Difference between revisions of "ApCoCoA-1:Bertini.BZCSolve"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Bertini.BZCSolve</title> | <title>Bertini.BZCSolve</title> | ||
| − | <short_description>Solves zero dimensional homogeneous or non-homogeneous polynomial | + | <short_description>Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with user defined configurations.</short_description> |
<syntax> | <syntax> | ||
| − | Bertini.BZCSolve( | + | Bertini.BZCSolve(P:LIST, SysTyp:STRING , ConfigSet:LIST):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
| Line 9: | Line 9: | ||
<itemize> | <itemize> | ||
| − | <item>@param <em> | + | <item>@param <em>P</em>: List of polynomials of the system.</item> |
| − | <item>@param <em>SysTyp</em>: Type of polynomials in the | + | <item>@param <em>SysTyp</em>: Type of polynomials in the List P. Homogeneous (<tt><quotes>hom</quotes></tt>) or non-homogeneous (<tt><quotes>Nhom</quotes></tt>).</item> |
| − | <item>@param <em>ConfigSet</em>: List of strings representing configurations to be used by | + | <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. 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 the finite (or real) solutions of the polynomial system.</item> | + | <item>@return A list of lists containing the finite (or real) solutions of the polynomial system P.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | -- | + | -- An example of 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. | + | -- We want to solve the zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0, for fixed higher precision. |
| − | Use S ::= QQ[x,y]; | + | Use S ::= QQ[x,y]; |
| − | + | P := [x^2+y^2-5,xy-2]; | |
SysTyp := <quotes>Nhom</quotes>; | SysTyp := <quotes>Nhom</quotes>; | ||
ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; | ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; | ||
-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | Bertini.BZCSolve( | + | Bertini.BZCSolve(P,SysTyp,ConfigSet); |
| − | -- And we achieve a list of lists containing all finite solutions | + | -- And we achieve a list of lists containing all finite solutions. |
---------------------------------------- | ---------------------------------------- | ||
[[Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, | [[Vector(500000000000000870080079571456753631209/500000000000000000000000000000000000000, | ||
| Line 49: | Line 49: | ||
-409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000)]] | -409661331378413177493500945204322606473/250000000000000000000000000000000000000000000000000000)]] | ||
| − | --For other Bertini output files please refer to | + | --The elements of lists are vectors. Each vector represents a complex number. For example Vector(5000/1000,-4150/1000) represents the complex number 5000/1000-4150/1000i |
| + | --For other Bertini output files please refer to ApCoCoA directory/Bertini. | ||
</example> | </example> | ||
<example> | <example> | ||
| − | -- | + | -- An example of 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. | + | -- We want to solve the zero dimensional homogenous system x^2-z^2=0, xy-z^2=0, for fixed higher precision. |
| − | Use S ::= QQ[x,y]; | + | Use S ::= QQ[x,y]; |
| − | + | P := [x^2-z^2, xy-z^2]; | |
SysTyp := <quotes>hom</quotes>; | SysTyp := <quotes>hom</quotes>; | ||
ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; | ConfigSet := [<quotes>MPTYPE: 1</quotes>, <quotes>PRECISION: 128</quotes>]; | ||
-- Then we compute the solution with | -- Then we compute the solution with | ||
| − | Bertini.BZCSolve( | + | Bertini.BZCSolve(P,SysTyp,ConfigSet); |
| − | -- And we achieve a list of lists containing all real solutions | + | -- And we achieve a list of lists containing all real solutions. |
---------------------------------------- | ---------------------------------------- | ||
[[-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | [[-1121226775607053112950715616047234987919/100000000000000000000000000000000000000000, | ||
| Line 80: | Line 81: | ||
-4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000]] | -4210800092649494941547012623104854361/31250000000000000000000000000000000000000000000000]] | ||
| − | --For other Bertini output files please refer to | + | --For other Bertini output files please refer to ApCoCoA directory/Bertini. |
</example> | </example> | ||
Revision as of 09:12, 12 May 2010
Bertini.BZCSolve
Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with user defined configurations.
Syntax
Bertini.BZCSolve(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.
@param P: List of polynomials of the system.
@param SysTyp: Type of polynomials in the List P. Homogeneous ("hom") or non-homogeneous ("Nhom").
@param ConfigSet: List of strings representing configurations to be used. Bertini uses multiple configuration settings. These configurations should be provided by the user. For details about configuration settings see Bertini manual http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf.
@return A list of lists containing the finite (or real) solutions of the polynomial system P.
Example
-- An example of zero dimensional Non-homogenous solving with fixed higher precision. -- We want to solve the zero dimensional non-homogenous system x^2+y^2-5=0, xy-2=0, for fixed higher precision. Use S ::= QQ[x,y]; P := [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(P,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)]] --The elements of lists are vectors. Each vector represents a complex number. For example Vector(5000/1000,-4150/1000) represents the complex number 5000/1000-4150/1000i --For other Bertini output files please refer to ApCoCoA directory/Bertini.
Example
-- An example of zero dimensional homogenous solving with fixed higher precision -- We want to solve the zero dimensional homogenous system x^2-z^2=0, xy-z^2=0, for fixed higher precision. Use S ::= QQ[x,y]; P := [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(P,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 ApCoCoA directory/Bertini.
See also
