# VMath

### Основное

#### Действия

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Вспомогательная страница к разделу ЗАДАЧА ФЕРМА-ТОРРИЧЕЛЛИ И ЕЕ РАЗВИТИЕ.
Satellite page for FERMAT-TORRICELLI PROBLEM AND ITS DEVELOPMENT

$$\mathcal X(x,m)= (-101777024779520\,m^{10}+67637109932800\,m^{12}-28125983290880\, m^{14}+92390290208400\,m^8$$ $$-1627860736000\,m^{18}+239139520000\,m^{20}-24316800000\,m^{22}+7839274313600\,m^{16}$$ $$+12034770970080\,m^4-973476728000\,m^2+24957720720+1156000000\,m^{24}-47638036331200\,m^6)x^{12}+$$ $$(1057753600000\,m^{22}+70099109888000\,m^{18}-10299702400000\,m^{20}+46890227123200\,m^2-$$ $$-1216111351680 -50864000000\,m^{24}-342277202745600\,m^{16}+2263880011072000\,m^6-$$ $$-4372199256105600\,m^8+ +4780726224314880\,m^{10}-3131574663942400\,m^{12}-574126007941120\,m^4+$$ $$+1269090482488320\,m^{14})\,x^{11}+$$ $$(95396638114658080\,m^8+27630611187936+12731834491928640\,m^4-49803166951719040\,m^6-$$ $$-1374654904096000 \,m^{18} +203089280960000\,m^{20}-1051893236180544\,m^2+66426155095044224\,m^{12}$$ $$-26149063086422400\,m^{14}- -103183518920296896\,m^{10}+1029996000000\,m^{24}+6797064979336000\,m^{16}-$$ $$-21145470400000\,m^{22})\,x^{10}+$$ $$(325554944810259840\,m^{14}-81152586773563200\,m^{16}+16229912430464000\,m^{18}+671797740164476800\,m^6$$ $$-1271081152232646720\,m^8+1355039442133362176\,m^{10}-387620255504256-12705596000000\,m^{24}$$ $$-173816969258301120\,m^4- -854555347076894784\,m^{12}+257186363200000\,m^{22}+14553452040427264\,m^2$$ $$-2426296749280000\,m^{20})x^9+$$ $$(19591957986000000\,m^{20}-6199506476676258368\,m^6-12079596510028707008\,m^{10}-2123656918400000\,m^{22}$$ $$+11540665992771685504\,m^8+ 648592066724155400\,m^{16} -138477622173829440\,m^2+3743870738330744+$$ $$+106504447500000\,m^{24}-2729941506306319360\,m^{14}- -128505867749736000\,m^{18}+7436244310107835008\,m^{12}$$ $$+1629206937077743520\,m^4)x^8+$$ $$(954590609331550784\,m^2-26226090508696128-46186092591294108928\,m^{12}+16259358390714072000\,m^{14}$$ $$+41284010765030177344\,m^6- -75359939428700788032\,m^8 +12574945492000000\,m^{22}-11047128926396288960\,m^4-$$ $$-3653977939434968000\,m^{16}+719207227341568000\,m^{18}+ +77157191783080201920\,m^{10}-640520815000000\,m^{24}-$$ $$-112928223839720000\,m^{20})x^7+$$ $$(-4878910007451401904\,m^2+55477320761009713664\,m^4+14864537420592735000\,m^{16}-2919660366365158000\,m^{18}$$ $$+478098324339320000\,m^{20} -54936767780100000\,m^{22}+210319291695715889024\,m^{12}-70596726574919824960\,m^{14}-$$ $$-203468806057711645856\,m^6+363459109138804026080\,m^8 +136361414202299224+2841555435750000\,m^{24}-$$ $$-362818521721008651872\,m^{10})x^6+$$ $$(-708856424885317094048\,m^{12}-528249135143694688+8669631684775048000\,m^{18}-1504718531439150000\,m^{20}+$$ $$+747091269383087990624\,m^6 -43891668486024862400\,m^{16}-207221060938582894000\,m^4+18558680304843299584\,m^2+$$ $$+179130856401700000\,m^{22}-9398922519250000\,m^{24} +225295109721825414400\,m^{14}-1305896250277173689232\,m^8$$ $$+1268113926256182458560\,m^{10})x^5+$$ $$(-524312805293318841640\,m^{14}-434618724841412500\,m^{22}+1505658829672692865-18697200074343544500\,m^{18}$$ $$+568907888980532219586\,m^4+23084815302140625\,m^{24}+ +92841397195866799375\,m^{16}-51890091280904453316\,m^2$$ $$+3513412201985501250\,m^{20}-3276215846869971629576\,m^{10}+ 1758242851775862992284\,m^{12}-2024428407357753482692\,m^6+$$ $$+3470944933032414032639\,m^8)x^4+$$ $$(-41215022073125000\,m^{24}+28546610264609778000\,m^{18}+769061629287450000\,m^{22}-3062827366400302680$$ $$+103469546799250831248\,m^2-135427165903660222600\,m^{16}-5974867789006660000\,m^{20}+865756130174079721760\,m^{14}$$ $$-1114518621872023564384\,m^4-6656222823593310144920\,m^8+6113155612903941522208\,m^{10}$$ $$-3135171086377328694528\,m^{12}+3938724253330522793296\,m^6)x^3+$$ $$+(125397192243838755200\,m^{16}+8740928618010767538976\,m^8-29244273007365880000\,m^{18}-947478910841300000\,m^{22}$$ $$-5210670809160062621856\,m^6+50988049348500000\,m^{24}-139027225688916975296\,m^2-$$ $$-956753411498858822720\,m^{14}+4199423436486098752+7083205640604500000\,m^{20}+3818969376618508563008\,m^{12}$$ $$+1473151356485803610016\,m^4-7833174951662473463680\,m^{10})x^2+$$ $$(4201274388868167743744\,m^6-60841786190891025600\,m^{16}-7056304169293532360896\,m^8+6196934033060116332032\,m^{10}-$$ $$-39438149465000000\,m^{24} -3469512807918465600-1176455185357383380608\,m^4+626531120710683139840\,m^{14}$$ $$+18047309551597072000\,m^{18}-5315448765287600000\,m^{20} +734708532374400000\,m^{22}+112620855241440112512\,m^2-$$ $$-2853567001342740263424\,m^{12}) x$$ $$+14506998025000000\,m^{24}-41501586347425838592\,m^2+428815243522348375936\,m^4+8040832471289227200\,m^{16}-$$ $$-5135799781252480000\,m^{18}+1939649619705040000\,m^{20}-273449463248000000\,m^{22}-178341355836090099200\,m^{14}+$$ $$+987637202450564939264\,m^{12}- -2290615617902387188224\,m^{10}+2648082670463298780096\,m^8-1560160146858537847296\,m^6$$ $$+1301832381140260416$$

$$\Phi(x,y) =3\,y(-7\,y+10\,x)(8\,x-y)(2\,x-9\,y)(x^2+y^2)^4+$$ $$+8\,(160\,x^5-2594\,x^4y+10117\,x^3y^2+3152\,x^2y^3-6209\,xy^4+183\,y^5)(x^2+y^2)^3-$$ $$-4\,(10144\,x^6-106368\,x^5y+344359\,x^4y^2+303368\,x^3y^3+32554\,x^2y^4-193808\,xy^5-16853\,y^6)(x^2+y^2)^2$$ $$+464160\,x^9-5133648\,x^8y+16256272\,x^7y^2+13641688\,x^6y^3+30110896\,x^5y^4+18744840\,x^4y^5+5862064\,x^3y^6$$ $$-1755512\,x^2y^7-8456720\,xy^8-1725016\,y^9$$ $$-1525888\,x^8+39680576\,x^7y-33850616\,x^6y^2-166109536\,x^5y^3-223425920\,x^4y^4$$ $$-101676416\,x^3y^5-3242008\,x^2y^6+65782560\,xy^7+20738736\,y^8$$ $$-16575808\,x^7-193724640\,x^6y+866119040\,x^5y^2+1175243584\,x^4y^3+995439872\,x^3y^4+215709120\,x^2y^5-338594752\,xy^6-159544672\,y^7$$ $$+222101328\,x^6+451294848\,x^5y-4348813904\,x^4y^2-4891089920\,x^3y^3-2228788624\,x^2y^4+1020074752\,xy^5+833843024\,y^6$$ $$-1192346240\,x^5+946668544\,x^4y+15106266176\,x^3y^2+10700238240\,x^2y^3-741654848\,xy^4-2916171360\,y^5$$ $$+3183428800\,x^4-10206078336\,x^3y-30287492000\,x^2y^2-5908009728\,xy^3+6312951120\,y^4$$ $$-2884333056\,x^3+27197129472\,x^2y+24275008896\,xy^2-7053822720\,y^3$$ $$-1152\, (2823793\,x^2-22813720\,xy-56866\,y^2)+4409856 (1491\,x+1234\,y)-2110116096 \ .$$

# Источники

Утешев А.Ю. От Ферма до Максвелла: о стационарных точках семейства потенциалов. Процессы управления и устойчивость. Т. 1 (17), под ред. Н.В.Смирнов. СПб: Издательский дом Федоровой Г.В., 2014, сс.506–521. Текст ЗДЕСЬ (pdf)

algebra2/optimiz/distance/torri/vspom1.txt · Последние изменения: 2020/06/17 00:52 — au