def testReduce(self):
F = (multiutil.polynomial(
{
(2, 0): rational.Integer(1),
(1, 2): rational.Integer(2)
}, rational.theRationalField, 2),
multiutil.polynomial(
{
(1, 1): rational.Integer(1),
(0, 3): rational.Integer(2),
(0, 0): rational.Integer(-1)
}, rational.theRationalField, 2))
rgb_expected = [
multiutil.polynomial({(1, 0): rational.Integer(1)},
rational.theRationalField, 2),
multiutil.polynomial(
{
(0, 3): rational.Integer(1),
(0, 0): rational.Rational(-1, 2)
}, rational.theRationalField, 2)
]
G_from_F = groebner.normal_strategy(F, self.lex)
rgb = groebner.reduce_groebner(G_from_F, self.lex)
self.assertEqual(2, len(rgb))
self.assertEqual(rgb_expected, rgb)
def testBuchberger(self):
"""
test Buchberger's algorithm.
http://www.geocities.com/famancin/buchberger.html
"""
F = (multiutil.polynomial(
{
(2, 0): rational.Integer(1),
(1, 2): rational.Integer(2)
}, rational.theRationalField, 2),
multiutil.polynomial(
{
(1, 1): rational.Integer(1),
(0, 3): rational.Integer(2),
(0, 0): rational.Integer(-1)
}, rational.theRationalField, 2))
G_from_F = groebner.buchberger(F, self.lex)
G_expected = list(F + (multiutil.polynomial(
{(1, 0): rational.Integer(1)}, rational.theRationalField, 2),
multiutil.polynomial(
{
(0, 3): rational.Integer(2),
(0, 0): rational.Integer(-1)
}, rational.theRationalField, 2)))
self.assertEqual(len(G_expected), len(G_from_F))
for p, q in zip(G_expected, G_from_F):
self.assertEqualUptoUnit(p, q)
def testNormalStrategy(self):
"""
test Buchberger's algorithm (normal strategy).
same example with testBuchberger.
"""
F = (multiutil.polynomial(
{
(2, 0): rational.Integer(1),
(1, 2): rational.Integer(2)
}, rational.theRationalField, 2),
multiutil.polynomial(
{
(1, 1): rational.Integer(1),
(0, 3): rational.Integer(2),
(0, 0): rational.Integer(-1)
}, rational.theRationalField, 2))
G_from_F = groebner.normal_strategy(F, self.lex)
G_expected = list(F + (multiutil.polynomial(
{(1, 0): rational.Integer(1)}, rational.theRationalField, 2),
multiutil.polynomial(
{
(0, 3): rational.Integer(2),
(0, 0): rational.Integer(-1)
}, rational.theRationalField, 2)))
self.assertEqual(len(G_expected), len(G_from_F))
for p, q in zip(G_expected, G_from_F):
self.assertEqualUptoUnit(p, q)
def __mul__(self, other):
"""
Output composite field of self and other.
"""
common_options = {"coeffring": rational.theIntegerRing,
"number_of_variables": 2}
flist = [((d, 0), c) for (d, c) in enumerate(self.polynomial)]
f = multiutil.polynomial(flist, **common_options)
g = zpoly(other.polynomial)
diff = multiutil.polynomial({(1, 0): 1, (0, 1):-1}, **common_options)
compos = f.resultant(g(diff), 0)
return NumberField([compos[i] for i in range(compos.degree() + 1)])
def __mul__(self, other):
"""
Output composite field of self and other.
"""
common_options = {"coeffring": rational.theIntegerRing,
"number_of_variables": 2}
flist = [((d, 0), c) for (d, c) in enumerate(self.polynomial)]
f = multiutil.polynomial(flist, **common_options)
g = zpoly(other.polynomial)
diff = multiutil.polynomial({(1, 0): 1, (0, 1):-1}, **common_options)
compos = f.resultant(g(diff), 0)
return NumberField([compos[i] for i in range(compos.degree() + 1)])
def _zero_polynomial(self):
"""
Return the zero polynomial in the polynomial ring.
"""
if self.number_of_variables == 1:
import nzmath.poly.uniutil as uniutil
return uniutil.polynomial((), self._coefficient_ring)
else:
import nzmath.poly.multiutil as multiutil
return multiutil.polynomial((), coeffring=self._coefficient_ring, number_of_variables=self.number_of_variables)
def _prepared_polynomial(self, preparation):
"""
Return a polynomial from given preparation, which is suited
for the first argument of uni-/multi-variable polynomials.
"""
if self.number_of_variables == 1:
import nzmath.poly.uniutil as uniutil
return uniutil.polynomial(preparation, self._coefficient_ring)
else:
import nzmath.poly.multiutil as multiutil
return multiutil.polynomial(preparation, self._coefficient_ring)
def testXYZ(self):
ctx = {}
multiutil.prepare_indeterminates("S T X Y", ctx)
self.assertTrue("X" in ctx)
for var in ctx:
exec "self.%s = ctx['%s']" % (var, var)
self.assertTrue(self.S)
self.assertTrue(self.T)
Z = rational.theIntegerRing
self.XY = multiutil.polynomial({(0, 0, 1, 1): 1}, Z)
self.assertEqual(self.XY, self.X * self.Y)
def _constant_polynomial(self, seed):
"""
Return a constant polynomial made from a constant seed.
seed should not be zero.
"""
if self.number_of_variables == 1:
import nzmath.poly.uniutil as uniutil
return uniutil.polynomial({0: seed}, self._coefficient_ring)
else:
import nzmath.poly.multiutil as multiutil
const = (0,) * self.number_of_variables
return multiutil.polynomial({const: seed}, self._coefficient_ring)
def testZero(self):
zero = multiutil.polynomial({}, self.Z, 2)
self.assertEqual(zero, self.Z2.zero)
def testOne(self):
one = multiutil.polynomial({(0, 0): 1}, self.Z)
self.assertEqual(one, self.Z2.one)
def testCreateElement(self):
"""
createElement method is tweaked in uniutil.
"""
one = multiutil.polynomial({(0, 0): 1}, self.Z)
self.assertEqual(one, self.Z2.createElement(1))