ApCoCoA-1:Bertini.BPMCSolve
From ApCoCoAWiki
Revision as of 08:14, 8 July 2009 by 132.231.54.1 (talk)
Bertini.BPMCSolve
Membership testing for positive dimensional homogeneous or non-homogeneous polynomial systems with default and user defined configurations.
Syntax
Bertini.BPMCSolve(M:LIST, SysTyp:STRING , MPoints:LIST, ConfigSet:LIST):LIST
Description
Please note:
Due to a Bug in Bertini.exe. This command is not working at the moment. Sorry for inconvienience.
Please note:
The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Please note: You need to write (or generate by using the function Bertini.BPCSolve) the witness date file and save it with the name "witness_data" in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message.
@param M: List of polynomials in the system.
@param SysTyp: Type of polynomials in the system. Homogeneous (hom) or non-homogeneous (Nhom).
@param MPoints: List of lists containig member points.
@param ConfigSet: List of strings representing configurations to be used by Bertini. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.
Example
-- Membership testing.
-- 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]; -- Define appropriate ring
M := [x^2+y^2+z^2-1,x^3+y^2+z^3-1,(y-x^2)*(z-x^3)(z-5)];
SysTyp := <quotes>Nhom</quotes>;
MPoints :=[[[<quotes>1.0</quotes>, <quotes>0.0</quotes>],[<quotes>0.0</quotes>, <quotes>0.0</quotes>],[<quotes>0.0</quotes>, <quotes>0.0</quotes> ]],[[<quotes>1.3650269</quotes>, <quotes>-0.31430820</quotes>],
[<quotes>1.7645087</quotes>, <quotes>-0.85807828</quotes>],[<quotes>2.1389007</quotes>, <quotes>-1.7258994</quotes>]]];
ConfigSet := [<quotes>TRACKTYPE: 3</quotes>];
-- Save the file witness_data in Bertini directory (.../ApCoCoA-1.2/Bertini/). In this example we can use the following file.
4
3
1
2
52
-1.166785212950430e+00 1.521789971835142e-01
-1.616047890597813e+00 1.058268838764849e-01
-5.961030659888400e-01 6.609460744279395e-01
3.402820445975955e-01 1.138623375499443e+00
52
-1.166785212944050e+00 1.521789971872898e-01
-1.616047890591587e+00 1.058268838859361e-01
-5.961030659786296e-01 6.609460744240216e-01
3.402820446021391e-01 1.138623375496336e+00
5.764108382960922e+03
0
1.734873693485822e-04
0.000000000000000e+00
10
1
0
52
-2.422854345162644e-01 -1.189872674924210e-01
-6.745869645545158e-01 4.545110360915127e-01
-6.872956163015966e-01 -6.172579436315559e-01
-1.569926571552054e-01 5.656479633802807e-01
52
-2.422854345172500e-01 -1.189872674937000e-01
-6.745869645535314e-01 4.545110360909158e-01
-6.872956163019345e-01 -6.172579436303723e-01
-1.569926571547650e-01 5.656479633810877e-01
1.561095057524474e+05
0
6.405759823400904e-06
0.000000000000000e+00
10
1
0
2
6
52
-7.038373231068352e-01 -2.162403904228003e-01
-4.976881440210303e-01 -1.529050464343886e-01
-3.519186615534176e-01 -1.081201952114001e-01
5.627895823455601e-01 8.041159177275276e-01
52
-7.038373231065269e-01 -2.162403904229307e-01
-4.976881440201402e-01 -1.529050464337667e-01
-3.519186615528762e-01 -1.081201952108912e-01
5.627895823462294e-01 8.041159177281618e-01
4.075142019924497e+02
0
2.453902207851219e-03
0.000000000000000e+00
10
1
0
52
1.898610234488268e-03 -4.421408852386620e-01
9.493051172441339e-04 -2.210704426193310e-01
-5.673332706884610e-01 -1.493349283113407e+00
2.373262793110350e-04 -5.526761065483275e-02
52
1.898610251798937e-03 -4.421408852387619e-01
9.493051304679831e-04 -2.210704426222535e-01
-5.673332706830064e-01 -1.493349283123950e+00
2.373262902925282e-04 -5.526761065449492e-02
3.066398663477320e+05
0
3.261154565160135e-06
0.000000000000000e+00
10
1
1
52
-6.229761033007827e-01 1.684523738679329e-02
-4.093008530287287e-01 -6.343477292447345e-01
3.992596856489433e-01 -8.227482667376285e-01
1.102900748495981e+00 -1.041829167553521e-01
52
-6.229761033006948e-01 1.684523738675710e-02
-4.093008530286687e-01 -6.343477292447014e-01
3.992596856489427e-01 -8.227482667376440e-01
1.102900748496019e+00 -1.041829167553287e-01
5.398183516037490e+02
0
1.852474998356568e-03
0.000000000000000e+00
10
1
3
52
-1.210461314997017e-01 -3.029584497165400e-01
1.783329221395743e-01 4.132877364865193e-01
-2.614892499199324e-01 -5.632996349913678e-01
3.818161428538239e-01 7.670690694284454e-01
52
-1.210461315029504e-01 -3.029584497152346e-01
1.783329221414592e-01 4.132877364863901e-01
-2.614892499195960e-01 -5.632996349922157e-01
3.818161428506615e-01 7.670690694281941e-01
1.246778576804046e+04
0
8.020670378884510e-05
0.000000000000000e+00
10
1
3
52
-3.488298126628631e-01 -3.555966140542573e-01
2.466599260139435e-01 2.514447771647409e-01
-1.744149063314315e-01 -1.777983070271286e-01
6.675888411742337e-01 1.040403031139058e+00
52
-3.488298126620772e-01 -3.555966140539323e-01
2.466599260128961e-01 2.514447771647634e-01
-1.744149063304533e-01 -1.777983070276539e-01
6.675888411754393e-01 1.040403031137790e+00
7.460719265569734e+02
0
1.340353341821709e-03
0.000000000000000e+00
10
1
2
52
-1.246393339637452e+00 3.759487591629001e-02
-1.280605664944876e+00 8.733576046642775e-01
-7.572318527678505e-01 1.771820567662229e+00
3.922399057550089e-01 2.362884789456477e+00
52
-1.246393339644282e+00 3.759487589431224e-02
-1.280605664952683e+00 8.733576046530384e-01
-7.572318527736278e-01 1.771820567660859e+00
3.922399057593087e-01 2.362884789437572e+00
1.983696430855635e+06
0
8.849647529365448e-07
0.000000000000000e+00
10
1
3
3
1
52
-2.376008243350482e+00 -8.540549413998020e-01
-1.188004121675241e+00 -4.270274706999010e-01
-1.188004121675241e+00 -4.270274706999010e-01
-1.188004121675241e+00 -4.270274706999010e-01
52
-2.376008243349693e+00 -8.540549413986449e-01
-1.188004121675527e+00 -4.270274706993148e-01
-1.188004121674908e+00 -4.270274706996682e-01
-1.188004121674938e+00 -4.270274706990106e-01
7.992947434695146e+02
0
1.251102935644591e-03
0.000000000000000e+00
10
1
0
-1
0
1 2
3.135235355709609e-02 -1.108624821570082e-03
3.352628225992291e-01 -9.416021668731618e-01
2
3
4
1.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
2 4
6.253261093686115e-01 5.160281388948399e-01
-3.897348247733157e-01 -1.443827461944881e-02
-7.153755062550494e-02 -1.821527150953511e-01
3.770447321019952e-01 1.006009772497220e-01
-2.164735341429737e-01 -2.310557712216083e-01
-1.922887028565794e-01 2.652232248569078e-01
-4.076286604189574e-01 2.069686434332095e-01
3.248357459173907e-01 6.913166635962354e-01
4
-4.050217717838341e-01 1.446567392472682e-01
-1.883638511032934e-01 -2.641793382250678e-01
-1.087274806186790e-01 6.398810283673082e-01
3.617000633187840e-01 -3.970690087541858e-01
2 1
-6.864117874802172e-03 2.043854826670122e-02
-9.696616879246138e-01 -2.434981737133552e-01
3
1
4
1.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
1 4
6.253261093686115e-01 5.160281388948399e-01
-3.897348247733157e-01 -1.443827461944881e-02
-7.153755062550494e-02 -1.821527150953511e-01
3.770447321019952e-01 1.006009772497220e-01
4
-4.050217717838341e-01 1.446567392472682e-01
-1.883638511032934e-01 -2.641793382250678e-01
-1.087274806186790e-01 6.398810283673082e-01
3.617000633187840e-01 -3.970690087541858e-01
3 0
4
1.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0.000000000000000e+00 0.000000000000000e+00
0 4
4
-4.050217717838341e-01 1.446567392472682e-01
-1.883638511032934e-01 -2.641793382250678e-01
-1.087274806186790e-01 6.398810283673082e-01
3.617000633187840e-01 -3.970690087541858e-01
-- Then we compute the witness point super sets with
$Bertini.BPMCSolve(M,SysTyp,MPoints,ConfigSet);
-- And we achieve a list of lists containing witness point supersets:
----------------------------------------
--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
See also
