Rekha Penmetsa
I am using Sage-Maxima for my project. I need to use "Differential Transformation" method to solve my differential equation.After applying this method,I will get univariate polynomial equation.I need to find roots of polynomial.
My polynomial equation is becoming very big. I need to simplify it before finding roots.
I used few simplification methods as shown in code. I could not simplify expression. Trying to do this many times but could not solve.
please anybody help me. I am new to sage.
In the code below array range is (0,10). n = 10 . I need to solve for n = 50. Equation will become very big. Here my problem is simplification. I need to simplify where ever possible in the code.
Code:
from sage.all import *
a,c1,c2 = var( 'a c1 c2')
Y = [ 0,0,c1,c2 ]
mu = 2.00*(10**(-9))
Ev = 1.06*(10**12)
d = 1.00*(10**(-9))
L = 20*d
Pi = 3.141592654
Iv = Pi*((d**4)/64)
kw = (300*(Ev*Iv/(L**4)))
musq = (mu/L)**2
for i in range(0,10):
Y.append(maxima.expand(((((-a)+musq*kw*(L**4)/(Ev*Iv))*(i+1)*(i+2)*Y[i+2])-(kw*(L**4)/(Ev*Iv))*Y[i])/((1-(a*musq))*(i+1)*(i+2)*(i+3)*(i+4))))
e1 = maxima.expand(sum(Y))
print 'e1'
print e1
z = []
for j in range(0,10):
z.append(maxima.ratexpand(j*Y[j]))
e2 = maxima.expand(sum(z))
print 'e2'
print e2
a11 = maxima.ratsimp(maxima.combine(maxima.expand(e1.coeff(c1))))
print 'a11'
print a11
a12 = maxima.ratsimp(maxima.combine(maxima.expand(e1.coeff(c2))))
print 'a12'
print a12
a21 = maxima.ratsimp(maxima.combine(maxima.expand(e2.coeff(c1))))
print 'a21'
print a21
a22 = maxima.ratsimp(maxima.combine(maxima.expand(e2.coeff(c2))))
print 'a22'
print a22
M = maxima.matrix([a11,a12],[a21,a22])
#print 'M'
#print M
maxima.ratmx = True
maxima.sparse = True
det = maxima.num(maxima.combine(maxima.ratexpand(M.determinant())))
print 'det'
print det
R = maxima.allroots(det)
print R
Rekha Penmetsa
why ratsimp is not working for bigger expressions and how can I simplify further ?