Numerically solving of a system of nonlinear inequalities

asked 2012-11-14 01:33:34 -0600

Hackstein gravatar image

updated 2015-01-17 15:34:38 -0600

FrédéricC gravatar image

Hello,

I have a highly nonlinear system of 14 inequalities in seven variables l_1, l_2,l_3, I_q1, I_q2,I_q,R_C consisting of inequalities like 0.2135674961e136 * I_q2 ^ 3 * I_q1 * l_1 ^ 2 * l_3 + 0.1359729300e138 * I_q2 ^ 2 * l_2 * l_1 ^ 3 * l_3 + 0.4748826459e137 * I_q2 * l_2 ^ 2 * l_1 ^ 3 * l_3 + 0.1023634311e139 * I_q2 ^ 2 * l_2 * I_q1 * l_1 ^ 2 * l_3 + 0.4926161933e138 * I_q2 * l_2 ^ 2 * I_q1 * l_1 ^ 2 * l_3 + 0.1817765067e139 * l_1 * l_2 * l_3 * I_q1 ^ 2 * I_q2 ^ 2 + 0.1022307261e139 * l_1 * l_2 ^ 2 * l_3 * I_q1 ^ 2 * I_q2 + 0.6124318199e136 * I_q2 ^ 3 * I_q1 ^ 2 * l_1 * l_3 + 0.4722141070e137 * l_2 ^ 3 * I_q1 * l_1 ^ 2 * l_3 + 0.1354133707e138 * l_1 * l_2 ^ 3 * l_3 * I_q1 ^ 2 + 0.4099750199e136 * l_2 * l_3 * I_q1 ^ 3 * I_q2 ^ 2 + 0.1431829278e136 * l_2 ^ 2 * l_3 * I_q1 ^ 3 * I_q2 + 0.2895936503e138 * l_1 * l_2 ^ 2 * l_3 ^ 2 * I_q1 ^ 2 + 0.4828612500e136 * l_1 ^ 2 * l_2 * l_3 * I_q2 ^ 3 + 0.1587988317e138 * l_1 ^ 2 * l_2 ^ 2 * l_3 * I_q2 ^ 2 + 0.1009872263e138 * l_1 ^ 2 * l_2 ^ 2 * l_3 ^ 2 * I_q1 + 0.5487021423e137 * l_1 ^ 2 * l_2 ^ 3 * l_3 * I_q2 + 0.8649483590e137 * I_q2 ^ 2 * l_2 * I_q1 * l_1 ^ 2 * I_q + 0.3020814254e137 * I_q2 * l_2 ^ 2 * I_q1 * l_1 ^ 2 * I_q + (0.4371323541e134 * I_q2 * l_2 ^ 2 * I_q1 * l_1 ^ 2 * l_3 + 0.1253532341e135 * l_1 * l_2 ^ 2 * l_3 * I_q1 ^ 2 * I_q2 + 0.1251639064e135 * I_q2 ^ 2 * l_2 * I_q1 * l_1 ^ 2 * l_3 + 0.3589233398e135 * l_1 * l_2 * l_3 * I_q1 ^ 2 * I_q2 ^ 2) * (I_q ^ 2 + 0.1824e4 * l_3) + 0.4611303613e136 * I_q2 ^ 2 * l_2 * l_1 ^ 3 * R_C * I_q1 * l_3 + 0.1610488249e136 * I_q2 * l_2 ^ 2 * l_1 ^ 3 * R_C * I_q1 * l_3 + 0.1331893542e137 * I_q2 ^ 2 * l_2 * I_q1 ^ 2 * l_1 ^ 2 * R_C * l_3 + 0.4651610646e136 * I_q2 * l_2 ^ 2 * I_q1 ^ 2 * l_1 ^ 2 * R_C * l_3 + 0.9547565330e134 * R_C * l_1 * l_2 ^ 2 * l_3 * I_q1 ^ 3 * I_q2 + 0.2733750000e135 * R_C * l_1 * l_2 * l_3 * I_q1 ^ 3 * I_q2 ^ 2 + 0.4083749998e138 * I_q * l_1 * l_2 * l_3 * I_q1 ^ 2 * I_q2 + 0.1424087112e138 * I_q * l_1 ^ 2 * l_2 * l_3 * I_q1 * I_q2 + 0.1012500000e137 * l_1 * l_2 * l_3 * I_q1 * I_q2 ^ 3 + 0.6072418752e138 * l_1 * l_2 * l_3 ^ 2 * I_q1 ^ 2 * I_q2 + 0.3329814043e138 * l_1 * l_2 ^ 2 * l_3 * I_q1 * I_q2 ^ 2 + 0.1150560165e138 * l_1 * l_2 ^ 3 * l_3 * I_q1 * I_q2 + 0.2117576562e138 * l_1 ^ 2 * l_2 * l_3 ^ 2 * I_q1 * I_q2 + 0.2480348871e138 * I_q * l_1 * l_2 * I_q1 ^ 2 * I_q2 ^ 2 + 0.8662567131e137 * I_q * l_1 * l_2 ^ 2 * I_q1 ^ 2 * I_q2 + 0.1947540375e138 * I_q * l_1 * l_2 ^ 2 * l_3 * I_q1 ^ 2 + 0.6791471439e137 * I_q * l_1 ^ 2 * l_2 ^ 2 * l_3 * I_q1 >0 or more complicated inequalities and I am looking for some particular numerical solutions, not necessarily for all solutions. (I know that there are solutions to the subsystem of the first 13 inequalties.) Is there a routine or another way in Sage to do this? If I understand correctly, solve tries to find all solutions by symbolic calculations and gives a RuntimeError: floating point exception.

Thanks a lot in advance,

Urs Hackstein

Addition: scipy.optimize.fsolve and newton_krylov solve systems numerically, but only systems of equalities, not those of inequalities.

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