Hi, 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 -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
