def primitiveTest():
for i in range(range1, range2):
m = ((prem(x**i + 1, x**power1 + x**power2 + 1, modulus=2) == 0)
and i == 2**power1 - 1)
if m == True:
print(i)
else:
i + 1
print('Not Primitive')
def main():
a = -6.6
b = -21.3
c = 14.8
minX = -6
maxX = 6
e = 0.0001
x = sympy.Symbol("x")
currEq = x ** 3 + a * x ** 2 + b * x + c
newEq = sympy.diff(currEq)
sturmSe = []
sturmSe.append(currEq)
sturmSe.append(newEq)
Na = 0
Nb = 0
while newEq != newEq.subs(x, minX):
currEq, newEq = newEq, -sympy.prem(currEq, newEq)
sturmSe.append(newEq)
for i in range(len(sturmSe) - 1):
eqMul = sturmSe[i] * sturmSe[i + 1]
if eqMul.subs(x, minX) < 0:
Na += 1
if eqMul.subs(x, maxX) < 0:
Nb += 1
sympy.pprint(sturmSe)
for i in sturmSe:
print("a", i.subs(x, minX))
print("b", i.subs(x, maxX))
print("\n")
print("\n Number of roots:")
print(Na - Nb)
roots = sympy.solve(sympy.Eq(sturmSe[1], 0), x)
print("\n All roots:")
print(roots)
DichotomyMethod(sturmSe[0], x, minX, min(roots), e)
MethodChord(sturmSe[0], x, minX, min(roots), e)
def our_euclid_prem(f, g, x):
"""
Μέγιστος κοινός διαιρέτης πολυωνύμων
f and g, deg(f) > deg(g) > 0 στους ακεραίους (ZZ).
Τα υπόλοιπα κάθε διαίρεσης υπολογίζονται με την
συνάρτηση prem(). Τα πρόσημα των υπολοίπων ΔΕΝ είναι
πάντα σωστά.
"""
print('gcd(f, g) using prem()', '\n')
print(f, '\n')
print(g, '\n')
our_es = [f, g]
while degree(g, x) > 0:
h = prem(f, g)
our_es.append(h)
f, g = g, h
print(g, '\n')
return our_es
def main():
n = 4
a = -14.4621
b = 60.6959
c = -70.9238
interval = (-10, 10)
e = 0.0001
x = sympy.Symbol("x")
f = [0] * n
f[0] = x**3 + a*x**2 + b*x + c
f[1] = 3*x**2 + 2*a*x + b
for i in xrange(2, n):
f[i] = -sympy.prem(f[i - 2], f[i - 1])
Na = 0
Nb = 0
for i in xrange(n - 1):
polim = f[i]*f[i + 1]
if polim.subs(x, interval[0]) < 0:
Na += 1
if polim.subs(x, interval[1]) < 0:
Nb += 1
print 'Number of roots: '.format(Na - Nb)
xValue = solve(Eq(f[1], 0), x)
print 'Root branch: '.format(xValue)
bisection(xValue, interval)
chords(xValue, interval)
if __name__ == "__main__":
main()
def test_rem_z():
x = var('x')
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
assert rem_z(p, -q, x) != prem(p, -q, x)
def test_rem_z():
x = var('x')
p = x**8 + x**6 - 3 * x**4 - 3 * x**3 + 8 * x**2 + 2 * x - 5
q = 3 * x**6 + 5 * x**4 - 4 * x**2 - 9 * x + 21
assert rem_z(p, -q, x) != prem(p, -q, x)
def main():
n = 4
a = 38.4621
b = 364.594
c = 914.196
left = -10
right = 10
e = 0.0001
x = sympy.Symbol("x")
f = [0 for i in range(n)]
f[0] = x**3 + a*x**2 + b*x + c
f[1] = 3*x**2 + 2*a*x + b
for i in range(2, n):
f[i] = -sympy.prem(f[i - 2], f[i - 1])
Na = 0
Nb = 0
for i in range(n - 1):
polim = f[i]*f[i + 1]
if polim.subs(x, left) < 0:
Na += 1
if polim.subs(x, right) < 0:
Nb += 1
print(Na - Nb)
xValue = solve(Eq(f[1], 0), x)
print (str(-19.3657805788685))
count1 = 0
left_d = left
right_d = xValue[0]
middle = (left_d + right_d) / 2
while (abs(left_d - middle) > e) or (abs(right_d - middle) > e):
if f[0].subs(x, left_d) * f[0].subs(x, middle) < 0:
right_d = middle
else:
left_d = middle
middle = (left_d + right_d) / 2
count1 += 1
print(middle)
print(count1)
two_diff = diff(f[1])
count2 = 0
if f[0].subs(x, xValue[0]) * two_diff.subs(x, xValue[0]) > 0:
xh0 = left
xh = xh0 - f[0].subs(x, xh0)*(xValue[0] - xh0)/(f[0].subs(x, xValue[0]) - f[0].subs(x, xh0))
while abs(xh - xh0) > e:
xh0 = xh
xh = xh0 - f[0].subs(x, xh0)*(xValue[0]-xh0)/(f[0].subs(x,xValue[0]) - f[0].subs(x,xh0))
count2 += 1
else:
xh0 = xValue[0]
xh = xh0 - f[0].subs(x, xh0)*(left - xh0)/(f[0].subs(x, left) - f[0].subs(x, xh0))
while abs(xh - xh0) > e:
xh0 = xh
xh = xh0 - f[0].subs(x, xh0) * (left - xh0) / (f[0].subs(x, left) - f[0].subs(x, xh0))
count2 += 1
print(str(-19.3657805788685))
print(count2)