I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[]
nor LinearSolve[]
can solve this system in a reasonable amount of time (I have not received an answer in an hour).
On the other hand, Maple gives me the correct answer in a few seconds.
The 76 linear equations $equations
in 76 $coefficients
are (also can be found here.):
$equations = Uncompress["1:eJztXUuPHVcRdsbxOCCEEIsIKRISWURZzu3nDHt2WaCIP2BQLFkYInDy570IzNx+1a3qOqe+73S3HeVmYcczp/q8qurUu/709++/ff3Ns2fP3n36+Mc3b9798Prm6V8vHv/4y39+fPX29e+nX/717Y/vll/+7c2/vhv/+dnjH9+++uHN9/9+9fbN/x7/e3P+8fPHP15VNQ7SwyDNHQ5SvX5+ASJ+\ 1/Xvnv7xXauGeF99LrZ7hvyn/ngAsg9DfvL4DwFZP7CQzR0NWbH7bO8xyFtztjUO2WOQ9mwDkOcTWuaczpaArDBIe7b160891B6HfNe+e/n0s3+8evvqv3dvHv/3mab7L5/hdL8s5aSJ+DxgvI5T/nPqTKomuAIB0sIgdZSNCJDAwtRe6i4P8tPlaTb4LM0DDNLiJ9Z2MHqfRmI8wZBVE4Y0uMBC1nc\ 0ZHy1BkHYORt6zuaBhWzps23j+/xJcxf6KWhYtjzhEA5Z009BHV+txr4uDPn0kwtew87ZxB9LjQn02bbzPtVz8/RyDV8D3zDJqeCN8MxtQekNNqKJu8H5Ac1rF/xRy7wt2sOpQu7v5rwS/BIqYtfDXOxxnUBpz0xZZyW53xFUsEiMYaFIgAQkHK2OBcQVBRKWPYQ4Tys8Ez8lVKUTqyo1ccVOK1n0nC\ 24z01eufhbpU/odMBbpZUses75rbpSaVrpjlOphoxjr4NJBH3T5heASjUkuE+KSnmJ0uGAhCkElCgpKvUkylUq/XWCSoWJo8ZtmC1Owa0WUM960mjDrNZtmHJIkx/SOkPeL0Mesl/pnYm8y5CHgiGAPJvUNX6VuMaVb7+8RJGT5pzSjhuQU7VmGbWRS4tmHuTmkgrrwCxa6AkYhF5c7qW+nwyn8J4iR\ nxrKh0u+z6Bwvd5/AzQykgI+jWTQ3pnyHuzFjNk2VJ/coYsqN3X+SHOcgMqUNwoY9CYNs/RWnNNz1nzJsF7WjWOGxMdnwChX4LCNeVv0ZgQN88pw14dn1OzN948d0+LJ7Qwtfh41EOygdmqJmS7OBk5BLiH2aqOygubUHW7vpFLiW+kKf35C4e385aYqewQoWh5L9LyllRV9hWovIfCriXxro0+0NRE\ jbeW5SuT47HLmqu+KEKa0z0uf2kxRwryAXFOO+uierUACYhzWk3BfZUtLmcyLsGA1dzcGS1z0PTe0HJOQ0srLe1MbGk5p8A9F9+nljniL6qWOeKvuHr/m7ico+mVdiYC2qnGBFq2KnCV7elhwhUNgAAd0t1DeGpwnx/PD5qkjSJlasrbP4yNImAQ1k+neAdb7UyLaNiLsDJptWVKeO/JVmKII1tFDgw\ jLHluqWv8uoiwIuKM0dtwCaiZ2e+owOHmpUBQlxa58aCuiFnJKmmjjArbvxr88B8Ze1hw0vzZkN+yku4uQX552gICWnnRzDEf7BrnpdW/0wHRWgYlafZPi4MNfSuAIGnQ8wBx0DEp7hrnpU1QtOcIiNbSkHTkFGCC0gIzfSuA8Kqx734/ya0mSDfOLhxGs4ssrZ0ZEZBSTpI2e+Fiy0AKr6JC6BLV9O\ BbmWrvoTPbSZnWujv6LWTeiGFTNOtkWIqcMh8d9nnRRXd4LH+nBTGhZnRRiWvhY31gBYrF91As4ah64CA4hnU0Q+riDiIF2dMyU087pXranNXT5qyOjtvq4iGaGtHic6rXuWfCQi/OloB0XCBbvM49cdU0MfQ7vs49HhlZQCeOm7A0lhp6loe3FxdKgEgCM9kB3m7PC5x9MG8SZy8tZtpBI3/Xr375V\ 9kvn5/2qKXl/OMzRNSLs0CYyLJFgKo63n25DGkdYS6wGcJON+xpAlzLjhQjAsmR+TDAD3dTi9X1lA/Ncy/T+n8TQ5q8YbZxvpK/tvh965NJmWV/iWntcdu4MoQCae0aMp7WruR6IK1dQQJp7RoyntbupF7j0sEhYVZOyYBd7U0aMi7RqlsJpLXPPGrnZCiCiMORsBdEjIKYCNj8sV5rVUQRj2B7R9Sq\ KDQi27PdtVaFZwq+Uun16T3q6XU44K5Pr9Zt6cTDQ55ex+lXlAzVQErNMC9BW8ZzgLnIPRVGZG/kdSXP0S4jVOL+B3MobIRK+5C6xpvYNdqsp+V39X0JgpxwPSdcDuD845szGiYU5fy1VXkUqp2blUPyKXdNPFnOnAlrGWlS6PFCXqLjprm0eQ9/17Mb5HLsbG8rMbIETkNHFwm7DBQbd4ZIMJcqf6e\ u53JBQddzaUPoU/wHdG7K42LNLEneUmZmCUe/CdmPeGxwY06bsGx6UYp5eeTE6xsNDdnSUiI9Z0trni24Wj4m3Z7t/iWj7NkeGpwzr9Y3s0ysbuuoArWUSFSBcrV2ASLWPvMoqxCz4J6zLlEJscdTnnvCf017+Ds6WrCL++k1JO027OhAfCAewYnYwD38HU2oXZytaCKh3aMdrfD2O2aIdsRG6NCTbs\ uN6G9Hq+RQdOJQmOGYZVEFYZ1dgGixOjILe38tHYWHKt52znxUwR/l2Y/e40k7ntW74W+Trnpe1RmkHvUb6QBNhVS6Wu0yxPXtLkM8rWNFw04Uxzh5eca3ZrlMzrNV2FI5z3f5Id5XhLjU5b9SkFwtDHzepq1+mVhLk19Lm7+ANl+dpM0nnbf5SindfEeK7XxqScmkzyyLOXnZ+LdmyPrxCsILZLevW\ 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0tcDPGYOdZ3YZMONW5fc0EHeXnD7Wv+3tx0qml5vq22y8oDgkKAlUOyhNvX3OJL6s3IP5VuX3NOrtnmcUoo7t5y3xusw43NgCvacWDifiHaLca0ARz4OAvIVEkYuDoLSJvPAFe0E1SAe5SZgg7yJnH/LlNUWd4k7v5k0gblTe7hxIWCuUGaWyfWPRzq+CXSDMDpDTlYTS6Vc93O3nwlJZWfPHZuPpLX\ RgojwrQiKMK7KtwlHMn81J6AgGSrXGV11KorQIjmF9EAAZkiiHv5ibZLtHeyYoI0xlti56zpOWu+jQTfk5yub9bw0Xq0dxJNc7f3iXub6/icmmz5lg50CyM0td7e5x4O05rIW6abW9fOq7aFC7vGC/4UUPVHVl8bz6WIlLXTINf0JQ/yI6+vzacvOUknRE3vI+prqxP62KrgfzRUek1fQun7iF4Vmr7\ BSH2KSh0OuGvxSSh9KVkObVn46WEWJocHevz3HLlcT2ZS9Y3J1pLTbVPR3wE9aU6jxvXYRPmU2dkc+KySnZtoJUgBElCPX1zebaRwtQ4QwfX2SBNEHWNuXO3CI5L3zrje+G2iQcSQpHlmGJK3/Lve+PdmRwGDvMVtUh3gmzM2fPR3ce1vIvqbtjsUtFhk7PkX90nYAOLvjm49GLc7aD5Gy5VALXeNCb\ REWtDucM8ugTjRAwTokO4exowG79vI84PGuZHVdocmfsl8JxnbnS97HPD0u65zEaOTjw9zXed2RykXcd7TH4+CisqIo2xYnWZ2Nezobt7ZMLEWjSZHXm4dXxJUKEXYPIhO1MFT+SI+DlP8DDfGRWtpyTQenNzXaxaMAj++gn2yG021U/xF5jNUeP8MLT8AjbMN1tC8mM7MA3wlBl1o2YzPI4zL2j9p7\ 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M0ccgXOMdqVB1TPd6qt4w45oHq+plBaIvwQ/UsLpFC+CTm9z02r55uC9jjp8klTO4bvRarnG5BS7rVurPi8aCORVGtFfB2emhnpR6nTgaMiuliYfoSFGNBDDeZGIQ2+446Oke6YOnZS9CXwqqMj1zsal3t+tUxFuouz/UjbW2ryosM35vzwHTh3p/WzCEgpMezBuTucc/PY3jlvKR+vPDzRRLI4FLE8\ zkKLhDRjKUg1dYMN/g/TGBw4"];
$coefficients = Uncompress["1:eJwtzLtNQ1EQRdEnoBE6sOd3TQ+O6AACJCKCR//C4q5k9iRnvX7+vH/dj+M4Xx7n/n3+nk+P5+Oyc92Jndypnd6ZnbVz23k7n//nF71qaGpp6+jSm/KCF7zgBS94wQte8IIXvOQlL3nJS17ykpe85CWveMUrXvGKV7ziFa94xWte85rXvOY1r3nNa17zhje84Q1veMMb3vCGN7zFW7zFW7zFW/0H\ Ks1gug=="];
and I try the following code to solve:
$result = Solve[$equations,$coefficients]
or
$matrix = CoefficientArrays[$equations, $coefficients];
$result = LinearSolve[$matrix[[2]], $matrix[[1]]]
Is there any way to solve this system with Mathematica in a reasonable amount of time?
scalar0
,k
, etc. Adding some assumptions might make a difference. $\endgroup$1 + e5 scalar0 != 0
,-1 + 2 e5 scalar0 + 6 e6 scalar0 != 0
, etc. Mathematica might require this as an assumption. $\endgroup$