def test_PolynomialRing():
sT(ZZ.inject('x'), "PolynomialRing(%s, (Symbol('x'),), "
'LexOrder())' % repr(ZZ))
sT(QQ.poly_ring('x', 'y', order=grlex),
"PolynomialRing(%s, (Symbol('x'), Symbol('y')), "
'GradedLexOrder())' % repr(QQ))
sT(ZZ.inject('x', 'y', 'z', 't').eject('t'),
"PolynomialRing(PolynomialRing(%s, (Symbol('t'),), "
"LexOrder()), (Symbol('x'), Symbol('y'), Symbol('z')), "
'LexOrder())' % repr(ZZ))
def test_PolynomialRing():
sT(ZZ.inject('x'),
f"UnivarPolynomialRing({ZZ!r}, (Symbol('x'),), LexOrder())")
sT(
QQ.poly_ring('x', 'y', order=grlex),
f"PolynomialRing({QQ!r}, (Symbol('x'), Symbol('y')), GradedLexOrder())"
)
sT(
ZZ.inject('x', 'y', 'z', 't').eject('t'),
f"PolynomialRing(UnivarPolynomialRing({ZZ!r}, (Symbol('t'),), "
"LexOrder()), (Symbol('x'), Symbol('y'), Symbol('z')), LexOrder())")
def test_units():
R = QQ.inject(x)
assert R.convert(1) == R.one
assert R.convert(x) != R.one
assert R.convert(1 + x) != R.one
R = QQ.poly_ring(x, order='ilex')
assert R.convert(1) == R.one
assert R.convert(x) != R.one
R = ZZ.inject(x)
assert R.convert(1) == R.one
assert R.convert(2) != R.one
assert R.convert(x) != R.one
assert R.convert(1 + x) != R.one
def test_conversion():
L = QQ.poly_ring(x, y, order='ilex')
G = QQ.inject(x, y)
assert L.convert(x) == L.convert(G.convert(x), G)
assert G.convert(x) == G.convert(L.convert(x), L)
pytest.raises(CoercionFailed, lambda: G.convert(L.convert(1 / (1 + x)), L))
R = ALG.inject(x, y)
assert R.convert(ALG(1), ALG) == R(1)
pytest.raises(CoercionFailed,
lambda: R.convert(ALG(1), QQ.algebraic_field(sqrt(2))))
R = R.drop(y)
pytest.raises(CoercionFailed, lambda: R.convert(G(y), R))
pytest.raises(CoercionFailed, lambda: R.convert(FF(8)(2)))
def test_localring():
Qxy = QQ.inject(x, y).field
R = QQ.poly_ring(x, y, order='ilex')
X = R.convert(x)
Y = R.convert(y)
assert x in R
assert 1 / x not in R
assert Y in R
assert X.ring == R.ring
assert X + Y == R.convert(x + y)
assert X - Y == R.convert(x - y)
assert X + 1 == R.convert(x + 1)
assert X**2 // X == X
assert R.convert(ZZ.inject(x, y).convert(x), ZZ.inject(x, y)) == X
assert R.convert(Qxy.convert(x), Qxy) == X
def test_build_order():
R = QQ.poly_ring(x,
y,
order=build_product_order((('lex', x), ('ilex', y)),
(x, y)))
assert R.order((1, 5)) == ((1, ), (-5, ))
def test_PolynomialRing():
assert str(ZZ.inject('x')) == 'ZZ[x]'
assert str(QQ.poly_ring('x', 'y', order=grlex)) == 'QQ[x,y]'
assert str(ZZ.inject('x', 'y', 'z', 't').eject('t')) == 'ZZ[t][x,y,z]'
