def check_comparison(a1, a2, cmp, result, expected):
if (result != expected):
print("a1 = {0}".format(a1))
print("a2 = {0}".format(a2))
print("cmp = {0}".format(cmp))
print("result = {0}".format(result))
print("expected = {0}".format(expected))
polypy_test.check(False)
else:
polypy_test.check(True)
polypy_test.init()
polypy_test.start("Construction and order")
a1 = polypy.AlgebraicNumber((x**2 - 2) * (x - 10), 1)
a2 = polypy.AlgebraicNumber((x**2 - 2), 1)
result = (a1 < a2)
check_comparison(a1, a2, "<", result, False)
result = (a1 == a2)
check_comparison(a1, a2, "==", result, True)
p = x**2
zero = polypy.AlgebraicNumber(p, 0)
result = zero.to_double() == 0.0
check_comparison(zero, 0, ".to_double ==", result, True)
p = x**2 - 1
one_neg = polypy.AlgebraicNumber(p, 0)
print "value_double =", value_double
print "expected_value =", expected_value
polypy_test.check(ok)
polypy_test.start("Polynomial Evaluation")
# polypy.trace_enable("polynomial")
# polypy.trace_enable("factorization")
# polypy.trace_enable("algebraic_number")
# polypy.trace_enable("coefficient")
# polypy.trace_enable("coefficient::sgn")
# polypy.trace_enable("coefficient::roots")
# polypy.trace_enable("coefficient::arith")
sqrt2 = polypy.AlgebraicNumber(x**2 - 2, 1)
sqrt2_4 = polypy.AlgebraicNumber(x**4 - 2, 1)
sqrt3 = polypy.AlgebraicNumber(x**2 - 3, 1)
assignment = polypy.Assignment()
assignment.set_value(x, sqrt2)
assignment.set_value(y, sqrt2_4)
assignment.set_value(z, sqrt3)
# print assignment
p = x + y + z
p_value = p.evaluate(assignment)
check_value(p, assignment, p_value, 4.335471485)
p = x**2
def check_comparison(a1, a2, cmp, result, expected):
if (result != expected):
print("a1 = {0}".format(a1))
print("a2 = {0}".format(a2))
print("cmp = {0}".format(cmp))
print("result = {0}".format(result))
print("expected = {0}".format(expected))
polypy_test.check(False)
else:
polypy_test.check(True)
polypy_test.init()
polypy_test.start("Construction and order")
a1 = polypy.AlgebraicNumber((x**2 - 2) * (x - 10), 1)
a2 = polypy.AlgebraicNumber((x**2 - 2), 1)
result = (a1 < a2)
check_comparison(a1, a2, "<", result, False)
result = (a1 == a2)
check_comparison(a1, a2, "==", result, True)
p = x**2
zero = polypy.AlgebraicNumber(p, 0)
result = zero.to_double() == 0.0
check_comparison(zero, 0, ".to_double ==", result, True)
p = x**2 - 1
one_neg = polypy.AlgebraicNumber(p, 0)
for I in p_feasible:
v = I.pick_value()
ok = I.contains(v)
if (not ok):
print "I =", I
print "v =", v
break
if (not ok):
print "p =", p
print "assignment =", assignment
print "sgn =", sgn_name[sgn]
polypy_test.check(ok)
assignment = polypy.Assignment()
assignment.set_value(y, polypy.AlgebraicNumber(x**2 - 2, 1))
assignment.set_value(z, polypy.AlgebraicNumber(x**2 - 3, 1))
# [-0.809841]
# -1 0 1
p_slow = ((2 * z) * y**2) * x**3 + ((1 * z**3) * y) * x**2 + (
(1 * z**2) * y**3) * x + (1 * z + 4)
p_expected = [1, 1, 1, 2, 1, 1]
check_feasible(p_slow, x, assignment, p_expected)
p_slow = (1 * y**3 + (2 * z**3) * y) * x**3 + ((2 * z) * y**3) * x**2 + (
(2 * z**2) * y**2 + 3)
# for random in xrange(1000):
# start = time.time()
# p = polypy_test.random_polynomial(3, 2, [x, y, z], 5)
polypy_test.start("Construction")
zero_int = polypy.Value(0)
one_int = polypy.Value(1)
two_int = polypy.Value(2)
three_int = polypy.Value(3)
check_comparison(zero_int, 0)
check_comparison(one_int, 1)
check_comparison(two_int, 2)
check_comparison(three_int, 3)
p = x**2 - 2
sqrt2_neg = polypy.Value(polypy.AlgebraicNumber(p, 0))
sqrt2_pos = polypy.Value(polypy.AlgebraicNumber(p, 1))
check_comparison(sqrt2_neg, -1.41421356237)
check_comparison(sqrt2_pos, 1.41421356237)
p = x**2 - 3
sqrt3_neg = polypy.Value(polypy.AlgebraicNumber(p, 0))
sqrt3_pos = polypy.Value(polypy.AlgebraicNumber(p, 1))
check_comparison(sqrt3_neg, -1.73205080757)
check_comparison(sqrt3_pos, 1.73205080757)
half_rat = one_int / two_int
third_rat = one_int / three_int
# roots = p.roots_isolate(assignment)
polypy_test.start("Polynomial Root Isolation: Bugs")
polypy.variable_order.set([x0, x1, x2, x3, x4, x5, x6, x7])
p = ((16 * x0**2 - 32 * x0 + 16) * x5**2 + ((32 * x0 - 32) * x1) * x5 +
(16 * x1**2)) * x7**2 + ((8 * x0**2 - 16 * x0 + 8) * x5**2 + (
(16 * x0**2 - 32 * x0 + 16) * x2**2 +
(-8 * x1**2))) * x7 + ((1 * x0**2 - 2 * x0 + 1) * x5**2 +
((-2 * x0 + 2) * x1) * x5 + (1 * x1**2))
p_lc = ((16 * x0**2 - 32 * x0 + 16) * x5**2 + ((32 * x0 - 32) * x1) * x5 +
(16 * x1**2))
assignment = polypy.Assignment()
v = polypy.AlgebraicNumber(32 * x**2 + (-64 * x) + 15, 0)
assignment.set_value(x0, v)
assignment.set_value(x1, 28)
assignment.set_value(x2, -1, 4)
assignment.set_value(x3, 3)
assignment.set_value(x4, 277771, 4096)
assignment.set_value(x5, 786743, 20480)
assignment.set_value(x6, -6437)
roots = p.roots_isolate(assignment)
check_roots(
p, assignment, roots,
[-166318.899794716301953293454440, -8961.48539760581031126063921576])
polypy.variable_order.set([x, w, y, z])
print("p = {0}".format(p))
print("assignment = {0}".format(assignment))
print("sgn = {0}".format(sgn))
print("expected_sgn = {0}".format(expected_sgn))
polypy_test.check(ok)
polypy_test.start("Sign Determination")
# polypy.trace_enable("polynomial")
# polypy.trace_enable("factorization")
# polypy.trace_enable("algebraic_number")
# polypy.trace_enable("coefficient")
# polypy.trace_enable("coefficient::sgn")
# polypy.trace_enable("coefficient::arith")
sqrt2 = polypy.AlgebraicNumber(x**2 - 2, 1)
sqrt2_4 = polypy.AlgebraicNumber(x**4 - 2, 1)
sqrt3 = polypy.AlgebraicNumber(x**2 - 3, 1)
assignment = polypy.Assignment()
assignment.set_value(x, sqrt2_4)
assignment.set_value(y, sqrt2)
assignment.set_value(z, sqrt3)
# print assignment
p = (x**2 - y)*z
check_sgn(p, assignment, 0)
p = (x**2 - y + z)*x
check_sgn(p, assignment, 1)