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

From ApCoCoAWiki
Line 1: Line 1:
 
<command>
 
<command>
 
<title>Bertini.BPCSolve</title>
 
<title>Bertini.BPCSolve</title>
−
<short_description>Solves, by finding witness point supersets, a positive dimensional homogeneous or non-homogeneous polynomial systems with user defined configurations. You can also use this function for sampling. </short_description>
+
<short_description> find witness point supersets of a positive dimensional homogeneous or non-homogeneous polynomial systems of equations. </short_description>
 
<syntax>
 
<syntax>
 
Bertini.BPCSolve(M:LIST, SysTyp:STRING ,  ConfigSet:LIST):LIST
 
Bertini.BPCSolve(M:LIST, SysTyp:STRING ,  ConfigSet:LIST):LIST
 
</syntax>
 
</syntax>
 
<description>
 
<description>
−
<em>Please note:</em>
 
−
Due to a Bug in Bertini.exe. Use of this function for doing sampling is not working at the moment. Sorry for inconvienience.
 
  
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.  
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.  
 
<par/>
 
<par/>
−
<em>Please note:</em> For <em>sampling</em> you need to write (or generate by a positive dimensional run) the witness data file and save it with the name <quotes>witness_data</quotes> in Bertini directory (.../ApCoCoA-1.2/Bertini/), Otherwise you will get an error message. 
 
  
 
<itemize>
 
<itemize>
−
<item>@param <em>M</em>: List of polynomials in the system.</item>
+
<item>@param <em>P</em>: List of polynomials of the given system.</item>
  
−
<item>@param <em>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt>hom</tt>) or nonhomogeneous (<tt>Nhom</tt>).</item>
+
<item>@param <em>SysTyp</em>: Type of polynomials in the system P. Homogeneous (<tt><quotes>hom</quotes></tt>) or nonhomogeneous (<tt><quotes>Nhom</quotes></tt>).</item>
  
−
<item>@param <em>ConfigSet</em>: List of strings representing Configurations to be used by Bertini. For details about configuration settings see Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item>
+
<item>@param <em>ConfigSet</em>: List of strings representing configurations to be used. Bertini uses multiple configuration settings. These configurations should be provided by the user. If you want to use default configurations then set ConfigSet := [<quotes>TRACKTYPE: 1</quotes>]. If you want to provide specific configurations then simply add them to ConfigSet. For details about configuration settings see Bertini manual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>.</item>
 
<item>@return A list of lists containing witness point supersets.</item>
 
<item>@return A list of lists containing witness point supersets.</item>
 
</itemize>
 
</itemize>
 
   
 
   
 +
<example>
 +
-- An example of homogeneous positive dimensional solving with default configurations.
 +
-- We want to solve a positive dimensional homogeneous system x^2-wy=0, x^3-zw^2=0.
 +
 +
Use S ::= QQ[x,y,z,w];       
 +
P := [x^2-wy, x^3-zw^2];
 +
SysTyp := <quotes>hom</quotes>;
 +
ConfigSet := [<quotes>TRACKTYPE: 1</quotes>];
 +
 +
-- Then we compute the solution with
 +
Bertini.BPCSolve(P,SysTyp,ConfigSet);
 +
 +
-- And we achieve a list of lists containing witness point supersets:
 +
----------------------------------------
 +
[
 +
[
 +
Vector(-755572432434347/12500000000000000, 1212469385646449/500000000000000000),
 +
Vector(1298004943638751/5000000000000000, -1142577751598529/10000000000000000),
 +
Vector(-2342040006871913/2500000000000000, 1179799639878209/1250000000000000),
 +
Vector(609385691937087/50000000000000000, 211745411898973/50000000000000000)
 +
],
 +
[
 +
Vector(1261061851901631/2500000000000000, 2488819338268271/5000000000000000),
 +
Vector(2282600091308383/5000000000000000, -1003166917277761/5000000000000000),
 +
Vector(-1266611634699783/100000000000000000, -3506599942546397/10000000000000000),
 +
Vector(-245572945934717/625000000000000, 2318280651577719/2500000000000000)
 +
],
 +
[
 +
Vector(-5499850009487371/10000000000000000, -1238476107570149/1000000000000000),
 +
Vector(1731610073705601/2000000000000000, -4674149620192353/10000000000000000),
 +
Vector(966993267243377/2500000000000000, 1501592012502773/2500000000000000),
 +
Vector(-1758972965024007/1000000000000000, 6238313035434359/10000000000000000)
 +
],
 +
[
 +
Vector(-1674674005500441/50000000000000000000000000000000, -139223041258509/4000000000000000000000000000000),
 +
Vector(2733406006983317/10000000000000000, -210607026124287/2000000000000000),
 +
Vector(-918496799516071/1000000000000000, 1142768401415781/1250000000000000),
 +
Vector(13944005158723/1250000000000000000000000000000, -3407948311604289/100000000000000000000000000000000)
 +
]
 +
]
 +
 +
 +
--For Bertini output files please refer to ApCoCoA directory/Bertini.
 +
</example>
 +
 +
 
<example>
 
<example>
 
-- Homogenous positive dimensional solving with User Configurations.
 
-- Homogenous positive dimensional solving with User Configurations.
Line 72: Line 115:
 
</example>
 
</example>
 
   
 
   
−
<example>
 
−
-- Sampling example
 
−
-- We want to solve 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];            --  Define appropriate ring
 
−
M := [(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 := <quotes>Nhom</quotes>;
 
−
ConfigSet := [<quotes>TRACKTYPE: 2</quotes>];
 
−
-- Save the file witness_data in Bertini directory (.../ApCoCoA-1.2/Bertini/). In this exammple we can use the following file.
 
−
 
−
4
 
−
3
 
−
1
 
−
2
 
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−
 
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4
 
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11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616
 
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2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808
 
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10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464
 
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2 1
 
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0 0
 
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1 4
 
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-968243920182752810821779675191937154181031805553599430760410790893393893116405891108811023162549190408504578231574853416140063932385133202033817346803324682775169132309096484271235910471095711063763245650830821405478244198574325425961287208139587864887965330899175198233062394106659663769049862725252463065901/1250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 7311448006747174192903870686080986201603570634181979069042325989088674754451674166686186153777478629857231244380836956378319003348458183094017826098813908997856092067894677751943051826703606646559539104827622717887029715132051365308596372917022150210107188206428051608136372281535503688906342433904643616771527/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 
−
8225965631495818775625604910822632178889629607931467802581947799486865970077010226487396195763221013502040298686845864405840403610330101152920253551663127354153216776446447748535275609487417477159902638344038748257483232527836356100084543225641891923114013960712341497180676457438814924630583696883652159074123/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 3369921357675189344659646312345926612831407625020030534484287891380530023226836051480703461860785294504499598322039429175881460045201833218572483567855581868080227490775833842860583254529488427317780230576466793391749753981469292188739508381453460825704097837801518452437000083304745293511930362039084834252987/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 
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7921378104275272870884228085501960605190566842222830914021073489806145133437726580507316027770895262159309477282025747538029253421216755381610040358657703607571289229427837402727465072761288976988752291301784480709516089189769951524046692059540321875602293662280512977357138717130028926249453565862522286450963/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 2621186393629176256455025002725546705748359086252815266486799636524328387484388619941196114168224017572862907686667931374973233203031063734677994150031175572107866633678109080187097699259059101709171768835463138982419283161487734312114108898803653521684084808234702174440049286517767880932623388068448805148713/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 
−
 
−
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
 
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0 4
 
−
 
−
4
 
−
4028259749117460225/18446744073709551616 -4330798452886879565/36893488147419103232
 
−
11914445949293424397/73786976294838206464 10011862545781538653/18446744073709551616
 
−
2033170931026697119/18446744073709551616 4595823280080588459/9223372036854775808
 
−
10271323522064441169/18446744073709551616 -16068244986954793375/73786976294838206464
 
−
 
−
 
−
 
−
-- Then we compute the solution with
 
−
$Bertini.BPCSolve(M,SysTyp,ConfigSet);
 
−
 
−
 
−
 
−
--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
 
−
</example>
 
  
  

Revision as of 13:10, 12 May 2010

Bertini.BPCSolve

find witness point supersets of a positive dimensional homogeneous or non-homogeneous polynomial systems of equations.

Syntax

Bertini.BPCSolve(M:LIST, SysTyp:STRING ,  ConfigSet:LIST):LIST

Description


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.


  • @param P: List of polynomials of the given system.

  • @param SysTyp: Type of polynomials in the system P. Homogeneous ("hom") or nonhomogeneous ("Nhom").

  • @param ConfigSet: List of strings representing configurations to be used. Bertini uses multiple configuration settings. These configurations should be provided by the user. If you want to use default configurations then set ConfigSet := ["TRACKTYPE: 1"]. If you want to provide specific configurations then simply add them to ConfigSet. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.

  • @return A list of lists containing witness point supersets.

Example

-- An example of homogeneous positive dimensional solving with default configurations.
-- We want to solve a positive dimensional homogeneous system x^2-wy=0, x^3-zw^2=0.

Use S ::= QQ[x,y,z,w];        
P := [x^2-wy, x^3-zw^2];
SysTyp := <quotes>hom</quotes>;
ConfigSet := [<quotes>TRACKTYPE: 1</quotes>];

-- Then we compute the solution with
Bertini.BPCSolve(P,SysTyp,ConfigSet);

-- And we achieve a list of lists containing witness point supersets:
----------------------------------------
[
[
Vector(-755572432434347/12500000000000000, 1212469385646449/500000000000000000),
 Vector(1298004943638751/5000000000000000, -1142577751598529/10000000000000000), 
Vector(-2342040006871913/2500000000000000, 1179799639878209/1250000000000000),
 Vector(609385691937087/50000000000000000, 211745411898973/50000000000000000)
],
 [
Vector(1261061851901631/2500000000000000, 2488819338268271/5000000000000000),
 Vector(2282600091308383/5000000000000000, -1003166917277761/5000000000000000),
 Vector(-1266611634699783/100000000000000000, -3506599942546397/10000000000000000),
 Vector(-245572945934717/625000000000000, 2318280651577719/2500000000000000)
],
 [
Vector(-5499850009487371/10000000000000000, -1238476107570149/1000000000000000), 
Vector(1731610073705601/2000000000000000, -4674149620192353/10000000000000000),
 Vector(966993267243377/2500000000000000, 1501592012502773/2500000000000000),
 Vector(-1758972965024007/1000000000000000, 6238313035434359/10000000000000000)
], 
[
Vector(-1674674005500441/50000000000000000000000000000000, -139223041258509/4000000000000000000000000000000),
 Vector(2733406006983317/10000000000000000, -210607026124287/2000000000000000),
 Vector(-918496799516071/1000000000000000, 1142768401415781/1250000000000000),
 Vector(13944005158723/1250000000000000000000000000000, -3407948311604289/100000000000000000000000000000000)
]
]


--For Bertini output files please refer to ApCoCoA directory/Bertini.


Example

-- Homogenous positive dimensional solving with User Configurations.
-- We want to solve positive dimensional homogenous system x^2-wy=0, x^3-zw^2=0, for fixed higher precision.

Use S ::= QQ[x,y,z,w];             --  Define appropriate ring 
M := [x^2-wy, x^3-zw^2];
SysTyp := <quotes>hom</quotes>;
ConfigSet := [<quotes>TRACKTYPE: 1</quotes>, <quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>];

-- Then we compute the solution with
$Bertini.BPCSolve(M,SysTyp,ConfigSet);

-- And we achieve a list of lists containing witness point supersets:
----------------------------------------
[[Vector(-3789467495454911613823851164626681463651/10000000000000000000000000000000000000000,
 1200734725407166211921788902942849185503/1000000000000000000000000000000000000000),
 Vector(-246001393466366309986866914393676541221/125000000000000000000000000000000000000,
 -279722792064708736248520972068122497257/500000000000000000000000000000000000000),
 Vector(4083988954899604873030242779673433634501/5000000000000000000000000000000000000000,
 -1611351492565067582850937617799756261201/500000000000000000000000000000000000000),
 Vector(7319342772891341731507480575523588267957/10000000000000000000000000000000000000000,
 19870617690036348352514491511362841819/78125000000000000000000000000000000000)],
 [Vector(3048866987455758258878751406208402973051/10000000000000000000000000000000000000000,
 -2898035102105205140344370335032912017083/5000000000000000000000000000000000000000),
 Vector(-5539460172405722710678127397246600460333/10000000000000000000000000000000000000000,
 626442207647239461619975960511872586713/5000000000000000000000000000000000000000),
 Vector(986380263365471019267174885767305829617/2500000000000000000000000000000000000000,
 736987741407866469670001545005869554379/2500000000000000000000000000000000000000),
 Vector(1400107689781321399920833229898425820819/5000000000000000000000000000000000000000,
 2191732091470400698700321524968735909/3125000000000000000000000000000000000)],
 [Vector(354996962262331142136973979259558150991/400000000000000000000000000000000000000,
 1816598489416934847206968307485748462499/1000000000000000000000000000000000000000),
 Vector(1967511413109990263685197237623604100867/1000000000000000000000000000000000000000,
 1727412577136936817572423873769337954923/1000000000000000000000000000000000000000),
 Vector(803360350133974614907008034061208613233/250000000000000000000000000000000000000,
 1081558694105850161535777129438751374871/1000000000000000000000000000000000000000),
 Vector(9143301947447558293770285751969676840889/100000000000000000000000000000000000000000,
 155856385824660750993297595625859090071/100000000000000000000000000000000000000)],
 [Vector(-825065032224960020386592540685453030181/50000000000000000000000000000000000000000000000000000000000000000000000000,
 -870815934189224420445215323683468742119/50000000000000000000000000000000000000000000000000000000000000000000000000),
 Vector(-2670487187708557160891411850766573823343/1000000000000000000000000000000000000000,
 2412331000084757896737353053811227631099/2500000000000000000000000000000000000000),
 Vector(-2260897026243730139776564722393608088003/1000000000000000000000000000000000000000,
 -5881973549623185468407939053314195499303/10000000000000000000000000000000000000000),
 Vector(-6276316819449156764984023481918376370437/1000000000000000000000000000000000000000000000000000000000000000000000000000,
 -457717591175786069863350181676761297761/25000000000000000000000000000000000000000000000000000000000000000000000000)]]

--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).




See also

Introduction to CoCoAServer

Bertini.BSolve

Bertini.BPMCSolve




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