Hello: Below I have given a program which tries to find the determinant of a matrix having real numbers and and symbols. The program compiles properly. But when I run the program it takes extremely long time to give the output. I have waited for nearly 4 hours before pressing Ctrl+C. How can I find determinants of such matrices of larger sizes? What method does GiNaC employ to calculate the determinant of a matrix having symbols? What method does GiNaC employ to calculate the characteristic polynomial of a matrix? // This is Example-1 given in the paper ``Numerical Computation of // Decentralized Fixed Modes'' by R.V.Patel and P.Misra, Automatica, // Vol.27, No.2, pp.375-382, 1991. #include <iostream> #include <ginac/ginac.h> using namespace GiNaC; using namespace std; int main() { symbol F11("F11"), F12("F12"), F13("F13"), F21("F21"), F22("F22"), F23("F23"), F31("F31"), F32("F32"), F33("F33"), F44("F44"), F45("F45"), F46("F46"), F54("F54"), F55("F55"), F56("F56"), F64("F64"), F65("F65"), F66("F66"), F77("F77"), F78("F78"), F79("F79"), F87("F87"), F88("F88"), F89("F89"), F97("F97"), F98("F98"), F99("F99"), s("s"); ex w1[8][8] = { {-2.902280128, 4.902280128, 3.698135576, -1.091710896, -1.339597088, -3.833588112, 0.1354525359, 0.1354525359}, {14.57598539, 8.663631092, 4.471485536, -6.163631092, -1.031929416, 1.692145555, -11.85191042, 0.5280631913}, {-13.01717766, 5.242845433, 6.808655713, 0.3658471056, -1.250335699, -9.401666250, 5.593010537, -0.1838540200}, {-9.358517860, 9.358517860, 9.233430521, -1.249825322, -1.102425449, -10.21076863, 0.9773381096, 0.9773381096}, {10.90157850, 10.33803799, 6.577811264, -6.527468755, -1.463336353, -1.277505940, -10.98858465, 1.391388959}, { 7.438961098, 6.026323164, 4.365195826, -4.228199859, -1.659477876, -1.136995967, -5.916479189, 0.6866298675}, { 4.590977560, 7.475549489, 4.982190956, -3.664980257, -2.282092104, -2.544374131, -5.126096156, 0.4770129007}, {16.85292654, 5.785447163, 2.204831037, -5.785447163, -1.798583916, 3.580616126, -11.47372649, 1.906247120}}; ex w2[8][9]={ { -6.288091946, -8.384122594, -10.48015324, 24.06096115, 8.869414499, 7.808913485, -2.620038311, -3.144045973, -13.10019155}, { 6.989292416, 9.319056555, 11.64882069, 16.40558839, 19.28474045, 8.940485304, 2.912205174, 3.494646208, 14.56102587}, {-13.54775782, -18.06367710, -22.57959637, 25.20750633, 18.08277192, 31.47867615, -5.644899094, -6.773878912, -28.22449547}, { -5.198332933, -6.931110578, -8.663888222, 23.84960895, 19.94822168, 17.03165000, -2.165972056, -2.599166467, -10.82986028}, { -7.648224421,-10.19763256, -12.74704070, 10.15737156, 9.939200440, 4.700713320, -3.186760175, -3.824112210, -15.93380088}, { -5.899533404, -7.866044538, -9.832555673, 19.48795695, 26.58611759, 31.63366095, -2.458138918, -2.949766702, -12.29069459}, {-6.288091946, -8.384122594, -10.48015324, 29.74830670, 25.04543540, 17.08815424, -2.620038311, -3.144045973, -13.10019155}, { 1.360132475, 1.813509966, 2.266887458, 17.73934984, 17.02037591, 14.47725433, 0.5667218645, 0.6800662374, 2.833609322}}; ex w3[9][8]={ {-2.632399367, -0.8816532905, 0.2216458770, 0.8816532905, 0.3060021972, -1.103299168, 1.223098002, 0.5276480743}, { 0.6965370444, -0.6965370444, -0.6386855981, 0.0878917469, 0.0698972579, 0.6507314098, -0.0120458116, -0.0120458116}, { 0.1251321667, 0.7413375337, 3.578384236, -0.2660527380, -0.0994345890, -3.687097343, -3.700738679, 2.940754836}, { 0.9728813679, -0.6824007787, 0.8321248154, 0.0737554812, 0.0515436172, -0.8059427381, -1.726710642, 1.440410961}, { 0.6338502954, 1.253223829, 1.874876846, -0.7779391327, -0.2226901107, -1.471703558, -0.7446180000, 1.113991924}, { 0.0725179078, -0.0725179078, -0.4003742177, 0.6048139599, -0.1581541911, 0.5700763364, -0.1697021187, -0.1697021187}, { 0.0952676686, -0.0687101141, 0.0066780601, 0.0905768308, -0.1072959550, 0.1535121891, 0.1560969942, 0.0472149362}, {-0.2252498152, 0.0992129486, 0.1715238903, 0.1417124980, -0.0477814471, -0.0948070092, 0.1258808196, 0.0636080200}, {-0.2314675213, 0.1207746598, 0.2092921292, 0.0112031403, -0.0280553044, -0.0858390289, 0.3357822914, -0.0594501770}}; ex w4[9][9]={ {F11, F12, F13, 0, 0, 0, 0, 0, 0 }, {F21, F22, F23, 0, 0, 0, 0, 0, 0 }, {F31, F32, F33, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, F44, F45, F46, 0, 0, 0 }, { 0, 0, 0, F54, F55, F56, 0, 0, 0 }, { 0, 0, 0, F64, F65, F66, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, F77, F78, F79}, { 0, 0, 0, 0, 0, 0, F87, F88, F89}, { 0, 0, 0, 0, 0, 0, F97, F98, F99}}; ex w5[8][8]={ {1,0,0,0,0,0,0,0}, {0,1,0,0,0,0,0,0}, {0,0,1,0,0,0,0,0}, {0,0,0,1,0,0,0,0}, {0,0,0,0,1,0,0,0}, {0,0,0,0,0,1,0,0}, {0,0,0,0,0,0,1,0}, {0,0,0,0,0,0,0,1}}; matrix A(8,8); matrix B(8,9); matrix C(9,8); matrix F(9,9); matrix I(8,8); //This loop fills A matrix with values. for(unsigned r=0;r<8;r++) { for(unsigned c=0;c<8;c++) { A.set(r,c,w1[r][c]); } } //This loop fills B matrix with values. for(unsigned r=0;r<8;r++) { for(unsigned c=0;c<9;c++) { B.set(r,c,w2[r][c]); } } // This loop fills C matrix with values. for(unsigned r=0;r<9;r++) { for(unsigned c=0;c<8;c++) { C.set(r,c,w3[r][c]); } } // This loop fills F matrix with values. for(unsigned r=0;r<9;r++) { for(unsigned c=0;c<9;c++) { F.set(r,c,w4[r][c]); } } // This loop fills I matrix with values. for(unsigned r=0;r<8;r++) { for(unsigned c=0;c<8;c++) { I.set(r,c,w5[r][c]); } } matrix AplusBFC = A.add(B.mul(F.mul(C))); matrix Af = I.mul_scalar(s).sub(AplusBFC); ex e1=determinant(Af); ex e2=charpoly(AplusBFC,s); cout << "R V Patel et al EXAMPLE-1:" << endl; cout << "MATRIX [A] = " << endl; cout << A << endl << endl; cout << "MATRIX [B] = " << endl; cout << B << endl << endl; cout << "MATRIX [C] = " << endl; cout << C << endl << endl; cout << "MATRIX [F] = " << endl; cout << F << endl << endl; cout << "MATRIX [AplusBFC] = " << endl; cout << AplusBFC << endl << endl; cout << "MATRIX [Af] = " << endl; cout << Af << endl << endl; cout << "Determinant |sI-AplusBFC| = " << endl; cout << e1 << endl; cout << "Characteristic polynomial of Af = " << endl; cout << e2 << endl << endl << endl; return 0; } Thanks for helping me. Sincerely, Anand