Hello!
Here is my representation of polynomials in Python as dictionaries.
zero = {}
one = {0:1}
two = {0:2}
x = {1:1}
x2 = {2:1} # x^2
poly = {2:3, 1:4, 0:5} # 3*x^2 + 4*x + 5
# Some functions...
def add_poly(poly1, poly2): # w1(x)+w2(x)
tmp = dict(poly1)
for k in poly2:
tmp[k] = tmp.get(k,0) + poly2[k]
if tmp[k] == 0: del tmp[k]
return tmp
def times_poly(number, poly): # n*w(x)
if number == 0: return {}
tmp = {}
for k in poly:
tmp[k] = number*poly[k]
return tmp
def mul_poly(poly1, poly2): # w1(x)*w2(x)
tmp = {}
for i in poly1:
for j in poly2:
tmp[i+j] = tmp.get(i+j,0) + poly1[i]*poly2[j]
return tmp
def diff_poly(poly): # [c*x^n]' = c*n*x^(n-1)
tmp = {}
for i in poly:
tmp[i-1] = i*poly[i]
if -1 in tmp: del tmp[-1]
return tmp
def eval_poly(poly, x): # w(x), Horner
i = max(i for i in poly)
p = poly[i]
while i > 0:
i = i-1
p = p * x + poly.get(i,0)
return p
def combine_poly(poly1, poly2): # w1(w2(x)), Horner
i = max(k for k in poly1)
tmp = {0:poly1[i]}
while i > 0:
i = i-1
tmp = add_poly(mul_poly(tmp, poly2), {0:poly1.get(i,0)})
return tmp
def pow_poly(poly, n):
# return combine_poly({n:1}, poly)
tmp = {0:1}
while n > 0:
tmp = mul_poly(tmp, poly)
n = n-1
return tmp
Regards,
Andrzej Kapanowski
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