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polyTrial1.py
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polyTrial1.py
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from pprint import pprint
trueCheck = 0 # A counter used for generating new variables
def newPoly(var,num_coeffs): # tested
dictPoly = {
'var': var,
'poly': [[num_coeffs[i],[]] for i in range(len(num_coeffs))]
}
return dictPoly
def addCoeffPoly(a,var,n,c): # tested
num_coeffs = [0,0,0,0]
num_coeffs[0] = 1
num_coeffs[n] = 1
ret = newPoly(var,num_coeffs)
ret['poly'][0][1].append(a)
ret['poly'][n][1].append(c)
return ret
def addPoly(a,b): # to be checked
num_coeffs = [0,0,0,0]
c = newPoly(a['var'],num_coeffs)
for i in range(4):
c['poly'][i][0] = a['poly'][i][0] + b['poly'][i][0]
minimum = len(a['poly'][i][1]) if len(a['poly'][i][1]) < len(b['poly'][i][1]) else len(b['poly'][i][1])
maximum = len(a['poly'][i][1]) if len(a['poly'][i][1]) > len(b['poly'][i][1]) else len(b['poly'][i][1])
for j in range(minimum):
c['poly'][i][1][j] = addPoly(a['poly'][i][1][j],b['poly'][i][1][j])
if maximum == len(a['poly'][i][1]):
for j in range(minimum,maximum):
c['poly'][i][1][j] = a['poly'][i][1][j]
else:
for j in range(minimum,maximum):
c['poly'][i][1][j] = b['poly'][i][1][j]
return c
def multiplyPoly(a,b): # tested
c = newPoly(a['var'],[0 for i in range(len(a['poly']))])
c['poly'][0][0] = a['poly'][0][0] * b['poly'][0][0]
c['poly'][1][0] = a['poly'][1][0] * b['poly'][0][0]
c['poly'][2][0] = a['poly'][0][0] * b['poly'][2][0]
c['poly'][3][0] = a['poly'][1][0] * b['poly'][2][0]
for i in range(len(a['poly'][0][1])): c['poly'][0][1].append(a['poly'][0][1][i])
for i in range(len(b['poly'][0][1])): c['poly'][0][1].append(b['poly'][0][1][i])
for i in range(len(a['poly'][1][1])): c['poly'][1][1].append(a['poly'][1][1][i])
for i in range(len(b['poly'][0][1])): c['poly'][1][1].append(b['poly'][0][1][i])
for i in range(len(a['poly'][0][1])): c['poly'][2][1].append(a['poly'][0][1][i])
for i in range(len(b['poly'][2][1])): c['poly'][2][1].append(b['poly'][2][1][i])
for i in range(len(a['poly'][1][1])): c['poly'][3][1].append(a['poly'][1][1][i])
for i in range(len(b['poly'][2][1])): c['poly'][3][1].append(b['poly'][2][1][i])
return c
def convConstToPoly(A,var): # tested
return [
[newPoly(var,[A[i][j],0,0,0]) for j in range(len(A[i]))]
for i in range(len(A))
]
def coeff(exp,poly): # tested
try:
num_coeff = poly['poly'][exp][0]
term_coeff = poly['poly'][exp][1][0]
for i in range(len(term_coeff['poly'])):
term_coeff['poly'][i][0] = term_coeff['poly'][i][0] * num_coeff
return term_coeff
except:
term_coeff = convConstToPoly([[0]],poly['var'])
return term_coeff[0][0]
def matrixProd(A,B):
global trueCheck
n = len(A)
if n == 1: return [[multiplyPoly(A[0][0],B[0][0])]]
else:
a = [[A[i][j] for j in range(int(n/2))] for i in range(int(n/2))]
b = [[A[i][j] for j in range(int(n/2),n)] for i in range(int(n/2))]
c = [[A[i][j] for j in range(int(n/2))] for i in range(int(n/2),n)]
d = [[A[i][j] for j in range(int(n/2),n)] for i in range(int(n/2),n)]
e = [[B[i][j] for j in range(int(n/2))] for i in range(int(n/2))]
f = [[B[i][j] for j in range(int(n/2),n)] for i in range(int(n/2))]
g = [[B[i][j] for j in range(int(n/2))] for i in range(int(n/2),n)]
h = [[B[i][j] for j in range(int(n/2),n)] for i in range(int(n/2),n)]
trueCheck = trueCheck + 1
l = 'x'+str(trueCheck)
k1 = [
[ addCoeffPoly(a[i][j],l,2,c[i][j]) for j in range(int(n/2)) ]
for i in range(int(n/2)) ]
k2 = [
[ addCoeffPoly(e[i][j],l,1,f[i][j]) for j in range(int(n/2)) ]
for i in range(int(n/2)) ]
k3 = [
[ addCoeffPoly(b[i][j],l,2,d[i][j]) for j in range(int(n/2)) ]
for i in range(int(n/2)) ]
k4 = [
[ addCoeffPoly(g[i][j],l,1,h[i][j]) for j in range(int(n/2)) ]
for i in range(int(n/2)) ]
print('k1')
pprint(k1)
print('k2')
pprint(k2)
print('k3')
pprint(k3)
print('k4')
pprint(k4)
ap = matrixProd(k1,k2)
bp = matrixProd(k3,k4)
a1 = [[0 for i in range(int(n/2))] for j in range(int(n/2))]
a2 = [[0 for i in range(int(n/2))] for j in range(int(n/2))]
a3 = [[0 for i in range(int(n/2))] for j in range(int(n/2))]
a4 = [[0 for i in range(int(n/2))] for j in range(int(n/2))]
print('A\'')
pprint(ap)
print('B\'')
pprint(bp)
for i in range(int(n/2)): # how to add the subsequent coefficients
for j in range(int(n/2)):
a1[i][j] = addPoly(coeff(0,ap[i][j]),coeff(0,bp[i][j]))
a2[i][j] = addPoly(coeff(1,ap[i][j]),coeff(1,bp[i][j]))
a3[i][j] = addPoly(coeff(2,ap[i][j]),coeff(2,bp[i][j]))
a4[i][j] = addPoly(coeff(3,ap[i][j]),coeff(3,bp[i][j]))
C = [[0 for i in range(n)] for j in range(n)]
for i in range(n):
for j in range(n):
if i<int(n/2) and j<int(n/2): C[i][j] = a1[i][j]
if i>=int(n/2) and j<int(n/2): C[i][j] = a2[i-int(n/2)][j]
if i<int(n/2) and j>=int(n/2): C[i][j] = a3[i][j-int(n/2)]
if i>=int(n/2) and j>=int(n/2): C[i][j] = a4[i-int(n/2)][j-int(n/2)]
return C
def actualMatrixProduct(A,B):
global trueCheck
trueCheck = 0
Ap = convConstToPoly(A,'x'+str(trueCheck))
Bp = convConstToPoly(B,'x'+str(trueCheck))
Cp = matrixProd(Ap,Bp)
C = [[ Cp[i][j]['poly'][0][0] for j in range(len(A))] for i in range(len(A))]
print('C')
return C
def stubTest():
pprint(newPoly('x',[9,90,10,3,4]))
a = newPoly('x',[1,0,1,0])
c = newPoly('x',[1,1,0,0])
d = addCoeffPoly(a,'y',2,c)
pprint(d)
a1 = newPoly('x',[11,0,11,0])
c1 = newPoly('x',[12,12,0,0])
d1 = addCoeffPoly(a1,'y',1,c1)
pprint(d1)
pprint(multiplyPoly(d1,d))
a = [[1,1],[1,1]]
pprint(convConstToPoly(a,'x0'))
print(coeff(1,d1))
print(coeff(3,d1))
e1 = {'var':'x','poly':[[12,[]],[12,[]],[0,[]],[0,[]]]}
e2 = {'var':'x','poly':[[12,[]],[1,[]],[10,[]],[11,[]]]}
print(addPoly(e1,e2))
def mainDriveTest():
A = [
[1,0],
[0,1]
]
B = [
[1,0],
[0,1]
]
d = actualMatrixProduct(A,B)
for i in range(len(d)):
for j in range(len(d)):
print(d[i][j], end = " ")
print('')
stubTest()
#mainDriveTest()