def test_sturm_q():
x = var('x')
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert sturm_q(p, q, x) == sturm(p)
assert sturm_q(-p, -q, x) != sturm(-p)
def test_sturm_q():
x = var('x')
p = x**3 - 7 * x + 7
q = 3 * x**2 - 7
assert sturm_q(p, q, x) == sturm(p)
assert sturm_q(-p, -q, x) != sturm(-p)
def partition(f, LB, UB):
Sseq = sturm(f)
print("sturm: \n", Sseq)
sL = []
[sL.append(Sseq[i].subs(x, LB)) for i in range(degree(f, x) + 1)]
print('sL = ', sL, '\n')
vsL = variations(sL)
print('vsL = ', vsL, '\n')
print("bounds using upperBound LMQ: ", UB, "\n")
sR = []
[sR.append(Sseq[i].subs(x, UB)) for i in range(0, degree(f, x) + 1)]
print('sR = ', sR, '\n')
vsR = variations(sR)
print('vsR = ', vsR, '\n')
number_of_roots = vsR - vsL
print("THE NUMBER OF REAL ROOTS BETWEEN", LB, " AND ", UB, " IS: ",
abs(number_of_roots))
return abs(number_of_roots)
def test():
#x = map(Symbol, ['x'])
x = Symbol('x')
P = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
sP = sturm(P)
print(sP[2])
def sturm_method(poly, a, b):
sturm_seq = sturm(poly)
nums = []
sign_changes = 0
for el in sturm_seq:
num = el.subs({x: a})
nums.append(num)
n = len(nums)
na = 0
for i in range(n - 1):
if nums[i + 1] * nums[i] < 0:
na += 1
nums.clear()
sign_changes = 0
for el in sturm_seq:
num = el.subs({x: b})
nums.append(num)
n = len(nums)
nb = 0
for i in range(n - 1):
if nums[i + 1] * nums[i] < 0:
nb += 1
return na - nb
def test_euclid_q():
x = var('x')
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert euclid_q(p, q, x)[-1] == -sturm(p)[-1]
def test_euclid_q():
x = var('x')
p = x**3 - 7 * x + 7
q = 3 * x**2 - 7
assert euclid_q(p, q, x)[-1] == -sturm(p)[-1]
