def main():
x = Symbol("x")
s = Poly(A(x), x)
num = list(reversed(s.coeffs()))[:11]
print s.as_basic()
print num
def main():
x=Symbol("x")
s = Poly(A(x), x)
num = [s.coeff(n) for n in range(11)]
print s.as_basic()
print num
def main():
x = Symbol("x")
s = Poly(A(x), x)
num = [s.coeff(n) for n in range(11)]
print s.as_basic()
print num
def main():
x=Symbol("x")
s = Poly(A(x), x)
num = list(reversed(s.coeffs()))[:11]
print s.as_basic()
print num
def new_poly(V_s, fields, n_coeffs):
"""Make a new polynomial function that has the same powers as V_s function
but with coefficients C1, C2..."""
from sympy import Poly
from sympy import diff, Symbol, var, simplify, sympify, S
from sympy.core.sympify import SympifyError
P = Poly(V_s, *fields)
d = P.as_dict()
e = {}
for key in d.iterkeys():
#print d[key], str(d[key])
for i in xrange(1, n_coeffs + 1):
if 'C' + str(i) in str(d[key]):
e[key] = sympify('C' + str(i))
P2 = Poly(e, *fields)
return str(P2.as_basic())
def new_poly(V_s, fields, n_coeffs):
"""Make a new polynomial function that has the same powers as V_s function
but with coefficients C1, C2..."""
from sympy import Poly
from sympy import diff, Symbol, var, simplify, sympify, S
from sympy.core.sympify import SympifyError
P = Poly(V_s,*fields)
d = P.as_dict()
e = {}
for key in d.iterkeys():
#print d[key], str(d[key])
for i in xrange(1, n_coeffs+1):
if 'C' + str(i) in str(d[key]):
e[key] = sympify('C'+str(i))
P2 = Poly(e,*fields)
return str(P2.as_basic())
def test_poly_div():
f = Poly(x**3-12*x**2-42, x)
g = Poly(x**2+x-3, x)
h = poly_div(f, g)
assert h[0] == Poly(x-13, x)
assert h[1] == Poly(16*x-81, x)
assert h[0].as_basic() == x-13
assert h[1].as_basic() == 16*x-81
assert f / g == Poly(x-13, x)
assert f % g == Poly(16*x-81, x)
assert divmod(f, g) == (Poly(x-13, x), Poly(16*x-81, x))
assert f / x == Poly(x**2-12*x, x)
assert f % x == Poly(-42, x)
assert divmod(f, x) == (Poly(x**2-12*x, x), Poly(-42, x))
assert f / sin(x) == f.as_basic() / sin(x)
assert f % sin(x) == 0
assert divmod(f, sin(x)) == (f.as_basic() / sin(x), 0)
assert poly_div(4*x**2*y-2*x*y-2*y+4*x+8, 2, x, y) == \
(Poly(2*x**2*y-x*y-y+2*x+4, x, y), Poly((), x, y))
assert poly_div(4*x**2*y-2*x*y-2*y+4*x+8, 2*y, x, y) == \
(Poly(2*x**2-x-1, x, y), Poly(4*x+8, x, y))
assert poly_div(x-1, y-1, x, y) == (Poly((), x, y), Poly(x-1, x, y))
assert poly_div(x**3-12*x**2-42, x-3, x) == \
(Poly(x**2-9*x-27, x), Poly(-123, x))
assert poly_div(2+2*x+x**2, 1, x) == (Poly(2+2*x+x**2, x), Poly(0, x))
assert poly_div(2+2*x+x**2, 2, x) == (Poly(1+x+x**2/2, x), Poly(0, x))
assert poly_div(3*x**3, x**2, x) == (Poly(3*x, x), Poly(0, x))
assert poly_div(1, x, x) == (Poly(0, x), Poly(1, x))
assert poly_div(x*y+2*x+y,x,x) == (Poly(2+y, x), Poly(y, x))
assert poly_div(x*y**2 + 1, [x*y+1, y+1], x, y) == \
([Poly(y, x, y), Poly(-1, x, y)], Poly(2, x, y))
assert poly_div(x**2*y+x*y**2+y**2, [x*y-1, y**2-1], x, y) == \
([Poly(x+y, x, y), Poly(1, x, y)], Poly(1+x+y, x, y))
assert poly_div(x**2*y+x*y**2+y**2, [y**2-1, x*y-1], x, y) == \
([Poly(1+x, x, y), Poly(x, x, y)], Poly(1+2*x, x, y))
f, g = 3*x**3 + x**2 + x + 5, 5*x**2 - 3*x + 1
q = Poly(Rational(3,5)*x + Rational(14, 25), x)
r = Poly(Rational(52, 25)*x + Rational(111, 25), x)
assert poly_div(f, g, x) == (q, r)
assert poly_div(Poly(f, x), Poly(g, x)) == (q, r)
q = Poly(15*x + 14, x)
r = Poly(52*x + 111, x)
assert poly_pdiv(f, g, x) == (q, r)
assert poly_pdiv(Poly(f, x), Poly(g, x)) == (q, r)
def test_poly_div():
f = Poly(x**3-12*x**2-42, x)
g = Poly(x**2+x-3, x)
h = poly_div(f, g)
assert h[0] == Poly(x-13, x)
assert h[1] == Poly(16*x-81, x)
assert h[0].as_basic() == x-13
assert h[1].as_basic() == 16*x-81
assert f / g == Poly(x-13, x)
assert f % g == Poly(16*x-81, x)
assert divmod(f, g) == (Poly(x-13, x), Poly(16*x-81, x))
assert f / x == Poly(x**2-12*x, x)
assert f % x == Poly(-42, x)
assert divmod(f, x) == (Poly(x**2-12*x, x), Poly(-42, x))
assert f / sin(x) == f.as_basic() / sin(x)
assert f % sin(x) == 0
assert divmod(f, sin(x)) == (f.as_basic() / sin(x), 0)
assert poly_div(4*x**2*y-2*x*y-2*y+4*x+8, 2, x, y) == \
(Poly(2*x**2*y-x*y-y+2*x+4, x, y), Poly((), x, y))
assert poly_div(4*x**2*y-2*x*y-2*y+4*x+8, 2*y, x, y) == \
(Poly(2*x**2-x-1, x, y), Poly(4*x+8, x, y))
assert poly_div(x-1, y-1, x, y) == (Poly((), x, y), Poly(x-1, x, y))
assert poly_div(x**3-12*x**2-42, x-3, x) == \
(Poly(x**2-9*x-27, x), Poly(-123, x))
assert poly_div(2+2*x+x**2, 1, x) == (Poly(2+2*x+x**2, x), Poly(0, x))
assert poly_div(2+2*x+x**2, 2, x) == (Poly(1+x+x**2/2, x), Poly(0, x))
assert poly_div(3*x**3, x**2, x) == (Poly(3*x, x), Poly(0, x))
assert poly_div(1, x, x) == (Poly(0, x), Poly(1, x))
assert poly_div(x*y+2*x+y,x,x) == (Poly(2+y, x), Poly(y, x))
assert poly_div(x*y**2 + 1, [x*y+1, y+1], x, y) == \
([Poly(y, x, y), Poly(-1, x, y)], Poly(2, x, y))
assert poly_div(x**2*y+x*y**2+y**2, [x*y-1, y**2-1], x, y) == \
([Poly(x+y, x, y), Poly(1, x, y)], Poly(1+x+y, x, y))
assert poly_div(x**2*y+x*y**2+y**2, [y**2-1, x*y-1], x, y) == \
([Poly(1+x, x, y), Poly(x, x, y)], Poly(1+2*x, x, y))
f, g = 3*x**3 + x**2 + x + 5, 5*x**2 - 3*x + 1
q = Poly(Rational(3,5)*x + Rational(14, 25), x)
r = Poly(Rational(52, 25)*x + Rational(111, 25), x)
assert poly_div(f, g, x) == (q, r)
assert poly_div(Poly(f, x), Poly(g, x)) == (q, r)
q = Poly(15*x + 14, x)
r = Poly(52*x + 111, x)
assert poly_pdiv(f, g, x) == (q, r)
assert poly_pdiv(Poly(f, x), Poly(g, x)) == (q, r)