A computer algebra system written in pure Python.zip

from sympy.polys.rings import ring from sympy.polys.fields import field from sympy.polys.domains import ZZ, QQ from sympy.polys.solvers import solve_lin_sys # Expected times on 3.4 GHz i7: # In [1]: %timeit time_solve_lin_sys_189x49() # 1 loops, best of 3: 864 ms per loop # In [2]: %timeit time_solve_lin_sys_165x165() # 1 loops, best of 3: 1.83 s per loop # In [3]: %timeit time_solve_lin_sys_10x8() # 1 loops, best of 3: 2.31 s per loop # Benchmark R_165: shows how fast are arithmetics in QQ. R_165, uk_0, uk_1, uk_2, uk_3, uk_4, uk_5, uk_6, uk_7, uk_8, uk_9, uk_10, uk_11, uk_12, uk_13, uk_14, uk_15, uk_16, uk_17, uk_18, uk_19, uk_20, uk_21, uk_22, uk_23, uk_24, uk_25, uk_26, uk_27, uk_28, uk_29, uk_30, uk_31, uk_32, uk_33, uk_34, uk_35, uk_36, uk_37, uk_38, uk_39, uk_40, uk_41, uk_42, uk_43, uk_44, uk_45, uk_46, uk_47, uk_48, uk_49, uk_50, uk_51, uk_52, uk_53, uk_54, uk_55, uk_56, uk_57, uk_58, uk_59, uk_60, uk_61, uk_62, uk_63, uk_64, uk_65, uk_66, uk_67, uk_68, uk_69, uk_70, uk_71, uk_72, uk_73, uk_74, uk_75, uk_76, uk_77, uk_78, uk_79, uk_80, uk_81, uk_82, uk_83, uk_84, uk_85, uk_86, uk_87, uk_88, uk_89, uk_90, uk_91, uk_92, uk_93, uk_94, uk_95, uk_96, uk_97, uk_98, uk_99, uk_100, uk_101, uk_102, uk_103, uk_104, uk_105, uk_106, uk_107, uk_108, uk_109, uk_110, uk_111, uk_112, uk_113, uk_114, uk_115, uk_116, uk_117, uk_118, uk_119, uk_120, uk_121, uk_122, uk_123, uk_124, uk_125, uk_126, uk_127, uk_128, uk_129, uk_130, uk_131, uk_132, uk_133, uk_134, uk_135, uk_136, uk_137, uk_138, uk_139, uk_140, uk_141, uk_142, uk_143, uk_144, uk_145, uk_146, uk_147, uk_148, uk_149, uk_150, uk_151, uk_152, uk_153, uk_154, uk_155, uk_156, uk_157, uk_158, uk_159, uk_160, uk_161, uk_162, uk_163, uk_164 = ring("uk_:165", QQ) def eqs_165x165(): return [ uk_0 + 50719*uk_1 + 2789545*uk_10 + 411400*uk_100 + 1683000*uk_101 + 166375*uk_103 + 680625*uk_104 + 2784375*uk_106 + 729*uk_109 + 456471*uk_11 + 4131*uk_110 + 11016*uk_111 + 4455*uk_112 + 18225*uk_113 + 23409*uk_115 + 62424*uk_116 + 25245*uk_117 + 103275*uk_118 + 2586669*uk_12 + 166464*uk_120 + 67320*uk_121 + 275400*uk_122 + 27225*uk_124 + 111375*uk_125 + 455625*uk_127 + 6897784*uk_13 + 132651*uk_130 + 353736*uk_131 + 143055*uk_132 + 585225*uk_133 + 943296*uk_135 + 381480*uk_136 + 1560600*uk_137 + 154275*uk_139 + 2789545*uk_14 + 631125*uk_140 + 2581875*uk_142 + 2515456*uk_145 + 1017280*uk_146 + 4161600*uk_147 + 411400*uk_149 + 11411775*uk_15 + 1683000*uk_150 + 6885000*uk_152 + 166375*uk_155 + 680625*uk_156 + 2784375*uk_158 + 11390625*uk_161 + 3025*uk_17 + 495*uk_18 + 2805*uk_19 + 55*uk_2 + 7480*uk_20 + 3025*uk_21 + 12375*uk_22 + 81*uk_24 + 459*uk_25 + 1224*uk_26 + 495*uk_27 + 2025*uk_28 + 9*uk_3 + 2601*uk_30 + 6936*uk_31 + 2805*uk_32 + 11475*uk_33 + 18496*uk_35 + 7480*uk_36 + 30600*uk_37 + 3025*uk_39 + 51*uk_4 + 12375*uk_40 + 50625*uk_42 + 130470415844959*uk_45 + 141482932855*uk_46 + 23151752649*uk_47 + 131193265011*uk_48 + 349848706696*uk_49 + 136*uk_5 + 141482932855*uk_50 + 578793816225*uk_51 + 153424975*uk_53 + 25105905*uk_54 + 142266795*uk_55 + 379378120*uk_56 + 153424975*uk_57 + 627647625*uk_58 + 55*uk_6 + 4108239*uk_60 + 23280021*uk_61 + 62080056*uk_62 + 25105905*uk_63 + 102705975*uk_64 + 131920119*uk_66 + 351786984*uk_67 + 142266795*uk_68 + 582000525*uk_69 + 225*uk_7 + 938098624*uk_71 + 379378120*uk_72 + 1552001400*uk_73 + 153424975*uk_75 + 627647625*uk_76 + 2567649375*uk_78 + 166375*uk_81 + 27225*uk_82 + 154275*uk_83 + 411400*uk_84 + 166375*uk_85 + 680625*uk_86 + 4455*uk_88 + 25245*uk_89 + 2572416961*uk_9 + 67320*uk_90 + 27225*uk_91 + 111375*uk_92 + 143055*uk_94 + 381480*uk_95 + 154275*uk_96 + 631125*uk_97 + 1017280*uk_99, uk_0 + 50719*uk_1 + 2789545*uk_10 + 413820*uk_100 + 1633500*uk_101 + 65340*uk_102 + 178695*uk_103 + 705375*uk_104 + 28215*uk_105 + 2784375*uk_106 + 111375*uk_107 + 4455*uk_108 + 97336*uk_109 + 2333074*uk_11 + 19044*uk_110 + 279312*uk_111 + 120612*uk_112 + 476100*uk_113 + 19044*uk_114 + 3726*uk_115 + 54648*uk_116 + 23598*uk_117 + 93150*uk_118 + 3726*uk_119 + 456471*uk_12 + 801504*uk_120 + 346104*uk_121 + 1366200*uk_122 + 54648*uk_123 + 149454*uk_124 + 589950*uk_125 + 23598*uk_126 + 2328750*uk_127 + 93150*uk_128 + 3726*uk_129 + 6694908*uk_13 + 729*uk_130 + 10692*uk_131 + 4617*uk_132 + 18225*uk_133 + 729*uk_134 + 156816*uk_135 + 67716*uk_136 + 267300*uk_137 + 10692*uk_138 + 29241*uk_139 + 2890983*uk_14 + 115425*uk_140 + 4617*uk_141 + 455625*uk_142 + 18225*uk_143 + 729*uk_144 + 2299968*uk_145 + 993168*uk_146 + 3920400*uk_147 + 156816*uk_148 + 428868*uk_149 + 11411775*uk_15 + 1692900*uk_150 + 67716*uk_151 + 6682500*uk_152 + 267300*uk_153 + 10692*uk_154 + 185193*uk_155 + 731025*uk_156 + 29241*uk_157 + 2885625*uk_158 + 115425*uk_159 + 456471*uk_16 + 4617*uk_160 + 11390625*uk_161 + 455625*uk_162 + 18225*uk_163 + 729*uk_164 + 3025*uk_17 + 2530*uk_18 + 495*uk_19 + 55*uk_2 + 7260*uk_20 + 3135*uk_21 + 12375*uk_22 + 495*uk_23 + 2116*uk_24 + 414*uk_25 + 6072*uk_26 + 2622*uk_27 + 10350*uk_28 + 414*uk_29 + 46*uk_3 + 81*uk_30 + 1188*uk_31 + 513*uk_32 + 2025*uk_33 + 81*uk_34 + 17424*uk_35 + 7524*uk_36 + 29700*uk_37 + 1188*uk_38 + 3249*uk_39 + 9*uk_4 + 12825*uk_40 + 513*uk_41 + 50625*uk_42 + 2025*uk_43 + 81*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 118331180206*uk_47 + 23151752649*uk_48 + 339559038852*uk_49 + 132*uk_5 + 146627766777*uk_50 + 578793816225*uk_51 + 23151752649*uk_52 + 153424975*uk_53 + 128319070*uk_54 + 25105905*uk_55 + 368219940*uk_56 + 159004065*uk_57 + 627647625*uk_58 + 25105905*uk_59 + 57*uk_6 + 107321404*uk_60 + 20997666*uk_61 + 307965768*uk_62 + 132985218*uk_63 + 524941650*uk_64 + 20997666*uk_65 + 4108239*uk_66 + 60254172*uk_67 + 26018847*uk_68 + 102705975*uk_69 + 225*uk_7 + 4108239*uk_70 + 883727856*uk_71 + 381609756*uk_72 + 1506354300*uk_73 + 60254172*uk_74 + 164786031*uk_75 + 650471175*uk_76 + 26018847*uk_77 + 2567649375*uk_78 + 102705975*uk_79 + 9*uk_8 + 4108239*uk_80 + 166375*uk_81 + 139150*uk_82 + 27225*uk_83 + 399300*uk_84 + 172425*uk_85 + 680625*uk_86 + 27225*uk_87 + 116380*uk_88 + 22770*uk_89 + 2572416961*uk_9 + 333960*uk_90 + 144210*uk_91 + 569250*uk_92 + 22770*uk_93 + 4455*uk_94 + 65340*uk_95 + 28215*uk_96 + 111375*uk_97 + 4455*uk_98 + 958320*uk_99, uk_0 + 50719*uk_1 + 2789545*uk_10 + 402380*uk_100 + 1534500*uk_101 + 313720*uk_102 + 191455*uk_103 + 730125*uk_104 + 149270*uk_105 + 2784375*uk_106 + 569250*uk_107 + 116380*uk_108 + 912673*uk_109 + 4919743*uk_11 + 432814*uk_110 + 1166716*uk_111 + 555131*uk_112 + 2117025*uk_113 + 432814*uk_114 + 205252*uk_115 + 553288*uk_116 + 263258*uk_117 + 1003950*uk_118 + 205252*uk_119 + 2333074*uk_12 + 1491472*uk_120 + 709652*uk_121 + 2706300*uk_122 + 553288*uk_123 + 337657*uk_124 + 1287675*uk_125 + 263258*uk_126 + 4910625*uk_127 + 1003950*uk_128 + 205252*uk_129 + 6289156*uk_13 + 97336*uk_130 + 262384*uk_131 + 124844*uk_132 + 476100*uk_133 + 97336*uk_134 + 707296*uk_135 + 336536*uk_136 + 1283400*uk_137 + 262384*uk_138 + 160126*uk_139 + 2992421*uk_14 + 610650*uk_140 + 124844*uk_141 + 2328750*uk_142 + 476100*uk_143 + 97336*uk_144 + 1906624*uk_145 + 907184*uk_146 + 3459600*uk_147 + 707296*uk_148 + 431644*uk_149 + 11411775*uk_15 + 1646100*uk_150 + 336536*uk_151 + 6277500*uk_152 + 1283400*uk_153 + 262384*uk_154 + 205379*uk_155 + 783225*uk_156 + 160126*uk_157 + 2986875*uk_158 + 610650*uk_159 + 2333074*uk_16 + 124844*uk_160 + 11390625*uk_161 + 2328750*uk_162 + 476100*uk_163 + 97336*uk_164 + 3025*uk_17 + 5335*uk_18 + 2530*uk_19 + 55*uk_2 + 6820*uk_20 + 3245*uk_21 + 12375*uk_22 + 2530*uk_23 + 9409*uk_24 + 4462*uk_25 + 12028*uk_26 + 5723*uk_27 + 21825*uk_28 + 4462*uk_29 + 97*uk_3 + 2116*uk_30 + 5704*uk_31 + 2714*uk_32 + 10350*uk_33 + 2116*uk_34 + 15376*uk_35 + 7316*uk_36 + 27900*uk_37 + 5704*uk_38 + 3481*uk_39 + 46*uk_4 + 13275*uk_40 + 2714*uk_41 + 50625*uk_42 + 10350*uk_43 + 2116*uk_44 + 130470415844959*uk_45 + 141482932855*uk_46 + 249524445217*uk_47 + 118331180206*uk_48 + 318979703164*uk_49 + 124*uk_5 + 151772600699*uk_50 + 578793816225*uk_51 + 118331180206*uk_52 + 153424975*uk_53 + 270585865*uk_54 + 128319070*uk_5