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

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<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>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. | ||

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− | + | This function solves a polynomial system of equations using multihomogeneous homotopy. The polynomial system of equations must be quadratic. If the system has <tt>N</tt> variables then multihomogeneous homotopy will introduce <tt>N</tt> homogeneous variables to solve the system. It uses total degree homotopy to find all isolated solutions and default configurations provided by Bertini. The system of polynomials should be non-homogeneous. The output will be the list of all finite solutions. | |

− | This function solves a polynomial system of equations using multihomogeneous homotopy. The system of | ||

<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 10:41, 25 May 2010

## Bertini.BMSolve

Solves a zero dimensional non-homogeneous polynomial system using multi-homogenization and default configurations.

### Syntax

Bertini.BMSolve(P: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 solves a polynomial system of equations using multihomogeneous homotopy. The polynomial system of equations must be quadratic. If the system has `N` variables then multihomogeneous homotopy will introduce `N` homogeneous variables to solve the system. It uses total degree homotopy to find all isolated solutions and default configurations provided by Bertini. The system of polynomials should be non-homogeneous. The output will be the list of all finite solutions.

@param

*P*: List of polynomials of the given system.@return A list of lists containing the finite solutions of the polynomial system P.

#### Example

-- We want to solve the non-homogenous polynomial system x[1]^2+x[2]^2-5=0, x[1]x[2]-2=0, using multi-homogenization. Use S ::= QQ[x[1..2]]; P := [x[1]^2+x[2]^2-5, x[1]x[2]-2]; -- Then we compute the solution with Bertini.BMSolve(P); -- And we achieve a list of lists containing finite solutions. ---------------------------------------- [ [ Vector(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000), Vector(1999999999999971/1000000000000000, 4135565953005217/100000000000000000000000000000) ], [ Vector(1000000000000003/500000000000000, 2604577577014449/50000000000000000000000000000), Vector(500000000000001/500000000000000, -619892334722183/25000000000000000000000000000) ], [ Vector(-2, 1724810333092189/1000000000000000000000000000000), Vector(-500000000000001/500000000000000, -355984244774691/200000000000000000000000000000) ], [ Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000), Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000) ] ] --For Bertini output files refer to ApCoCoA directory/Bertini. ------------------------------------------

#### Example

-- We want to solve the non-homogenous polynomial system (29/16)z[1]^3 - 2z[1]z[2], z[2] - z[1]^2, using multi-homogenization. Use S ::= QQ[z[1..2]]; P := [(29/16)z[1]^3 - 2z[1]z[2], z[2] - z[1]^2]; -- Then we compute the solution with Bertini.BMSolve(P); -- And we achieve a list of lists containing finite solutions. ---------------------------------------- [ [ Vector(-1754775022937541/1000000000000000000000000000, -6761671559595563/10000000000000000000000000000), Vector(947843957587963/25000000000000000000000000000, 623113227620389/5000000000000000000000000000) ], [ Vector(-85573832182963743719/50000000000000000000000000000000, -89829012439528360233/250000000000000000000000000000000), Vector(-230164951873451072943/2500000000000000000000000000000000, 298328875801698252183/10000000000000000000000000000000000) ], [ Vector(-1479267029218781/1000000000000000000000000000, -5565180110034249/10000000000000000000000000000), Vector(-4881416330105221/50000000000000000000000000000, 856957743028027/5000000000000000000000000000) ] ] --For Bertini output files refer to ApCoCoA directory/Bertini. ------------------------------------------

### See also

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