ApCoCoA-1:Bertini.BPCSolve
From ApCoCoAWiki
Revision as of 08:35, 30 November 2009 by 132.231.54.1 (talk)
Bertini.BPCSolve
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.
Syntax
Bertini.BPCSolve(M:LIST, SysTyp:STRING , ConfigSet:LIST):LIST
Description
Please note:
Due to a Bug in Bertini.exe. Use of this function for doing sampling 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: For sampling you need to write (or generate by a positive dimensional run) the witness data 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 nonhomogeneous (Nhom).
@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.
@return A list of lists containing witness point supersets.
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/).
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 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 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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/).
See also
