Difference between revisions of "ApCoCoA-1:Bertini.BZCSolve"
From ApCoCoAWiki
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-409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000)]] | -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000)]] | ||
</example> | </example> | ||
| + | |||
| + | |||
| + | <example> | ||
| + | -- Zero dimensional homogenous solving with fixed higher precision | ||
| + | -- We want to solve zero dimensional homogenous system x^2-z^2=0, xy-z^2=0, for fixed higher precision. | ||
| + | |||
| + | Use S ::= QQ[x,y]; -- Define appropriate ring | ||
| + | M := [x^2-z^2, xy-z^2]; | ||
| + | SysTyp := <quotes>hom</quotes>; | ||
| + | ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; | ||
| + | |||
| + | -- Then we compute the solution with | ||
| + | Bertini.BZCSolve(M,SysTyp,ConfigSet); | ||
| + | |||
| + | -- And we achieve a list of lists containing all real solutions: | ||
| + | ---------------------------------------- | ||
| + | [[-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | ||
| + | -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | ||
| + | -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000], | ||
| + | [-666269356331265789905402745641735631587/1250000000000000000000000000000000000000, | ||
| + | -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, | ||
| + | 666269356331265789905402745641735631587/1250000000000000000000000000000000000000], | ||
| + | [-1961395985465574251430275441821775811231/20000000000000000000000000000000000000000000000000000, | ||
| + | 1604689603443950100804972123829819895459/2500000000000000000000000000000000000000, | ||
| + | -9839275092234527567507618459170114455473/100000000000000000000000000000000000000000000000000000], | ||
| + | [-1197970328164235882805480928545099670003/10000000000000000000000000000000000000000000000000000, | ||
| + | 3209379206887735502321156763919697536571/5000000000000000000000000000000000000000, | ||
| + | -4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000]] | ||
| + | |||
| + | --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/). | ||
| + | </example> | ||
| + | |||
| + | |||
</description> | </description> | ||
Revision as of 11:40, 1 July 2009
Bertini.BZCSolve
Solves zero dimensional Homogeneous or Non-Homogeneous polynomial system with User Configurations.
Syntax
Bertini.BZCSolve(M:LIST, SysTyp:STRING , ConfigSet: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 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 detials about configuraion settings see Bertini mannul http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.
Example
-- Zero dimensional Non-homogenous solving with fixed higher precision -- We want to solve zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0, for fixed higher precision. Use S ::= QQ[x,y]; -- Define appropriate ring M := [x^2+y^2-5,xy-2]; SysTyp := <quotes>Nhom</quotes>; ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; -- Then we compute the solution with Bertini.BZCSolve(M,SysTyp,ConfigSet); -- And we achieve a list of lists containing all finite solutions: ---------------------------------------- [[Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, 41243336046164965623860294533917 3594181/200000000000000000000000000000000000000000000000000000), Vector(199999999999999920289038441185562687901/100000000000000000000000000000000000000, -4918613303067726249865351347506841944303/5000000000000000000000000000000000000000000000000000000)], [Vector(999999999999996907691691548150283767063/500000000000000000000000000000000000000, 4026821783991733021565024336088959292491/1000000000000000000000000000000000000000000000000000000), Vector(1000000000000008119524837615406734621127/1000000000000000000000000000000000000000, -9202828375000265851232972557923998357683/1000000000000000000000000000000000000000000000000000000)], [Vector(-1999999999999981470621955122058645854307/1000000000000000000000000000000000000000, -2219296880596437220953595963738223862847/100000000000000000000000000000000000000000000000000000), Vector(-1000000000000016429280952166817619195409/1000000000000000000000000000000000000000, 2246895233251384601549113345810086172711/100000000000000000000000000000000000000000000000000000)], [Vector(-9999999999999986714415752390569533003343/10000000000000000000000000000000000000000, 2376331150450927561422763997224327498341/1000000000000000000000000000000000000000000000000000000), Vector(-200000000000000126515279556718539177417/100000000000000000000000000000000000000, -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000)]]
Example
-- Zero dimensional homogenous solving with fixed higher precision -- We want to solve zero dimensional homogenous system x^2-z^2=0, xy-z^2=0, for fixed higher precision. Use S ::= QQ[x,y]; -- Define appropriate ring M := [x^2-z^2, xy-z^2]; SysTyp := <quotes>hom</quotes>; ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; -- Then we compute the solution with Bertini.BZCSolve(M,SysTyp,ConfigSet); -- And we achieve a list of lists containing all real solutions: ---------------------------------------- [[-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, -1121226775607053112950715616047234987919/100000000000000000000000000000000000000000], [-666269356331265789905402745641735631587/1250000000000000000000000000000000000000, -666269356331265789905402745641735631587/1250000000000000000000000000000000000000, 666269356331265789905402745641735631587/1250000000000000000000000000000000000000], [-1961395985465574251430275441821775811231/20000000000000000000000000000000000000000000000000000, 1604689603443950100804972123829819895459/2500000000000000000000000000000000000000, -9839275092234527567507618459170114455473/100000000000000000000000000000000000000000000000000000], [-1197970328164235882805480928545099670003/10000000000000000000000000000000000000000000000000000, 3209379206887735502321156763919697536571/5000000000000000000000000000000000000000, -4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000]] --For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
See also
