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from sympy.core.expr import Expr
from sympy.core.symbol import Dummy
from sympy.core.sympify import _sympify
from sympy.polys.polyerrors import CoercionFailed
from sympy.polys.polytools import Poly, parallel_poly_from_expr
from sympy.polys.domains import QQ
from sympy.polys.matrices import DomainMatrix
from sympy.polys.matrices.domainscalar import DomainScalar
class MutablePolyDenseMatrix:
"""
A mutable matrix of objects from poly module or to operate with them.
Examples
========
>>> from sympy.polys.polymatrix import PolyMatrix
>>> from sympy import Symbol, Poly
>>> x = Symbol('x')
>>> pm1 = PolyMatrix([[Poly(x**2, x), Poly(-x, x)], [Poly(x**3, x), Poly(-1 + x, x)]])
>>> v1 = PolyMatrix([[1, 0], [-1, 0]], x)
>>> pm1*v1
PolyMatrix([
[ x**2 + x, 0],
[x**3 - x + 1, 0]], ring=QQ[x])
>>> pm1.ring
ZZ[x]
>>> v1*pm1
PolyMatrix([
[ x**2, -x],
[-x**2, x]], ring=QQ[x])
>>> pm2 = PolyMatrix([[Poly(x**2, x, domain='QQ'), Poly(0, x, domain='QQ'), Poly(1, x, domain='QQ'), \
Poly(x**3, x, domain='QQ'), Poly(0, x, domain='QQ'), Poly(-x**3, x, domain='QQ')]])
>>> v2 = PolyMatrix([1, 0, 0, 0, 0, 0], x)
>>> v2.ring
QQ[x]
>>> pm2*v2
PolyMatrix([[x**2]], ring=QQ[x])
"""
def __new__(cls, *args, ring=None):
if not args:
# PolyMatrix(ring=QQ[x])
if ring is None:
raise TypeError("The ring needs to be specified for an empty PolyMatrix")
rows, cols, items, gens = 0, 0, [], ()
elif isinstance(args[0], list):
elements, gens = args[0], args[1:]
if not elements:
# PolyMatrix([])
rows, cols, items = 0, 0, []
elif isinstance(elements[0], (list, tuple)):
# PolyMatrix([[1, 2]], x)
rows, cols = len(elements), len(elements[0])
items = [e for row in elements for e in row]
else:
# PolyMatrix([1, 2], x)
rows, cols = len(elements), 1
items = elements
elif [type(a) for a in args[:3]] == [int, int, list]:
# PolyMatrix(2, 2, [1, 2, 3, 4], x)
rows, cols, items, gens = args[0], args[1], args[2], args[3:]
elif [type(a) for a in args[:3]] == [int, int, type(lambda: 0)]:
# PolyMatrix(2, 2, lambda i, j: i+j, x)
rows, cols, func, gens = args[0], args[1], args[2], args[3:]
items = [func(i, j) for i in range(rows) for j in range(cols)]
else:
raise TypeError("Invalid arguments")
# PolyMatrix([[1]], x, y) vs PolyMatrix([[1]], (x, y))
if len(gens) == 1 and isinstance(gens[0], tuple):
gens = gens[0]
# gens is now a tuple (x, y)
return cls.from_list(rows, cols, items, gens, ring)
@classmethod
def from_list(cls, rows, cols, items, gens, ring):
# items can be Expr, Poly, or a mix of Expr and Poly
items = [_sympify(item) for item in items]
if items and all(isinstance(item, Poly) for item in items):
polys = True
else:
polys = False
# Identify the ring for the polys
if ring is not None:
# Parse a domain string like 'QQ[x]'
if isinstance(ring, str):
ring = Poly(0, Dummy(), domain=ring).domain
elif polys:
p = items[0]
for p2 in items[1:]:
p, _ = p.unify(p2)
ring = p.domain[p.gens]
else:
items, info = parallel_poly_from_expr(items, gens, field=True)
ring = info['domain'][info['gens']]
polys = True
# Efficiently convert when all elements are Poly
if polys:
p_ring = Poly(0, ring.symbols, domain=ring.domain)
to_ring = ring.ring.from_list
convert_poly = lambda p: to_ring(p.unify(p_ring)[0].rep.to_list())
elements = [convert_poly(p) for p in items]
else:
convert_expr = ring.from_sympy
elements = [convert_expr(e.as_expr()) for e in items]
# Convert to domain elements and construct DomainMatrix
elements_lol = [[elements[i*cols + j] for j in range(cols)] for i in range(rows)]
dm = DomainMatrix(elements_lol, (rows, cols), ring)
return cls.from_dm(dm)
@classmethod
def from_dm(cls, dm):
obj = super().__new__(cls)
dm = dm.to_sparse()
R = dm.domain
obj._dm = dm
obj.ring = R
obj.domain = R.domain
obj.gens = R.symbols
return obj
def to_Matrix(self):
return self._dm.to_Matrix()
@classmethod
def from_Matrix(cls, other, *gens, ring=None):
return cls(*other.shape, other.flat(), *gens, ring=ring)
def set_gens(self, gens):
return self.from_Matrix(self.to_Matrix(), gens)
def __repr__(self):
if self.rows * self.cols:
return 'Poly' + repr(self.to_Matrix())[:-1] + f', ring={self.ring})'
else:
return f'PolyMatrix({self.rows}, {self.cols}, [], ring={self.ring})'
@property
def shape(self):
return self._dm.shape
@property
def rows(self):
return self.shape[0]
@property
def cols(self):
return self.shape[1]
def __len__(self):
return self.rows * self.cols
def __getitem__(self, key):
def to_poly(v):
ground = self._dm.domain.domain
gens = self._dm.domain.symbols
return Poly(v.to_dict(), gens, domain=ground)
dm = self._dm
if isinstance(key, slice):
items = dm.flat()[key]
return [to_poly(item) for item in items]
elif isinstance(key, int):
i, j = divmod(key, self.cols)
e = dm[i,j]
return to_poly(e.element)
i, j = key
if isinstance(i, int) and isinstance(j, int):
return to_poly(dm[i, j].element)
else:
return self.from_dm(dm[i, j])
def __eq__(self, other):
if not isinstance(self, type(other)):
return NotImplemented
return self._dm == other._dm
def __add__(self, other):
if isinstance(other, type(self)):
return self.from_dm(self._dm + other._dm)
return NotImplemented
def __sub__(self, other):
if isinstance(other, type(self)):
return self.from_dm(self._dm - other._dm)
return NotImplemented
def __mul__(self, other):
if isinstance(other, type(self)):
return self.from_dm(self._dm * other._dm)
elif isinstance(other, int):
other = _sympify(other)
if isinstance(other, Expr):
Kx = self.ring
try:
other_ds = DomainScalar(Kx.from_sympy(other), Kx)
except (CoercionFailed, ValueError):
other_ds = DomainScalar.from_sympy(other)
return self.from_dm(self._dm * other_ds)
return NotImplemented
def __rmul__(self, other):
if isinstance(other, int):
other = _sympify(other)
if isinstance(other, Expr):
other_ds = DomainScalar.from_sympy(other)
return self.from_dm(other_ds * self._dm)
return NotImplemented
def __truediv__(self, other):
if isinstance(other, Poly):
other = other.as_expr()
elif isinstance(other, int):
other = _sympify(other)
if not isinstance(other, Expr):
return NotImplemented
other = self.domain.from_sympy(other)
inverse = self.ring.convert_from(1/other, self.domain)
inverse = DomainScalar(inverse, self.ring)
dm = self._dm * inverse
return self.from_dm(dm)
def __neg__(self):
return self.from_dm(-self._dm)
def transpose(self):
return self.from_dm(self._dm.transpose())
def row_join(self, other):
dm = DomainMatrix.hstack(self._dm, other._dm)
return self.from_dm(dm)
def col_join(self, other):
dm = DomainMatrix.vstack(self._dm, other._dm)
return self.from_dm(dm)
def applyfunc(self, func):
M = self.to_Matrix().applyfunc(func)
return self.from_Matrix(M, self.gens)
@classmethod
def eye(cls, n, gens):
return cls.from_dm(DomainMatrix.eye(n, QQ[gens]))
@classmethod
def zeros(cls, m, n, gens):
return cls.from_dm(DomainMatrix.zeros((m, n), QQ[gens]))
def rref(self, simplify='ignore', normalize_last='ignore'):
# If this is K[x] then computes RREF in ground field K.
if not (self.domain.is_Field and all(p.is_ground for p in self)):
raise ValueError("PolyMatrix rref is only for ground field elements")
dm = self._dm
dm_ground = dm.convert_to(dm.domain.domain)
dm_rref, pivots = dm_ground.rref()
dm_rref = dm_rref.convert_to(dm.domain)
return self.from_dm(dm_rref), pivots
def nullspace(self):
# If this is K[x] then computes nullspace in ground field K.
if not (self.domain.is_Field and all(p.is_ground for p in self)):
raise ValueError("PolyMatrix nullspace is only for ground field elements")
dm = self._dm
K, Kx = self.domain, self.ring
dm_null_rows = dm.convert_to(K).nullspace(divide_last=True).convert_to(Kx)
dm_null = dm_null_rows.transpose()
dm_basis = [dm_null[:,i] for i in range(dm_null.shape[1])]
return [self.from_dm(dmvec) for dmvec in dm_basis]
def rank(self):
return self.cols - len(self.nullspace())
MutablePolyMatrix = PolyMatrix = MutablePolyDenseMatrix
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