def test3():
x, a, b, c = map(Symbol, ['x', 'a', 'b', 'c'])
#f = x**3 - 8.99085235595703*x**2 + 14.963430343676*x + 24.954282699633
f = x**3 - 8.990852355957031 * x**2 + 14.96343034367601 * x + 24.95428269963304
#f = (x + 1) * (x - 4.995426177978516)**2
f = expand(f)
print('f : ', f)
f_ = diff(f)
print('f_ : ', f_)
a0 = gcd(f, f_)
print('a0 : ', a0)
b1 = quo(f, a0)
print('b1 : ', b1)
c1 = quo(f_, a0)
print('c1 : ', c1)
d1 = c1 - diff(b1)
print('d1 : ', d1)
a1 = gcd(b1, d1)
print('a1 : ', a1)
b2 = quo(b1, a1)
print('b2 : ', b2)
L = sqf_list(f)
#L = sqf(f)
print(L)
def test2():
x, a, b, c = map(Symbol, ['x', 'a', 'b', 'c'])
#f = 2*x**2 + 5*x**3 + 4*x**4 + x**5
f = (x + 2) * x**2 * (x + 1)**2
f = expand(f)
#print('ex : ', expand((x + 2) * (x**2 + x)**2))
print('f : ', f)
f_ = diff(f)
print('f_ : ', f_)
a0 = gcd(f, f_)
print('a0 : ', a0)
b1 = quo(f, a0)
print('b1 : ', b1)
c1 = quo(f_, a0)
print('c1 : ', c1)
d1 = c1 - diff(b1)
print('d1 : ', d1)
a1 = gcd(b1, d1)
print('a1 : ', a1)
b2 = quo(b1, a1)
print('b2 : ', b2)
c2 = quo(d1, a1)
print('c2 : ', c2)
d2 = c2 - diff(b2)
print('d2 : ', d2)
a2 = gcd(b2, d2)
print('a2 : ', a2)
b3 = quo(b2, a2)
print('b3 : ', b3)
L = sqf_list(f)
#sqf(f)
print(L)
def GPD_meth(poly, var, div, myorder):
x, y = symbols('x y')
zero = symbols('0')
dlen = len(div) # num of dividents
q = []
NotDivide = False
divoccur = True
for k in range(0, len(div)): # init list of quos
q.append(zero)
###############################################
for i in range(0, len(div)):
#print("iteration",i)
if poly == 0:
break
if NotDivide == True:
NotDivide = False
while NotDivide == False:
LTP = LT(poly, var, order=myorder) # check if LTD divides LTP
LTD = LT(div[i], var, order=myorder)
#print("check3")
if quo(LTP, LTD) != 0 and rem(LTP, LTD) == 0:
#print("leading tems divisor/divident0:",LTP,LTD)
divLT = simplify(LTP / LTD) #works thatsgood
#print(divLT)
##########check changes in quo rem################
if q[i] == zero: # if quo is initialized
q[i] = simplify(divLT)
else:
q[i] = simplify(q[i] + divLT)
poly = simplify(poly - simplify(divLT * div[i]))
#print("check0",poly)
#print("new poly,new quo",poly,q[i])
##################################################
else:
NotDivide = True
break
return poly, q # final results
def log_to_atan(f, g):
"""Convert complex logarithms to real arctangents.
Given a real field K and polynomials f and g in K[x], with g != 0,
returns a sum h of arctangents of polynomials in K[x], such that:
df d f + I g
-- = -- I log( ------- )
dx dx f - I g
"""
if f.degree < g.degree:
f, g = -g, f
p, q = poly_div(f, g)
if q.is_zero:
return 2*atan(p.as_basic())
else:
s, t, h = poly_gcdex(g, -f)
A = 2*atan(quo(f*s+g*t, h))
return A + log_to_atan(s, t)
def log_to_atan(f, g):
"""Convert complex logarithms to real arctangents.
Given a real field K and polynomials f and g in K[x], with g != 0,
returns a sum h of arctangents of polynomials in K[x], such that:
df d f + I g
-- = -- I log( ------- )
dx dx f - I g
"""
if f.degree < g.degree:
f, g = -g, f
p, q = poly_div(f, g)
if q.is_zero:
return 2*atan(p.as_basic())
else:
s, t, h = poly_gcdex(g, -f)
A = 2*atan(quo(f*s+g*t, h))
return A + log_to_atan(s, t)