def _repr_(self):
"""
Return a string representation of this system.
EXAMPLE::
sage: P.<a,b,c,d> = PolynomialRing(GF(127))
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence(I); F # indirect doctest
[a + 2*b + 2*c + 2*d - 1,
a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a,
2*a*b + 2*b*c + 2*c*d - b,
b^2 + 2*a*c + 2*b*d - c]
If the system contains 20 or more polynomials, a short summary
is printed::
sage: sr = mq.SR(allow_zero_inversions=True,gf2=True)
sage: F,s = sr.polynomial_system(); F
Polynomial Sequence with 36 Polynomials in 20 Variables
"""
if len(self) < 20:
return Sequence_generic._repr_(self)
else:
return "Polynomial Sequence with %d Polynomials in %d Variables"%(len(self),self.nvariables())
def _repr_(self):
"""
Return a string representation of this system.
EXAMPLE::
sage: P.<a,b,c,d> = PolynomialRing(GF(127))
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence(I); F # indirect doctest
[a + 2*b + 2*c + 2*d - 1,
a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a,
2*a*b + 2*b*c + 2*c*d - b,
b^2 + 2*a*c + 2*b*d - c]
If the system contains 20 or more polynomials, a short summary
is printed::
sage: sr = mq.SR(allow_zero_inversions=True,gf2=True)
sage: F,s = sr.polynomial_system(); F
Polynomial Sequence with 56 Polynomials in 20 Variables
"""
if len(self) < 20:
return Sequence_generic._repr_(self)
else:
return "Polynomial Sequence with %d Polynomials in %d Variables"%(len(self),self.nvariables())
def __init__(self, parts, ring, immutable=False, cr=False, cr_str=None):
"""
Construct a new system of multivariate polynomials.
INPUT:
- ``part`` - a list of lists with polynomials
- ``ring`` - a multivariate polynomial ring
- ``immutable`` - if ``True`` the sequence is immutable (default: ``False``)
- ``cr`` - print a line break after each element (default: ``False``)
- ``cr_str`` - print a line break after each element if 'str'
is called (default: ``None``)
EXAMPLES::
sage: P.<a,b,c,d> = PolynomialRing(GF(127),4)
sage: I = sage.rings.ideal.Katsura(P)
sage: Sequence([I.gens()], I.ring()) # indirect doctest
[a + 2*b + 2*c + 2*d - 1, a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a, 2*a*b + 2*b*c + 2*c*d - b, b^2 + 2*a*c + 2*b*d - c]
If an ideal is provided, the generators are used.::
sage: Sequence(I)
[a + 2*b + 2*c + 2*d - 1, a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a, 2*a*b + 2*b*c + 2*c*d - b, b^2 + 2*a*c + 2*b*d - c]
If a list of polynomials is provided, the system has only one
part.::
sage: Sequence(I.gens(), I.ring())
[a + 2*b + 2*c + 2*d - 1, a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a, 2*a*b + 2*b*c + 2*c*d - b, b^2 + 2*a*c + 2*b*d - c]
"""
Sequence_generic.__init__(self,
sum(parts, tuple()),
ring,
check=False,
immutable=immutable,
cr=cr,
cr_str=cr_str,
use_sage_types=True)
self._ring = ring
self._parts = parts
def __init__(self, parts, ring, immutable=False, cr=False, cr_str=None):
"""
Construct a new system of multivariate polynomials.
INPUT:
- ``part`` - a list of lists with polynomials
- ``ring`` - a multivariate polynomial ring
- ``immutable`` - if ``True`` the sequence is immutable (default: ``False``)
- ``cr`` - print a line break after each element (default: ``False``)
- ``cr_str`` - print a line break after each element if 'str'
is called (default: ``None``)
EXAMPLES::
sage: P.<a,b,c,d> = PolynomialRing(GF(127),4)
sage: I = sage.rings.ideal.Katsura(P)
sage: Sequence([I.gens()], I.ring()) # indirect doctest
[a + 2*b + 2*c + 2*d - 1, a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a, 2*a*b + 2*b*c + 2*c*d - b, b^2 + 2*a*c + 2*b*d - c]
If an ideal is provided, the generators are used.::
sage: Sequence(I)
[a + 2*b + 2*c + 2*d - 1, a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a, 2*a*b + 2*b*c + 2*c*d - b, b^2 + 2*a*c + 2*b*d - c]
If a list of polynomials is provided, the system has only one
part.::
sage: Sequence(I.gens(), I.ring())
[a + 2*b + 2*c + 2*d - 1, a^2 + 2*b^2 + 2*c^2 + 2*d^2 - a, 2*a*b + 2*b*c + 2*c*d - b, b^2 + 2*a*c + 2*b*d - c]
"""
Sequence_generic.__init__(self, sum(parts,tuple()), ring, check=False, immutable=immutable,
cr=cr, cr_str=cr_str, use_sage_types=True)
self._ring = ring
self._parts = parts