Unable to coerce into background ring.")
# test whether x coerces to background univariate
# power series ring of parent
elif xparent == parent._bg_ps_ring():
self._bg_value = x
elif parent._bg_ps_ring().has_coerce_map_from(xparent):
# previous test may fail if precision or term orderings of
# base rings do not match
self._bg_value = parent._bg_ps_ring(x)
else:
# x is a univariate power series, but not from the
# background power series ring
#
# convert x to a polynomial and send to background
# ring of parent
x = x.polynomial()
self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
# test whether x coerces to underlying polynomial ring of parent
elif is_PolynomialRing(xparent):
self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
else:
try:
x = parent._poly_ring(x)
#self._value = x
self._bg_value = parent._send_to_bg(x).add_bigoh(prec)
except (TypeError, AttributeError):
raise TypeError(
"Input does not coerce to any of the expected rings.")
self._go_to_fg = parent._send_to_fg
self._prec = self._bg_value.prec()
# self._parent is used a lot by the class PowerSeries
self._parent = self.parent()