Difference between revisions of "ApCoCoA-1:Bertini.BPCSolve"
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| + | This function uses total degree homotopy to find all isolated solutions of a zero dimensional system of polynomial equaions. It enables you to use all kinds of user configurations provided by Bertini. Please read about configuration settings provided in Bertini manual. The system of polynomials may be homogeneous or nonhomogeneous. For homogeneous polynomial system the output will be the list of all real solutions and for nonhomogeneous system the output will be the list of all finite solutions. | ||
<itemize> | <itemize> | ||
<item>@param <em>P</em>: List of polynomials of the given system.</item> | <item>@param <em>P</em>: List of polynomials of the given system.</item> | ||
Revision as of 10:37, 13 May 2010
Bertini.BPCSolve
Find witness point supersets of a positive dimensional homogeneous or non-homogeneous polynomial systems of equations.
Syntax
Bertini.BPCSolve(P: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.
This function uses total degree homotopy to find all isolated solutions of a zero dimensional system of polynomial equaions. It enables you to use all kinds of user configurations provided by Bertini. Please read about configuration settings provided in Bertini manual. The system of polynomials may be homogeneous or nonhomogeneous. For homogeneous polynomial system the output will be the list of all real solutions and for nonhomogeneous system the output will be the list of all finite solutions.
@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
-- An example of homogenous positive dimensional solving with user configurations. -- We want to solve a positive dimensional homogenous polynomial system x^2-wy=0, x^3-zw^2=0, for fixed higher precision. Use S ::= QQ[x,y,z,w]; P := [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(P,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 Bertini output files please refer to ApCoCoA directory/Bertini.
See also
