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)