-- An example of sampling using default configurations
-- We want to sample positive dimensional homogenous system (y-x^2)*(x^2+y^2+z^2-1)*(x-5), (z-x^3)*(x^2+y^2+z^2-1)*(y-5),
-- (y-x^2)*(z-x^3)*(x^2+y^2+z^2-1)*(z-5).
Use S ::= QQ[x,y,z];
P := [(y-x^2)*(x^2+y^2+z^2-1)*(x-5), (z-x^3)*(x^2+y^2+z^2-1)*(y-5),(y-x^2)*(z-x^3)*(x^2+y^2+z^2-1)*(z-5)];
SysTyp := "Nhom";
ConfigSet := ["TRACKTYPE: 2"];
-- Save the file 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 compute the sample points with
Bertini.BPCSSolve(P,SysTyp,ConfigSet);
--Then you need to interact with ApCoCoAServer. At this stage the ApCoCoAServer will look like this
NOTE: You have requested to use adaptive path tracking. Please make sure that you have
setup the following tolerances appropriately:
COEFFBOUND: 1.060000000000e+02, DEGREEBOUND: 8.000000000000e+00
AMPSAFETYDIGITS1: 1, AMPSAFETYDIGITS2: 1, AMPMAXPREC: 1024
*************** Components to Sample ****************
Dimension 2: 1 classified component
-----------------------------------------------------
degree 2: 1 component
Dimension 1: 4 classified components
-----------------------------------------------------
degree 1: 3 components
degree 3: 1 component
Dimension 0: 1 classified component
-----------------------------------------------------
degree 1: 1 component
Please select a dimension to sample (-1 to quit):
-- Now depending on the information in ApCoCoAServer you need to select a dimension to sample. Lets enter 2 (for dimension 2)
-- At this stage you will have the following information in ApCoCoAServer
Dimension 2: 1 classified component
-----------------------------------------------------
degree 2: 1 component
Please select a component to sample (-1 to quit):
-- According to the information in ApCoCoAServer dimensioin 2 has 1 classified component
-- Now enter 0 for first component (note that 0 means first component, 1 means second component and so on)
-- At this stage you will get the following message in ApCoCoAServer.
How many points you would like to find on component 0 of dimension 2(-1 to quit)?
-- Lets say we need two points. Then we enter 2.
-- Now you will have the following message in ApCoCoAServer.
Enter 0 to write the sample points to a file or enter 1 to display the sample points to the screen:
--Definitely we enter 0. Because we want sample points in a file.
--The next message in ApCoCoAServer will be
Enter the name of the file where to write the sample points (max of 255 characters):
--Enter the name "witness_data" for the file. This is important. If you provide some other name
--then you will get error message in ApCoCoA GUI. Now you are done and you can see your
--required points as list of lists in ApCoCoA GUI.
---------------------------------------------------------------
[
[
Vector(1757273644596243375574545953819515856489/100000000000000000000000000000000000,
8147772211058790989036635734369200777823/1000000000000000000000000000000000000),
Vector(-431733868086111204913711309223667436531/250000000000000000000000000000000000,
-37962521351941262128928875924787458113/2000000000000000000000000000000000),
Vector(-1557380603151899455989605438122949238809/100000000000000000000000000000000000,
564916712400652233062432018034019557871/50000000000000000000000000000000000)
],
[
Vector(-121943356274388147122353428227028494517/6250000000000000000000000000000000,
1360624366795248157000895588285686343567/100000000000000000000000000000000000),
Vector(269101922754170957542913598304064433393/12500000000000000000000000000000000,
65533729956025537516221610150609783991/6250000000000000000000000000000000),
Vector(-845765805387772422259623073262578114251/500000000000000000000000000000000000,
-1174655199638212258677283490719018859963/50000000000000000000000000000000000)
]
]
--For Bertini output files please refer to ApCoCoA directory/Bertini.
|