Difference between revisions of "ApCoCoA-1:Bertini.BSolve"

From ApCoCoAWiki
Line 1: Line 1:
 
<command>
 
<command>
 
<title>Bertini.BSolve</title>
 
<title>Bertini.BSolve</title>
<short_description>Solves zero dimensional homogeneous or non-homogeneous polynomial systems with default configurations.</short_description>
+
<short_description>Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations.</short_description>
 
<syntax>
 
<syntax>
 
Bertini.BSolve(M:LIST, SysTyp:STRING)
 
Bertini.BSolve(M:LIST, SysTyp:STRING)
Line 9: Line 9:
  
 
<itemize>
 
<itemize>
<item>@param <em>M</em>: List of polynomials in the system.</item>
+
<item>@param <em>P</em>: List of polynomials of the given system.</item>
<item>@param <em>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt>hom</tt>) or nonhomogeneous (<tt>Nhom</tt>).</item>
+
<item>@param <em>SysTyp</em>: Type of polynomials in the list P. Homogeneous (<tt><quotes>hom</quotes></tt>) or nonhomogeneous (<tt><quotes>Nhom</quotes></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.</item>
  
Line 20: Line 20:
  
 
Use S ::= QQ[x,y];            --  Define appropriate ring  
 
Use S ::= QQ[x,y];            --  Define appropriate ring  
M := [x^2+y^2-5, xy-2];
+
P := [x^2+y^2-5, xy-2];
 
SysTyp := <quotes>Nhom</quotes>;
 
SysTyp := <quotes>Nhom</quotes>;
  
 
-- Then we compute the solution with
 
-- Then we compute the solution with
Bertini.BSolve(M,SysTyp);
+
Bertini.BSolve(P,SysTyp);
  
 
-- And we achieve a list of lists containing all finite solutions:
 
-- And we achieve a list of lists containing all finite solutions:
Line 37: Line 37:
 
Vector(-9999999999999943/10000000000000000, -2154842536286333/500000000000000000000000000000)]]
 
Vector(-9999999999999943/10000000000000000, -2154842536286333/500000000000000000000000000000)]]
  
--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
+
--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/).
 
</example>
 
</example>
 
<example>
 
<example>
Line 48: Line 48:
  
 
-- Then we compute the solution with
 
-- Then we compute the solution with
$Bertini.BSolve(M,SysTyp);
+
Bertini.BSolve(M,SysTyp);
  
 
-- And we achieve a list of lists containing all real solutions:
 
-- And we achieve a list of lists containing all real solutions:
Line 58: Line 58:
 
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]]
 
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]]
  
--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.2/Bertini/).
+
--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/).
 
------------------------------------
 
------------------------------------
 
</example>
 
</example>

Revision as of 08:17, 12 May 2010

Bertini.BSolve

Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations.

Syntax

Bertini.BSolve(M:LIST, SysTyp:STRING)

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 given system.

  • @param SysTyp: Type of polynomials in the list P. Homogeneous ("hom") or nonhomogeneous ("Nhom").

  • @return A list of lists containing the finite (or real) solutions of the polynomial system.


Example

-- Zero Dimensional Non-Homogeneous Solving
-- We want to solve zero dimensional non-homogeneous system x^2+y^2-5=0, xy-2=0. 

Use S ::= QQ[x,y];             --  Define appropriate ring 
P := [x^2+y^2-5, xy-2];
SysTyp := <quotes>Nhom</quotes>;

-- Then we compute the solution with
Bertini.BSolve(P,SysTyp);

-- And we achieve a list of lists containing all finite solutions:
----------------------------------------
[[Vector(400000000000003/200000000000000, -3416759775755413/500000000000000000000000000000), 
Vector(9999999999999927/10000000000000000, 8966048861359829/1000000000000000000000000000000)],
[Vector(2499999999999963/2500000000000000, 5007041073746771/100000000000000000000000000000),
Vector(249999999999999/125000000000000, -1089183184148021/25000000000000000000000000000)],
[Vector(-9999999999999969/10000000000000000, 191792591213411/125000000000000000000000000000),
Vector(-1999999999999999/1000000000000000, 2443331461729629/2500000000000000000000000000000)],
[Vector(-250000000000001/125000000000000, 4347064  850996171/1000000000000000000000000000000),
Vector(-9999999999999943/10000000000000000, -2154842536286333/500000000000000000000000000000)]]

--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/).

Example

-- Zero Dimensional Homogeneous Solving
-- We want to solve zero dimensional homogeneous system x^2-z^2=0, xy-z^2=0.

Use S ::= QQ[x,y,z];             --  Define appropriate ring 
M := [x^2-z^2, xy-z^2];
SysTyp := <quotes>hom</quotes>;

-- Then we compute the solution with
Bertini.BSolve(M,SysTyp);

-- And we achieve a list of lists containing all real solutions:
----------------------------------------
[[2190685167348543/5000000000000000, 2190685167348543/5000000000000000, 2190685167348543/5000000000000000],
[1237092982347763/5000000000000000, 1237092982347763/5000000000000000, -1237092982347763/5000000000000000],
[3235177805819999/100000000000000000000000000000, 9932123317905381/10000000000000000, 
621807549382663/5000000000000000000000000000], [3006769352985381/100000000000000000000000000000,
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]]

--For other Bertini output files please refer to Bertini directory (.../ApCoCoA-1.4/Bertini/).
------------------------------------



See also

Introduction to CoCoAServer

Bertini.BPCSolve

Bertini.BZCSolve

Bertini.BMSolve

Bertini.BUHSolve