Hello, I'm trying to solve a matrix Lyapunov equation A*X+X*A^T=-I, where A is given by: [ 0 0 0 0 1 -1 0 0] [ 0 0 0 0 0 1 -1 0] [ 0 0 0 0 0 0 1 -1] [ 0 0 0 0 0 0 0 1] [-1 0 0 0 a1 0 0 0] [ 1 -1 0 0 0 a2 0 0] [ 0 1 -1 0 0 0 a3 0] [ 0 0 1 -1 0 0 0 a4] with a1,a2,a3,a4 variables, I is dentity matrix, and X defined as [x11 x12 x13 x14 x15 x16 x17 x18] [x12 x22 x23 x24 x25 x26 x27 x28] [x13 x23 x33 x34 x35 x36 x37 x38] [x14 x24 x34 x44 x45 x46 x47 x48] [x15 x25 x35 x45 x55 x56 x57 x58] [x16 x26 x36 x46 x56 x66 x67 x68] [x17 x27 x37 x47 x57 x67 x77 x78] [x18 x28 x38 x48 x58 x68 x78 x88] with defined variables xij
After couple of tries, I found out that sage accepts the following command solve(A*X+X*A.transpose()+I,X.arguments()) but the result: [[x11 == r239, x12 == r235, x13 == r245, x14 == -a4^2*r228 - (a2*r228 - r237 + r242 - r246)*a4 - r228 + r231 + r245, x15 == r251, x16 == r243, x17 == r241, x18 == -a2*r228 - a4*r228 + r237 - r242 + r246, x22 == r252, x23 == -a4*r246 + r226 - r228 + r250, x24 == r250, x25 == r249, x26 == r248, x27 == r247, x28 == r246, x33 == -a4*r240 + r225 - r226 + r244, x34 == r244, x35 == -(r228 + r231)*a4 - a1*r231 - a2*r228 + r237 + r238 - r242 + r246, x36 == r242, x37 == -a3*r226 - a4*r226 + r236 + r240 - r246, x38 == r240, x44 == a4^2*r225 + 1/2*(2*r240 + 1) *a4 + r225 + r244, x45 == r238, x46 == r237, x47 == r236, x48 == a4*r225 + r240 + 1/2, x55 == r234, x56 == r233, x57 == r232, x58 == r231, x66 == r230, x67 == r229, x68 == r228, x77 == r227, x78 == r226, x88 == r225]] is not exactly what I expected. Any hints? On a related matter, is there a reason why cholesky_decomposition method does not compute the exact solution in case of an exact input matrix (say, from QQbar)? In the help it says that the implementation uses standard recursion, with which one can compute the exact solution. Thanks, Ivica --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
