Difference between revisions of "ApCoCoA-1:Bertini.BPMCSolve"

From ApCoCoAWiki
Line 37: Line 37:
 
           [<quotes>1.7645087</quotes>, <quotes>-0.85807828</quotes>],[<quotes>2.1389007</quotes>, <quotes>-1.7258994</quotes>]]];
 
           [<quotes>1.7645087</quotes>, <quotes>-0.85807828</quotes>],[<quotes>2.1389007</quotes>, <quotes>-1.7258994</quotes>]]];
 
ConfigSet := [<quotes>TRACKTYPE: 3</quotes>];
 
ConfigSet := [<quotes>TRACKTYPE: 3</quotes>];
−
-- Save the file witness_data in Bertini directory (.../ApCoCoA-1.2/Bertini/).  
+
-- Save the file witness_data in Bertini directory (.../ApCoCoA-1.2/Bertini/). In this example we can use the following file.
 +
 
 +
4
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3
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1
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1
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-1
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0
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1 2
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3.135235355709609e-02 -1.108624821570082e-03
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3.352628225992291e-01 -9.416021668731618e-01
 +
 
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2
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3
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4
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1.000000000000000e+00 0.000000000000000e+00
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0.000000000000000e+00 0.000000000000000e+00
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0.000000000000000e+00 0.000000000000000e+00
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0.000000000000000e+00 0.000000000000000e+00
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0.000000000000000e+00 0.000000000000000e+00
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2 4
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6.253261093686115e-01 5.160281388948399e-01
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3.248357459173907e-01 6.913166635962354e-01
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4
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-4.050217717838341e-01 1.446567392472682e-01
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3.617000633187840e-01 -3.970690087541858e-01
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 +
2 1
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-6.864117874802172e-03 2.043854826670122e-02
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-9.696616879246138e-01 -2.434981737133552e-01
 +
 
 +
3
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1
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4
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1.000000000000000e+00 0.000000000000000e+00
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0.000000000000000e+00 0.000000000000000e+00
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0.000000000000000e+00 0.000000000000000e+00
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0.000000000000000e+00 0.000000000000000e+00
 +
 
 +
0.000000000000000e+00 0.000000000000000e+00
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1 4
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6.253261093686115e-01 5.160281388948399e-01
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-3.897348247733157e-01 -1.443827461944881e-02
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-7.153755062550494e-02 -1.821527150953511e-01
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3.770447321019952e-01 1.006009772497220e-01
 +
 
 +
4
 +
-4.050217717838341e-01 1.446567392472682e-01
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-1.883638511032934e-01 -2.641793382250678e-01
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-1.087274806186790e-01 6.398810283673082e-01
 +
3.617000633187840e-01 -3.970690087541858e-01
 +
 
 +
3 0
 +
 
 +
4
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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
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-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
 
-- Then we compute the witness point super sets with

Revision as of 08:14, 8 July 2009

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
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3.402820445975955e-01 1.138623375499443e+00
52
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3.402820446021391e-01 1.138623375496336e+00
5.764108382960922e+03
0
1.734873693485822e-04
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0
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-1.569926571547650e-01 5.656479633810877e-01
1.561095057524474e+05
0
6.405759823400904e-06
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1
0
2
6
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5.627895823455601e-01 8.041159177275276e-01
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-3.519186615528762e-01 -1.081201952108912e-01
5.627895823462294e-01 8.041159177281618e-01
4.075142019924497e+02
0
2.453902207851219e-03
0.000000000000000e+00
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1
0
52
1.898610234488268e-03 -4.421408852386620e-01
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-5.673332706884610e-01 -1.493349283113407e+00
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1.898610251798937e-03 -4.421408852387619e-01
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-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
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1.102900748495981e+00 -1.041829167553521e-01
52
-6.229761033006948e-01 1.684523738675710e-02
-4.093008530286687e-01 -6.343477292447014e-01
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5.398183516037490e+02
0
1.852474998356568e-03
0.000000000000000e+00
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1
3
52
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1.246778576804046e+04
0
8.020670378884510e-05
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1
3
52
-3.488298126628631e-01 -3.555966140542573e-01
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-1.744149063314315e-01 -1.777983070271286e-01
6.675888411742337e-01 1.040403031139058e+00
52
-3.488298126620772e-01 -3.555966140539323e-01
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1.340353341821709e-03
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52
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1.983696430855635e+06
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8.849647529365448e-07
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1
3
3
1
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-1.188004121674938e+00 -4.270274706990106e-01
7.992947434695146e+02
0
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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
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0.000000000000000e+00 0.000000000000000e+00

0.000000000000000e+00 0.000000000000000e+00
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-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

Introduction to CoCoAServer

Bertini.BSolve

Bertini.BPCSolve




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