def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
"""
if R.ngens() == 0:
return False;
base_ring = R.base_ring()
return ( sage.rings.finite_rings.constructor.is_FiniteField(base_ring)
or is_RationalField(base_ring)
or (base_ring.is_prime_field() and base_ring.characteristic() <= 2147483647)
or is_RealField(base_ring)
or is_ComplexField(base_ring)
or is_RealDoubleField(base_ring)
or is_ComplexDoubleField(base_ring)
or number_field.all.is_NumberField(base_ring)
or ( sage.rings.fraction_field.is_FractionField(base_ring) and ( base_ring.base_ring().is_prime_field() or base_ring.base_ring() is ZZ ) )
or base_ring is ZZ
or is_IntegerModRing(base_ring) )
def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
"""
if R.ngens() == 0:
return False;
base_ring = R.base_ring()
return ( sage.rings.finite_rings.constructor.is_FiniteField(base_ring)
or is_RationalField(base_ring)
or (base_ring.is_prime_field() and base_ring.characteristic() <= 2147483647)
or is_RealField(base_ring)
or is_ComplexField(base_ring)
or is_RealDoubleField(base_ring)
or is_ComplexDoubleField(base_ring)
or number_field.all.is_NumberField(base_ring)
or ( sage.rings.fraction_field.is_FractionField(base_ring) and ( base_ring.base_ring().is_prime_field() or base_ring.base_ring() is ZZ ) )
or base_ring is ZZ
or is_IntegerModRing(base_ring) )
def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(ZZ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
TESTS:
Avoid non absolute number fields (see :trac:`23535`)::
sage: K.<a,b> = NumberField([x^2-2,x^2-5])
sage: can_convert_to_singular(K['s,t'])
False
"""
if R.ngens() == 0:
return False
base_ring = R.base_ring()
if (base_ring is ZZ
or sage.rings.finite_rings.finite_field_constructor.is_FiniteField(
base_ring) or is_RationalField(base_ring)
or is_IntegerModRing(base_ring) or is_RealField(base_ring)
or is_ComplexField(base_ring) or is_RealDoubleField(base_ring)
or is_ComplexDoubleField(base_ring)):
return True
elif base_ring.is_prime_field():
return base_ring.characteristic() <= 2147483647
elif number_field.number_field_base.is_NumberField(base_ring):
return base_ring.is_absolute()
elif sage.rings.fraction_field.is_FractionField(base_ring):
B = base_ring.base_ring()
return B.is_prime_field() or B is ZZ or is_FiniteField(B)
elif is_RationalFunctionField(base_ring):
return base_ring.constant_field().is_prime_field()
else:
return False
def can_convert_to_singular(R):
"""
Returns True if this ring's base field or ring can be
represented in Singular, and the polynomial ring has at
least one generator. If this is True then this polynomial
ring can be represented in Singular.
The following base rings are supported: finite fields, rationals, number
fields, and real and complex fields.
EXAMPLES::
sage: from sage.rings.polynomial.polynomial_singular_interface import can_convert_to_singular
sage: can_convert_to_singular(PolynomialRing(QQ, names=['x']))
True
sage: can_convert_to_singular(PolynomialRing(QQ, names=[]))
False
TESTS:
Avoid non absolute number fields (see :trac:`23535`)::
sage: K.<a,b> = NumberField([x^2-2,x^2-5])
sage: can_convert_to_singular(K['s,t'])
False
"""
if R.ngens() == 0:
return False;
base_ring = R.base_ring()
if (base_ring is ZZ
or sage.rings.finite_rings.finite_field_constructor.is_FiniteField(base_ring)
or is_RationalField(base_ring)
or is_IntegerModRing(base_ring)
or is_RealField(base_ring)
or is_ComplexField(base_ring)
or is_RealDoubleField(base_ring)
or is_ComplexDoubleField(base_ring)):
return True
elif base_ring.is_prime_field():
return base_ring.characteristic() <= 2147483647
elif number_field.number_field_base.is_NumberField(base_ring):
return base_ring.is_absolute()
elif sage.rings.fraction_field.is_FractionField(base_ring):
B = base_ring.base_ring()
return B.is_prime_field() or B is ZZ or is_FiniteField(B)
elif is_RationalFunctionField(base_ring):
return base_ring.constant_field().is_prime_field()
else:
return False
def _singular_init_(self, singular=singular):
"""
Return a newly created Singular ring matching this ring.
EXAMPLES::
sage: PolynomialRing(QQ,'u_ba')._singular_init_()
// characteristic : 0
// number of vars : 1
// block 1 : ordering lp
// : names u_ba
// block 2 : ordering C
"""
if not can_convert_to_singular(self):
raise TypeError("no conversion of this ring to a Singular ring defined")
if self.ngens()==1:
_vars = '(%s)'%self.gen()
if "*" in _vars: # 1.000...000*x
_vars = _vars.split("*")[1]
order = 'lp'
else:
_vars = str(self.gens())
order = self.term_order().singular_str()
base_ring = self.base_ring()
if is_RealField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
precision = base_ring.precision()
digits = sage.arith.all.integer_ceil((2*precision - 2)/7.0)
self.__singular = singular.ring("(real,%d,0)"%digits, _vars, order=order, check=False)
elif is_ComplexField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
precision = base_ring.precision()
digits = sage.arith.all.integer_ceil((2*precision - 2)/7.0)
self.__singular = singular.ring("(complex,%d,0,I)"%digits, _vars, order=order, check=False)
elif is_RealDoubleField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
self.__singular = singular.ring("(real,15,0)", _vars, order=order, check=False)
elif is_ComplexDoubleField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
self.__singular = singular.ring("(complex,15,0,I)", _vars, order=order, check=False)
elif base_ring.is_prime_field():
self.__singular = singular.ring(self.characteristic(), _vars, order=order, check=False)
elif sage.rings.finite_rings.finite_field_constructor.is_FiniteField(base_ring):
# not the prime field!
gen = str(base_ring.gen())
r = singular.ring( "(%s,%s)"%(self.characteristic(),gen), _vars, order=order, check=False)
self.__minpoly = (str(base_ring.modulus()).replace("x",gen)).replace(" ","")
if singular.eval('minpoly') != "(" + self.__minpoly + ")":
singular.eval("minpoly=%s"%(self.__minpoly) )
self.__minpoly = singular.eval('minpoly')[1:-1]
self.__singular = r
elif number_field.number_field_base.is_NumberField(base_ring) and base_ring.is_absolute():
# not the rationals!
gen = str(base_ring.gen())
poly=base_ring.polynomial()
poly_gen=str(poly.parent().gen())
poly_str=str(poly).replace(poly_gen,gen)
r = singular.ring( "(%s,%s)"%(self.characteristic(),gen), _vars, order=order, check=False)
self.__minpoly = (poly_str).replace(" ","")
if singular.eval('minpoly') != "(" + self.__minpoly + ")":
singular.eval("minpoly=%s"%(self.__minpoly) )
self.__minpoly = singular.eval('minpoly')[1:-1]
self.__singular = r
elif sage.rings.fraction_field.is_FractionField(base_ring) and (base_ring.base_ring() is ZZ or base_ring.base_ring().is_prime_field() or is_FiniteField(base_ring.base_ring())):
if base_ring.ngens()==1:
gens = str(base_ring.gen())
else:
gens = str(base_ring.gens())
if not (not base_ring.base_ring().is_prime_field() and is_FiniteField(base_ring.base_ring())) :
self.__singular = singular.ring( "(%s,%s)"%(base_ring.characteristic(),gens), _vars, order=order, check=False)
else:
ext_gen = str(base_ring.base_ring().gen())
_vars = '(' + ext_gen + ', ' + _vars[1:];
R = self.__singular = singular.ring( "(%s,%s)"%(base_ring.characteristic(),gens), _vars, order=order, check=False)
self.base_ring().__minpoly = (str(base_ring.base_ring().modulus()).replace("x",ext_gen)).replace(" ","")
singular.eval('setring '+R._name);
self.__singular = singular("std(ideal(%s))"%(self.base_ring().__minpoly),type='qring')
elif sage.rings.function_field.function_field.is_RationalFunctionField(base_ring) and base_ring.constant_field().is_prime_field():
gen = str(base_ring.gen())
self.__singular = singular.ring( "(%s,%s)"%(base_ring.characteristic(),gen), _vars, order=order, check=False)
elif is_IntegerModRing(base_ring):
ch = base_ring.characteristic()
if ch.is_power_of(2):
exp = ch.nbits() -1
self.__singular = singular.ring("(integer,2,%d)"%(exp,), _vars, order=order, check=False)
else:
self.__singular = singular.ring("(integer,%d)"%(ch,), _vars, order=order, check=False)
elif base_ring is ZZ:
self.__singular = singular.ring("(integer)", _vars, order=order, check=False)
else:
raise TypeError("no conversion to a Singular ring defined")
return self.__singular
def _singular_init_(self, singular=singular_default):
"""
Return a newly created Singular ring matching this ring.
EXAMPLES::
sage: PolynomialRing(QQ,'u_ba')._singular_init_()
// characteristic : 0
// number of vars : 1
// block 1 : ordering lp
// : names u_ba
// block 2 : ordering C
"""
if not can_convert_to_singular(self):
raise TypeError, "no conversion of this ring to a Singular ring defined"
if self.ngens()==1:
_vars = '(%s)'%self.gen()
if "*" in _vars: # 1.000...000*x
_vars = _vars.split("*")[1]
order = 'lp'
else:
_vars = str(self.gens())
order = self.term_order().singular_str()
base_ring = self.base_ring()
if is_RealField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
precision = base_ring.precision()
digits = sage.rings.arith.integer_ceil((2*precision - 2)/7.0)
self.__singular = singular.ring("(real,%d,0)"%digits, _vars, order=order, check=False)
elif is_ComplexField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
precision = base_ring.precision()
digits = sage.rings.arith.integer_ceil((2*precision - 2)/7.0)
self.__singular = singular.ring("(complex,%d,0,I)"%digits, _vars, order=order, check=False)
elif is_RealDoubleField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
self.__singular = singular.ring("(real,15,0)", _vars, order=order, check=False)
elif is_ComplexDoubleField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
self.__singular = singular.ring("(complex,15,0,I)", _vars, order=order, check=False)
elif base_ring.is_prime_field():
self.__singular = singular.ring(self.characteristic(), _vars, order=order, check=False)
elif sage.rings.finite_rings.constructor.is_FiniteField(base_ring):
# not the prime field!
gen = str(base_ring.gen())
r = singular.ring( "(%s,%s)"%(self.characteristic(),gen), _vars, order=order, check=False)
self.__minpoly = (str(base_ring.modulus()).replace("x",gen)).replace(" ","")
if singular.eval('minpoly') != "(" + self.__minpoly + ")":
singular.eval("minpoly=%s"%(self.__minpoly) )
self.__minpoly = singular.eval('minpoly')[1:-1]
self.__singular = r
elif number_field.all.is_NumberField(base_ring) and base_ring.is_absolute():
# not the rationals!
gen = str(base_ring.gen())
poly=base_ring.polynomial()
poly_gen=str(poly.parent().gen())
poly_str=str(poly).replace(poly_gen,gen)
r = singular.ring( "(%s,%s)"%(self.characteristic(),gen), _vars, order=order, check=False)
self.__minpoly = (poly_str).replace(" ","")
if singular.eval('minpoly') != "(" + self.__minpoly + ")":
singular.eval("minpoly=%s"%(self.__minpoly) )
self.__minpoly = singular.eval('minpoly')[1:-1]
self.__singular = r
elif sage.rings.fraction_field.is_FractionField(base_ring) and (base_ring.base_ring() is ZZ or base_ring.base_ring().is_prime_field()):
if base_ring.ngens()==1:
gens = str(base_ring.gen())
else:
gens = str(base_ring.gens())
self.__singular = singular.ring( "(%s,%s)"%(base_ring.characteristic(),gens), _vars, order=order, check=False)
elif is_IntegerModRing(base_ring):
ch = base_ring.characteristic()
if ch.is_power_of(2):
exp = ch.nbits() -1
self.__singular = singular.ring("(integer,2,%d)"%(exp,), _vars, order=order, check=False)
else:
self.__singular = singular.ring("(integer,%d)"%(ch,), _vars, order=order, check=False)
elif base_ring is ZZ:
self.__singular = singular.ring("(integer)", _vars, order=order, check=False)
else:
raise TypeError, "no conversion to a Singular ring defined"
return self.__singular
def _singular_init_(self, singular=singular):
"""
Return a newly created Singular ring matching this ring.
EXAMPLES::
sage: PolynomialRing(QQ,'u_ba')._singular_init_()
polynomial ring, over a field, global ordering
// coefficients: QQ
// number of vars : 1
// block 1 : ordering lp
// : names u_ba
// block 2 : ordering C
"""
if not can_convert_to_singular(self):
raise TypeError("no conversion of this ring to a Singular ring defined")
if self.ngens()==1:
_vars = '(%s)'%self.gen()
if "*" in _vars: # 1.000...000*x
_vars = _vars.split("*")[1]
order = 'lp'
else:
_vars = str(self.gens())
order = self.term_order().singular_str()
base_ring = self.base_ring()
if is_RealField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
precision = base_ring.precision()
digits = sage.arith.all.integer_ceil((2*precision - 2)/7.0)
self.__singular = singular.ring("(real,%d,0)"%digits, _vars, order=order, check=False)
elif is_ComplexField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
precision = base_ring.precision()
digits = sage.arith.all.integer_ceil((2*precision - 2)/7.0)
self.__singular = singular.ring("(complex,%d,0,I)"%digits, _vars, order=order, check=False)
elif is_RealDoubleField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
self.__singular = singular.ring("(real,15,0)", _vars, order=order, check=False)
elif is_ComplexDoubleField(base_ring):
# singular converts to bits from base_10 in mpr_complex.cc by:
# size_t bits = 1 + (size_t) ((float)digits * 3.5);
self.__singular = singular.ring("(complex,15,0,I)", _vars, order=order, check=False)
elif base_ring.is_prime_field():
self.__singular = singular.ring(self.characteristic(), _vars, order=order, check=False)
elif sage.rings.finite_rings.finite_field_constructor.is_FiniteField(base_ring):
# not the prime field!
gen = str(base_ring.gen())
r = singular.ring( "(%s,%s)"%(self.characteristic(),gen), _vars, order=order, check=False)
self.__minpoly = (str(base_ring.modulus()).replace("x",gen)).replace(" ","")
if singular.eval('minpoly') != "(" + self.__minpoly + ")":
singular.eval("minpoly=%s"%(self.__minpoly) )
self.__minpoly = singular.eval('minpoly')[1:-1]
self.__singular = r
elif number_field.number_field_base.is_NumberField(base_ring) and base_ring.is_absolute():
# not the rationals!
gen = str(base_ring.gen())
poly=base_ring.polynomial()
poly_gen=str(poly.parent().gen())
poly_str=str(poly).replace(poly_gen,gen)
r = singular.ring( "(%s,%s)"%(self.characteristic(),gen), _vars, order=order, check=False)
self.__minpoly = (poly_str).replace(" ","")
if singular.eval('minpoly') != "(" + self.__minpoly + ")":
singular.eval("minpoly=%s"%(self.__minpoly) )
self.__minpoly = singular.eval('minpoly')[1:-1]
self.__singular = r
elif sage.rings.fraction_field.is_FractionField(base_ring) and (base_ring.base_ring() is ZZ or base_ring.base_ring().is_prime_field() or is_FiniteField(base_ring.base_ring())):
if base_ring.ngens()==1:
gens = str(base_ring.gen())
else:
gens = str(base_ring.gens())
if not (not base_ring.base_ring().is_prime_field() and is_FiniteField(base_ring.base_ring())) :
self.__singular = singular.ring( "(%s,%s)"%(base_ring.characteristic(),gens), _vars, order=order, check=False)
else:
ext_gen = str(base_ring.base_ring().gen())
_vars = '(' + ext_gen + ', ' + _vars[1:];
R = self.__singular = singular.ring( "(%s,%s)"%(base_ring.characteristic(),gens), _vars, order=order, check=False)
self.base_ring().__minpoly = (str(base_ring.base_ring().modulus()).replace("x",ext_gen)).replace(" ","")
singular.eval('setring '+R._name);
from sage.misc.stopgap import stopgap
stopgap("Denominators of fraction field elements are sometimes dropped without warning.", 17696)
self.__singular = singular("std(ideal(%s))"%(self.base_ring().__minpoly),type='qring')
elif sage.rings.function_field.function_field.is_RationalFunctionField(base_ring) and base_ring.constant_field().is_prime_field():
gen = str(base_ring.gen())
self.__singular = singular.ring( "(%s,%s)"%(base_ring.characteristic(),gen), _vars, order=order, check=False)
elif is_IntegerModRing(base_ring):
ch = base_ring.characteristic()
if ch.is_power_of(2):
exp = ch.nbits() -1
self.__singular = singular.ring("(integer,2,%d)"%(exp,), _vars, order=order, check=False)
else:
self.__singular = singular.ring("(integer,%d)"%(ch,), _vars, order=order, check=False)
elif base_ring is ZZ:
self.__singular = singular.ring("(integer)", _vars, order=order, check=False)
else:
raise TypeError("no conversion to a Singular ring defined")
return self.__singular