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from __future__ import annotations
from typing import Iterable, Union
from fractions import Fraction
from itertools import zip_longest
def is_scalar(obj):
return isinstance(obj, (Fraction, int))
POLY_COLOR = None
# POLY_COLOR = '36' # Uncomment to have color
class PolyRenderBase:
def render(self, poly: Poly) -> str:
raise NotImplementedError()
def hint(self, poly: Poly) -> int:
raise NotImplementedError()
class Poly:
def __init__(self, vec: Iterable, letter='x', renderer=None):
'''
vec: big-endian coefficients
'''
from render import UnicodeRender
self.vec = list(vec)
self.letter = letter
self.renderer = renderer or UnicodeRender()
self._trim_zeros()
def _trim_zeros(self):
'''
Trim trailing zeros in coefficients: [0, 1, 1, 0] -> [0, 1, 1]
Needed for multiplication to work correctly
'''
len_zeros = 0
for c in reversed(self.vec):
if c != 0:
break
len_zeros += 1
if len_zeros > 0:
self.vec = self.vec[:-len_zeros]
def __mul__(self, rhs: Union[Poly, Fraction, int]):
if is_scalar(rhs):
return Poly([c * rhs for c in self.vec])
elif isinstance(rhs, Poly):
# no fft 4 u
result = [0] * (self.deg() + rhs.deg() + 1)
self._trim_zeros()
rhs._trim_zeros()
for i in range(len(self.vec)):
for j in range(len(rhs.vec)):
if all(c != 0 for c in (self.vec[i], rhs.vec[j])):
result[i + j] += self.vec[i] * rhs.vec[j]
return Poly(result)
else:
raise TypeError(f'{type(rhs)} not supported')
def __truediv__(self, rhs: Union[Fraction, int]):
if is_scalar(rhs):
return Poly([c * Fraction(1, rhs) for c in self.vec])
else:
raise TypeError(f'{type(rhs)} not supported')
def __add__(self, rhs: Union[Poly, Fraction, int]):
if is_scalar(rhs):
return Poly([self.vec[0] + rhs] + self.vec[1:])
elif isinstance(rhs, Poly):
result = []
for pair in zip_longest(self.vec, rhs.vec):
result.append(sum(c for c in pair if c is not None))
return Poly(result)
def __sub__(self, rhs: Union[Poly, Fraction, int]):
return self + (-rhs)
def __neg__(self):
return Poly(-c for c in self.vec)
def deg(self):
'''
Get degree of poly
'''
d = len(self.vec) - 1
for c in reversed(self.vec):
if c != 0:
return d
else:
d -= 1
return max(d, 0)
def shift(self, deg):
'''
divide by x^deg, drop rest
'''
for i in range(deg):
del self.vec[0]
def __repr__(self):
return self.renderer.render(self)
def hint(self):
return self.renderer.hint(self)
class Row:
'''
Matrix row.
'''
def __init__(self, it: Iterable):
def make_poly(obj):
if isinstance(obj, (int, Fraction)):
return Poly([obj])
elif isinstance(obj, Poly):
return obj
else:
raise TypeError(f'{type(obj)} not supported')
self.lst = list(map(make_poly, it))
self.hints = 1 * len(self.lst)
def __add__(self, obj: Row):
'''
Add another row
'''
assert isinstance(obj, Row)
assert len(obj.lst) == len(self.lst)
pairs = zip(self.lst, obj.lst)
return Row(map(lambda x: x[0] + x[1], pairs))
def __mul__(self, k: Union[int, Fraction]):
'''
Multiply by int or fractions.Fraction
'''
assert isinstance(k, (int, Fraction))
return Row(map(lambda x: x * k, self.lst))
def __iter__(self):
return iter(self.lst)
def __getitem__(self, key):
return self.lst[key]
def __setitem__(self, key, val):
self.lst[key] = val
def __len__(self):
return len(self.lst)
def __repr__(self):
parts = []
for el, hint in zip(self.lst, self.hints):
part = '{el: >{hint}}'.format(el=repr(el), hint=hint)
if el.deg() > 0 and POLY_COLOR is not None:
part = '\x1b[' + POLY_COLOR + 'm' + part + '\x1b[0m'
parts.append(part)
return ('[' + ' '.join(parts) + ']')
def get_hints(self):
'''
Get hints for other structures to align items
'''
return [el.hint() for el in self.lst]
def set_hints(self, hints):
'''
Set hints to align items within row
'''
self.hints = hints
class Matrix:
'''
Matrix. You can apply three elementary transforms to self.
'''
def __init__(self, rows):
def make_row(obj):
if isinstance(obj, Row):
return obj
else:
return Row(obj)
self.rows = list(map(make_row, rows))
assert all(len(row) == len(self.rows[0]) for row in self.rows)
def make_S(self, i: int, j: int, lbd: Union[int, Fraction], axis=0):
'''
if axis == 0, do transform on rows, else on cols
M[i] = M[i] + M[j] * lbd
'''
if axis == 0:
self.rows[i] = self.rows[i] + self.rows[j] * lbd
else:
for row in self.rows:
row[i] = row[i] + row[j] * lbd
def make_U(self, i: int, j: int, axis=0):
'''
if axis == 0, do transform on rows, else on cols
Swap M[i] and M[j]
'''
if axis == 0:
self.rows[i], self.rows[j] = self.rows[j], self.rows[i]
else:
for row in self.rows:
row[i], row[j] = row[j], row[i]
def make_D(self, i: int, lbd: Union[int, Fraction], axis=0):
'''
if axis == 0, do transform on rows, else on cols
Multiply M[i] by rational lbd
'''
if axis == 0:
self.rows[i] = self.rows[i] * lbd
else:
for row in self.rows:
row[i] = row[i] * lbd
def det(self) -> Poly:
'''
Get determinant of matrix
'''
assert all(len(row) == len(self.rows) for row in self.rows)
if len(self.rows) == 1:
return self.rows[0][0]
res = Poly([0])
try:
for i in range(len(self.rows[0])):
cofactor = Matrix([
self.rows[j][:i] + self.rows[j][i + 1:]
for j in range(1, len(self.rows))
])
res += cofactor.det() * (-1) ** i * self.rows[0][i]
except Exception as e:
print(self)
raise e
return res
def __sub__(self, oth):
return self + (-oth)
def __neg__(self):
rows = [row * (-1) for row in self.rows]
return Matrix(rows)
def __add__(self, oth):
rows = [row1 + row2 for row1, row2 in zip(self.rows, oth.rows)]
return Matrix(rows)
def __repr__(self):
hints = [row.get_hints() for row in self.rows]
max_hints = []
for i in range(len(hints)):
max_hints.append(max(hints[j][i] for j in range(len(hints))))
for row in self.rows:
row.set_hints(max_hints)
return '\n'.join(repr(row) for row in self.rows)
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