def test_PolyElement():
Ruv, u, v = ring("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Ruv)
Rx_zzi, xz = ring("x", ZZ_I)
assert str(x - x) == "0"
assert str(x - 1) == "x - 1"
assert str(x + 1) == "x + 1"
assert str(x**2) == "x**2"
assert str(x**(-2)) == "x**(-2)"
assert str(x**QQ(1, 2)) == "x**(1/2)"
assert str((u**2 + 3 * u * v + 1) * x**2 * y + u +
1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1"
assert str((u**2 + 3 * u * v + 1) * x**2 * y +
(u + 1) * x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x"
assert str((u**2 + 3 * u * v + 1) * x**2 * y + (u + 1) * x +
1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1"
assert str((-u**2 + 3 * u * v - 1) * x**2 * y - (u + 1) * x -
1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1"
assert str(-(v**2 + v + 1) * x + 3 * u * v +
1) == "-(v**2 + v + 1)*x + 3*u*v + 1"
assert str(-(v**2 + v + 1) * x - 3 * u * v +
1) == "-(v**2 + v + 1)*x - 3*u*v + 1"
assert str((1 + I) * xz + 2) == "(1 + 1*I)*x + (2 + 0*I)"
def test_PolyRing():
assert srepr(ring("x", ZZ, lex)[0]) == "PolyRing((Symbol('x'),), ZZ, lex)"
assert srepr(
ring("x,y", QQ,
grlex)[0]) == "PolyRing((Symbol('x'), Symbol('y')), QQ, grlex)"
assert srepr(
ring("x,y,z", ZZ["t"], lex)
[0]) == "PolyRing((Symbol('x'), Symbol('y'), Symbol('z')), ZZ[t], lex)"
def test_PolyRing():
assert str(ring("x", ZZ,
lex)[0]) == "Polynomial ring in x over ZZ with lex order"
assert str(
ring("x,y", QQ,
grlex)[0]) == "Polynomial ring in x, y over QQ with grlex order"
assert str(
ring("x,y,z", ZZ["t"],
lex)[0]) == "Polynomial ring in x, y, z over ZZ[t] with lex order"
def test_PolyElement():
Ruv, u,v = ring("u,v", ZZ);
Rxyz, x,y,z = ring("x,y,z", Ruv.to_domain())
assert str(x - x) == "0"
assert str(x - 1) == "x - 1"
assert str(x + 1) == "x + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + u + 1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1"
assert str((-u**2 + 3*u*v - 1)*x**2*y - (u + 1)*x - 1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1"
def test_PolyElement():
Ruv, u,v = ring("u,v", ZZ);
Rxyz, x,y,z = ring("x,y,z", Ruv)
assert str(x - x) == "0"
assert str(x - 1) == "x - 1"
assert str(x + 1) == "x + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + u + 1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1"
assert str((-u**2 + 3*u*v - 1)*x**2*y - (u + 1)*x - 1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1"
assert str(-(v**2 + v + 1)*x + 3*u*v + 1) == "-(v**2 + v + 1)*x + 3*u*v + 1"
assert str(-(v**2 + v + 1)*x - 3*u*v + 1) == "-(v**2 + v + 1)*x - 3*u*v + 1"
def test_PolyElement():
Ruv, u,v = ring("u,v", ZZ)
Rxyz, x,y,z = ring("x,y,z", Ruv)
assert str(x - x) == "0"
assert str(x - 1) == "x - 1"
assert str(x + 1) == "x + 1"
assert str(x**2) == "x**2"
assert str(x**(-2)) == "x**(-2)"
assert str(x**QQ(1, 2)) == "x**(1/2)"
assert str((u**2 + 3*u*v + 1)*x**2*y + u + 1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x"
assert str((u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1"
assert str((-u**2 + 3*u*v - 1)*x**2*y - (u + 1)*x - 1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1"
assert str(-(v**2 + v + 1)*x + 3*u*v + 1) == "-(v**2 + v + 1)*x + 3*u*v + 1"
assert str(-(v**2 + v + 1)*x - 3*u*v + 1) == "-(v**2 + v + 1)*x - 3*u*v + 1"
def test_PolyElement():
Ruv, u, v = ring("u,v", ZZ)
Rxyz, x, y, z = ring("x,y,z", Ruv)
assert str(x - x) == "0"
assert str(x - 1) == "x - 1"
assert str(x + 1) == "x + 1"
assert str(x**2) == "x**2"
assert str(x**(-2)) == "x**(-2)"
assert str(x**QQ(1, 2)) == "x**(1/2)"
assert (str((u**2 + 3 * u * v + 1) * x**2 * y + u +
1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1")
assert (str((u**2 + 3 * u * v + 1) * x**2 * y +
(u + 1) * x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x")
assert (str((u**2 + 3 * u * v + 1) * x**2 * y + (u + 1) * x +
1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1")
assert (str((-(u**2) + 3 * u * v - 1) * x**2 * y - (u + 1) * x -
1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1")
assert str(-(v**2 + v + 1) * x + 3 * u * v +
1) == "-(v**2 + v + 1)*x + 3*u*v + 1"
assert str(-(v**2 + v + 1) * x - 3 * u * v +
1) == "-(v**2 + v + 1)*x - 3*u*v + 1"
def test_PolyRing():
assert str(ring("x", ZZ, lex)[0]) == "Polynomial ring in x over ZZ with lex order"
assert str(ring("x,y", QQ, grlex)[0]) == "Polynomial ring in x, y over QQ with grlex order"
assert str(ring("x,y,z", ZZ["t"], lex)[0]) == "Polynomial ring in x, y, z over ZZ[t] with lex order"
import numpy as np
import numpy.linalg as la
from math import log, ceil, floor
from scipy import linalg as scila
from sympy import Poly
from sympy.polys import ring, QQ
RR, x = ring("x", QQ)
# setup code
def randomvec(n, seedNumber=0):
np.random.seed(seedNumber)
return np.random.rand(n)
def vectorToToeplitz(v, N=-1):
band_width = len(v)
if (N <= 0):
N = band_width
assert (band_width <= N)
H = np.zeros((N * 2 - 1, N))
for col in range(N):
H[col:col + band_width, col] = v
return H
def toeplitzToHankle(M):
return M[:, ::-1]
def test_PolyElement():
R, x, y = ring("x,y", ZZ)
assert srepr(3*x**2*y + 1) == "PolyElement(PolyRing((Symbol('x'), Symbol('y')), ZZ, lex), [((2, 1), 3), ((0, 0), 1)])"
def test_PolyRing():
assert srepr(ring("x", ZZ, lex)[0]) == "PolyRing((Symbol('x'),), ZZ, lex)"
assert srepr(ring("x,y", QQ, grlex)[0]) == "PolyRing((Symbol('x'), Symbol('y')), QQ, grlex)"
assert srepr(ring("x,y,z", ZZ["t"], lex)[0]) == "PolyRing((Symbol('x'), Symbol('y'), Symbol('z')), ZZ[t], lex)"
def test_PolyElement():
R, x, y = ring("x,y", ZZ)
assert srepr(3*x**2*y + 1) == "PolyElement(PolyRing((Symbol('x'), Symbol('y')), ZZ, lex), [((2, 1), 3), ((0, 0), 1)])"