Bertini.BPMCSolve |
Syntax |
Bertini.BPMCSolve(P:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):Output in ApCoCoAServer |
Description |
Example |
-- An example of Membership testing using default configurations. -- We want to test membership for the points [ [ [1.0, 0.0], [0.0, 0.0], [0.0, 0.0 ] ], [ [1.3650269, -0.31430820], -- [1.7645087, -0.85807828], [2.1389007, -1.7258994] ] ], where the polynomial system is -- x^2+y^2+z^2-1=0, x^3+y^2+z^3-1=0, (y-x^2)*(z-x^3)(z-5)=0. Use S ::= QQ[x,y,z]; P := [x^2+y^2+z^2-1,x^3+y^2+z^3-1,(y-x^2)*(z-x^3)(z-5)]; SysTyp := "Nhom"; MPoints :=[ [ ["1.0", "0.0"], ["0.0", "0.0"], ["0.0", "0.0" ] ], [ ["1.3650269", "-0.31430820"], ["1.7645087", "-0.85807828"], ["2.1389007", "-1.7258994"] ] ]; ConfigSet := ["TRACKTYPE: 3"]; -- Save the file named witness_data in ApCoCoA directory/Bertini. In this example we can use the following file. 4 3 1 2 52 5.565526640875543e-01 3.486877417858003e-01 3.500659632917004e-01 -6.132734154671150e-01 -5.721270410075433e-01 2.012168578122028e-03 6.863472388783394e-01 5.972202311132409e-01 52 5.565526640873006e-01 3.486877417858785e-01 3.500659632926851e-01 -6.132734154660159e-01 -5.721270410085784e-01 2.012168576850362e-03 6.863472388783461e-01 5.972202311130588e-01 1.000000000000000e+00 0 3.319220103162024e-03 0.000000000000000e+00 10 1 0 0 52 5.036510877340633e-01 1.454616573815811e-01 -5.531197782767149e-01 1.264217225328824e-01 4.692782265207243e-01 -7.716455726951312e-01 8.298040333939428e-01 6.089446696116878e-01 52 5.036510877340730e-01 1.454616573815189e-01 -5.531197782770511e-01 1.264217225329790e-01 4.692782265211026e-01 -7.716455726952207e-01 8.298040333939808e-01 6.089446696117080e-01 1.000000000000000e+00 0 1.494343809475570e-03 0.000000000000000e+00 10 1 0 0 2 6 52 1.777791036661873e+00 -5.879389926987107e-01 8.371810169339621e-01 -5.381722763592328e-01 3.596166136115721e-01 -3.879323179323894e-01 1.337065929459078e-01 -2.473259991477609e-01 52 1.777791036661789e+00 -5.879389926985648e-01 8.371810169340158e-01 -5.381722763590965e-01 3.596166136114090e-01 -3.879323179324481e-01 1.337065929459972e-01 -2.473259991477353e-01 9.239465819894503e+00 0 2.311369308586180e-02 0.000000000000000e+00 10 1 3 0 52 2.801078874321721e-01 5.815307461738819e-01 3.602184484724343e-01 -6.856646564513529e-01 -9.183171422752723e-01 1.429861040336559e-01 7.942652024873893e-01 7.828205287876466e-01 52 2.801078874345398e-01 5.815307461783135e-01 3.602184484733199e-01 -6.856646564552420e-01 -9.183171422767007e-01 1.429861040419545e-01 7.942652024894031e-01 7.828205287870957e-01 9.903193701737050e+01 0 6.113734060564361e-04 0.000000000000000e+00 10 1 3 0 52 7.794026532326790e-01 6.438486770366723e-01 -5.511209013756149e-01 -4.552697655906182e-01 3.897013266163394e-01 3.219243385183361e-01 1.054343379801123e+00 5.809168127219385e-01 52 7.794026532326920e-01 6.438486770366824e-01 -5.511209013756679e-01 -4.552697655905938e-01 3.897013266164013e-01 3.219243385183344e-01 1.054343379801143e+00 5.809168127219345e-01 4.374295962959485e+00 0 2.286082168348384e-01 0.000000000000000e+00 10 1 0 0 52 2.480644358066108e-01 2.812814217076330e-01 -5.317945942111184e-01 1.336818293531960e-01 1.829122341866813e-01 -7.805728420468510e-01 8.915030044886882e-01 7.610652719830333e-01 52 2.480644358050654e-01 2.812814217073318e-01 -5.317945942103757e-01 1.336818293522557e-01 1.829122341846779e-01 -7.805728420469515e-01 8.915030044881618e-01 7.610652719839810e-01 6.015239676438355e+02 0 5.166904527784629e-05 0.000000000000000e+00 10 1 3 0 52 1.429155740109253e+00 -5.743679627312509e-01 7.145778700546264e-01 -2.871839813656256e-01 2.279525891501262e-01 -7.528357666690323e-01 1.786444675136565e-01 -7.179599534140634e-02 52 1.429155740109399e+00 -5.743679627313251e-01 7.145778700546536e-01 -2.871839813657727e-01 2.279525891502284e-01 -7.528357666688903e-01 1.786444675135966e-01 -7.179599534147321e-02 1.651321081771953e+01 0 8.707915499833527e-03 0.000000000000000e+00 10 1 1 0 52 7.185714193516700e-01 -2.226007471289887e+00 5.081067233904082e-01 -1.574024977920998e+00 3.592857096758350e-01 -1.113003735644943e+00 -9.638142491390969e-01 5.075337374339561e-01 52 7.185714193515241e-01 -2.226007471290154e+00 5.081067233903571e-01 -1.574024977921150e+00 3.592857096758574e-01 -1.113003735645067e+00 -9.638142491392726e-01 5.075337374340601e-01 3.841442764800970e+01 0 2.603188596646477e-02 0.000000000000000e+00 10 1 2 0 3 1 52 1.299580404330397e+00 -6.044565403080021e-01 6.497902021651987e-01 -3.022282701540011e-01 6.497902021651987e-01 -3.022282701540011e-01 6.497902021651987e-01 -3.022282701540011e-01 52 1.299580404330128e+00 -6.044565403085679e-01 6.497902021653607e-01 -3.022282701541981e-01 6.497902021650848e-01 -3.022282701542752e-01 6.497902021649185e-01 -3.022282701538901e-01 6.896280458897404e+00 0 4.394857579432204e-03 0.000000000000000e+00 10 1 0 0 -1 2 1 2 108723397967774785/1152921504606846976 -1276921637840786251/73786976294838206464 -1830867849111980429/36893488147419103232 -4584732275555858575/4611686018427387904 2 3 4 1 0 0 0 0 0 0 0 0 0 2 4 367776963113838806789/20000000000000000 8578223665279742151/100000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 4 4028259749117460225/18446744073709551616 -4330798452886879565/36893488147419103232 11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616 2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808 10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464 2 1 -5527276071396270107/73786976294838206464 6119401794520521373/18446744073709551616 5101220359790769903/36893488147419103232 -8579339317661386167/9223372036854775808 3 1 4 1 0 0 0 0 0 0 0 0 0 1 4 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 -3156090912479527573/100000000000000000 4338464515047412657/2000000000000000000000 4 4028259749117460225/18446744073709551616 -4330798452886879565/36893488147419103232 11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616 2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808 10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464 3 0 4 1 0 0 0 0 0 0 0 0 0 0 4 4 4028259749117460225/18446744073709551616 -4330798452886879565/36893488147419103232 11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616 2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808 10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464 -- Then we test membership with Bertini.BPMCSolve(P,SysTyp,MPoints,ConfigSet); -- And we can see the related information in ApCoCoAServer. Please note that -- you will get only the following message in ApCoCoA GUI. ---------------------------------------- Please refer to ApCoCoAServer for results of computation. --For Bertini output files please refer to ApCoCoA directory/Bertini. |
Example |
-- An example of Membership testing using user configurations. -- We want to test membership for the points [ [ [1.0, 0.0], [0.0, 0.0], [0.0, 0.0 ] ], [ [1.3650269, -0.31430820], -- [1.7645087, -0.85807828], [2.1389007, -1.7258994] ] ], where the polynomial system is -- x^2+y^2+z^2-1=0, x^3+y^2+z^3-1=0, (y-x^2)*(z-x^3)(z-5)=0. Use S ::= QQ[x,y,z]; P := [x^2+y^2+z^2-1,x^3+y^2+z^3-1,(y-x^2)*(z-x^3)(z-5)]; SysTyp := "Nhom"; MPoints :=[ [ ["1.0", "0.0"], ["0.0", "0.0"], ["0.0", "0.0" ] ], [ ["1.3650269", "-0.31430820"], ["1.7645087", "-0.85807828"], ["2.1389007", "-1.7258994"] ] ]; ConfigSet := ["TRACKTYPE: 3", "MPTYPE: 0"]; -- Save the file named witness_data in ApCoCoA directory/Bertini. Use the file of previous example. -- Then we test membership with Bertini.BPMCSolve(P,SysTyp,MPoints,ConfigSet); -- And we can see the related information in ApCoCoAServer. Please note that -- you will get only the following message in ApCoCoA GUI. ---------------------------------------- Please refer to ApCoCoAServer for results of computation. --For Bertini output files please refer to ApCoCoA directory/Bertini. |
See Also |