def homothety_rotation_decomposition(m):
r"""
Return a couple composed of the homothety and a rotation matrix.
The coefficients of the returned pair are either in the ground field of
``m`` or in the algebraic field ``AA``.
EXAMPLES::
sage: from flatsurf.geometry.matrix_2x2 import homothety_rotation_decomposition
sage: R.<x> = PolynomialRing(QQ)
sage: K.<sqrt2> = NumberField(x^2 - 2, embedding=1.4142)
sage: m = matrix([[sqrt2, -sqrt2],[sqrt2,sqrt2]])
sage: a,rot = homothety_rotation_decomposition(m)
sage: a
2
sage: rot
[ 1/2*sqrt2 -1/2*sqrt2]
[ 1/2*sqrt2 1/2*sqrt2]
"""
if not is_similarity(m):
raise ValueError("the matrix must be a similarity")
det = m.det()
if not det.is_square():
if not AA.has_coerce_map_from(m.base_ring()):
l = map(number_field_to_AA, m.list())
M = MatrixSpace(AA, 2)
m = M(l)
else:
m = m.change_ring(AA)
sqrt_det = det.sqrt()
return sqrt_det, m / sqrt_det
def homothety_rotation_decomposition(m):
r"""
Return a couple composed of the homothety and a rotation matrix.
The coefficients of the returned pair are either in the ground field of
``m`` or in the algebraic field ``AA``.
EXAMPLES::
sage: from flatsurf.geometry.matrix_2x2 import homothety_rotation_decomposition
sage: R.<x> = PolynomialRing(QQ)
sage: K.<sqrt2> = NumberField(x^2 - 2, embedding=1.4142)
sage: m = matrix([[sqrt2, -sqrt2],[sqrt2,sqrt2]])
sage: a,rot = homothety_rotation_decomposition(m)
sage: a
2
sage: rot
[ 1/2*sqrt2 -1/2*sqrt2]
[ 1/2*sqrt2 1/2*sqrt2]
"""
if not is_similarity(m):
raise ValueError("the matrix must be a similarity")
det = m.det()
if not det.is_square():
if not AA.has_coerce_map_from(m.base_ring()):
l = map(number_field_to_AA,m.list())
M = MatrixSpace(AA,2)
m = M(l)
else:
m = m.change_ring(AA)
sqrt_det = det.sqrt()
return sqrt_det, m / sqrt_det
def _coerce_map_from_(self, P):
r"""
Return whether ``P`` coerces into this symbolic subring.
INPUT:
- ``P`` -- a parent.
OUTPUT:
A boolean or ``None``.
TESTS::
sage: from sage.symbolic.subring import GenericSymbolicSubring
sage: GenericSymbolicSubring(vars=tuple()).has_coerce_map_from(SR) # indirect doctest # not tested see #19231
False
::
sage: from sage.symbolic.subring import SymbolicSubring
sage: C = SymbolicSubring(no_variables=True)
sage: C.has_coerce_map_from(ZZ) # indirect doctest
True
sage: C.has_coerce_map_from(QQ) # indirect doctest
True
sage: C.has_coerce_map_from(RR) # indirect doctest
True
sage: C.has_coerce_map_from(RIF) # indirect doctest
True
sage: C.has_coerce_map_from(CC) # indirect doctest
True
sage: C.has_coerce_map_from(CIF) # indirect doctest
True
sage: C.has_coerce_map_from(AA) # indirect doctest
True
sage: C.has_coerce_map_from(QQbar) # indirect doctest
True
sage: C.has_coerce_map_from(SR) # indirect doctest
False
"""
if P == SR:
# Workaround; can be deleted once #19231 is fixed
return False
from sage.rings.real_mpfr import mpfr_prec_min
from sage.rings.all import (ComplexField, RLF, CLF, AA, QQbar,
InfinityRing)
from sage.rings.real_mpfi import is_RealIntervalField
from sage.rings.complex_interval_field import is_ComplexIntervalField
if isinstance(P, type):
return SR._coerce_map_from_(P)
elif RLF.has_coerce_map_from(P) or \
CLF.has_coerce_map_from(P) or \
AA.has_coerce_map_from(P) or \
QQbar.has_coerce_map_from(P):
return True
elif (P is InfinityRing or is_RealIntervalField(P)
or is_ComplexIntervalField(P)):
return True
elif ComplexField(mpfr_prec_min()).has_coerce_map_from(P):
return P not in (RLF, CLF, AA, QQbar)
def _coerce_map_from_(self, P):
r"""
Return whether ``P`` coerces into this symbolic subring.
INPUT:
- ``P`` -- a parent.
OUTPUT:
A boolean or ``None``.
TESTS::
sage: from sage.symbolic.subring import GenericSymbolicSubring
sage: GenericSymbolicSubring(vars=tuple()).has_coerce_map_from(SR) # indirect doctest # not tested see #19231
False
::
sage: from sage.symbolic.subring import SymbolicSubring
sage: C = SymbolicSubring(no_variables=True)
sage: C.has_coerce_map_from(ZZ) # indirect doctest
True
sage: C.has_coerce_map_from(QQ) # indirect doctest
True
sage: C.has_coerce_map_from(RR) # indirect doctest
True
sage: C.has_coerce_map_from(RIF) # indirect doctest
True
sage: C.has_coerce_map_from(CC) # indirect doctest
True
sage: C.has_coerce_map_from(CIF) # indirect doctest
True
sage: C.has_coerce_map_from(AA) # indirect doctest
True
sage: C.has_coerce_map_from(QQbar) # indirect doctest
True
sage: C.has_coerce_map_from(SR) # indirect doctest
False
"""
if P == SR:
# Workaround; can be deleted once #19231 is fixed
return False
from sage.rings.real_mpfr import mpfr_prec_min
from sage.rings.all import (ComplexField,
RLF, CLF, AA, QQbar, InfinityRing)
from sage.rings.real_mpfi import is_RealIntervalField
from sage.rings.complex_interval_field import is_ComplexIntervalField
if isinstance(P, type):
return SR._coerce_map_from_(P)
elif RLF.has_coerce_map_from(P) or \
CLF.has_coerce_map_from(P) or \
AA.has_coerce_map_from(P) or \
QQbar.has_coerce_map_from(P):
return True
elif (P is InfinityRing or
is_RealIntervalField(P) or is_ComplexIntervalField(P)):
return True
elif ComplexField(mpfr_prec_min()).has_coerce_map_from(P):
return P not in (RLF, CLF, AA, QQbar)