# Difference between revisions of "ApCoCoA-1:Bertini.BUHSolve"

Line 7: | Line 7: | ||

</syntax> | </syntax> | ||

<description> | <description> | ||

− | + | <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>M</em>: List of polynomials in the system to be solved. | + | <itemize> |

+ | <item>@param <em>M</em>: List of polynomials in the system to be solved.</item> | ||

− | <em>SSys</em>: List of polynomials in the start system for homotopy. | + | <item><em>SSys</em>: List of polynomials in the start system for homotopy.</item> |

− | <em>Gamma</em>: Complex number in the form "a+b*I" ( e.g. "0.8 - 1.2*I" ). | + | <item><em>Gamma</em>: Complex number in the form "a+b*I" ( e.g. "0.8 - 1.2*I" ).</item> |

− | <em>SSol</em>: List of lists containing the start solution for the homotopy. Further, the elements of Lists are strings. | + | <item><em>SSol</em>: List of lists containing the start solution for the homotopy. Further, the elements of Lists are strings.</item> |

− | |||

− | |||

+ | <item><em>ConfigSet</em>: List of strings representing Configurations to be used by bertini. Note that if you want to use default configraions then the ConfigSet := ["USERHOMOTOPY: 1"], otherwise add more configurations in ConfigSet accordingly. For details about configuration settings see Bertini mannual <tt>http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf</tt>. </item> | ||

+ | </itemize> | ||

<example> | <example> | ||

Line 55: | Line 56: | ||

<type>cocoaserver</type> | <type>cocoaserver</type> | ||

</types> | </types> | ||

+ | |||

+ | <see>Bertini.BCMSolve</see> | ||

+ | <see>Bertini.BCSolve</see> | ||

+ | <see>Bertini.BMSolve</see> | ||

+ | <see>Bertini.BSolve</see> | ||

+ | |||

<key>buhsolve</key> | <key>buhsolve</key> | ||

+ | <key>bertini.buhsolve</key> | ||

<key>solve zero dimensional non-homogeneous polynomial system by user defined homotopy</key> | <key>solve zero dimensional non-homogeneous polynomial system by user defined homotopy</key> | ||

− | |||

<wiki-category>Package_bertini</wiki-category> | <wiki-category>Package_bertini</wiki-category> | ||

</command> | </command> |

## Revision as of 10:40, 23 April 2009

## BUHSolve

Solves zero dimensional non-homogeneous polynomial system by user definged homotopy.

### Syntax

Bertini.BUHSolve(M:LIST, SSys:LIST, Gamma:STRING, SSol:LIST OF LIST, 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 to be solved.*SSys*: List of polynomials in the start system for homotopy.*Gamma*: Complex number in the form "a+b*I" ( e.g. "0.8 - 1.2*I" ).*SSol*: List of lists containing the start solution for the homotopy. Further, the elements of Lists are strings.*ConfigSet*: List of strings representing Configurations to be used by bertini. Note that if you want to use default configraions then the ConfigSet := ["USERHOMOTOPY: 1"], otherwise add more configurations in ConfigSet accordingly. For details about configuration settings see Bertini mannual`http://www.nd.edu/~sommese/bertini/BertiniUsersManual.pdf`.

#### Example

-- We want to solve the system x^2-1=0, y^2-1=0, where Gamma=0.8-1.2I. -- The two start solutions for the homotopy are [[-1.0, 0.0 ],[-1.0,0.0]] and [[1.0, 0.0],[1.0,0.0]]. -- The start system for the homotopy is x^2=0, y^2=0. Use S ::= QQ[x,y]; -- Define appropriate ring M := [x^2-1, y^2-1]; SSys := [x^2,y^2]; Gamma := "0.8 - 1.2*I"; SSol := [[["-1.0", "0.0"], ["-1.0","0.0"]],[["1.0", "0.0"],["1.0","0.0"]]]; ConfigSet := ["USERHOMOTOPY: 12"]; -- Then we compute the solution with $Bertini.BUHSolve(M, SSys, Gamma, SSol, ConfigSet); -- And we achieve: ---------------------------------------- The number of real finite solutions are: 2 The real finite solutions are: -1.000000000000043e+00 2.460120586181259e-14 -1.000000000000043e+00 2.460120586181259e-14 1.000000000000043e+00 -2.460120586181259e-14 1.000000000000043e+00 -2.460120586181259e-14 For summary of all solutions refer to ApCoCoAServer