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

From ApCoCoAWiki
(Corrected example.)
Line 9: Line 9:
  
 
<itemize>
 
<itemize>
<item>@param <em>M</em>: List of polynomials in the system to be solved.</item>
+
<item>@param <em>M</em>: List of polynomials in the system.</item>
<item>@param <em>SysTyp</em>: Type of the system to be solved. Homogeneous (<tt>hom</tt>) or nonhomogeneous (<tt>Nhom</tt>).</item>
+
<item>@param <em>SysTyp</em>: Type of polynomials in the system. Homogeneous (<tt>hom</tt>) or nonhomogeneous (<tt>Nhom</tt>).</item>
 
</itemize>
 
</itemize>
  
Line 24: Line 24:
 
Bertini.BSolve(M,SysTyp);
 
Bertini.BSolve(M,SysTyp);
  
-- And we achieve:
+
-- And we achieve a list of lists containing all finite solutions:
 
----------------------------------------
 
----------------------------------------
The number of real finite solutions are:
+
[[Vector(400000000000003/200000000000000, -3416759775755413/500000000000000000000000000000),
4     
+
Vector(9999999999999927/10000  000000000000, 8966048861359829/1000000000000000000000000000000)],
The real finite solutions are:
+
[Vector(2499999999999963/2500000000000000, 5007041073746  771/100000000000000000000000000000),
                                       
+
Vector(249999999999999/125000000000000, -1089183184148021/250000000000000000000000000  00)],
2.000000000000052e+00 -1.207721921243940e-14
+
[Vector(-9999999999999969/10000000000000000, 191792591213411/125000000000000000000000000000),
9.999999999999164e-01 1.727395183148409e-14
+
Vector(-19999999999999  99/1000000000000000, 2443331461729629/2500000000000000000000000000000)],
 
+
[Vector(-250000000000001/125000000000000, 4347064  850996171/1000000000000000000000000000000),
-9.999999999999680e-01 -1.380221440309691e-14
+
Vector(-9999999999999943/10000000000000000, -2154842536286333/5000000000000000  00000000000000)]]
-2.000000000000005e+00 -8.389594590085023e-15
 
 
 
9.999999999999293e-01 2.686603221243866e-14
 
2.000000000000473e+00 4.530296702485832e-13
 
 
 
-2.000000000000031e+00 -1.809322618557695e-15
 
-9.999999999999383e-01 -2.558999563654189e-15
 
 
 
For summary of all solutions refer to ApCoCoAServer.
 
 
 
 
</example>
 
</example>
 
<example>
 
<example>
Line 56: Line 46:
 
$Bertini.BSolve(M,SysTyp);
 
$Bertini.BSolve(M,SysTyp);
  
-- And we achieve:
+
-- And we achieve a list of lists containing all real finite solutions:
 
----------------------------------------
 
----------------------------------------
The number of real solutions are:
+
[[2190685167348543/5000000000000000, 2190685167348543/5000000000000000, 2190685167348543/5000000000000000],
4     
+
[1237092982347  763/5000000000000000, 1237092982347763/5000000000000000, -1237092982347763/5000000000000000],
The real solutions are:
+
[3235177805819999/1000000000  00000000000000000000, 9932123317905381/10000000000000000,
                                       
+
621807549382663/5000000000000000000000000000], [30067693529  85381/100000000000000000000000000000,
 
+
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]]
4.750270171019972e-01 7.277175694441498e-01
 
4.750270171019972e-01 7.277175694441498e-01
 
4.750270171019972e-01 7.277175694441498e-01
 
 
 
-1.161874166440340e+00 -1.121939725361908e+00
 
-1.161874166440340e+00 -1.121939725361908e+00
 
1.161874166440340e+00 1.121939725361908e+00
 
 
 
-1.213218743783253e-14 9.540042296620362e-14
 
1.297490331797821e+00 -3.349764345312171e-01
 
-9.696352192508132e-14 -3.162549982974766e-13
 
 
 
 
 
-2.845295858183006e-14 1.079961801218032e-13
 
1.297490331797885e+00 -3.349764345312022e-01
 
-9.799048563439788e-14 -3.558617333271439e-13
 
 
 
For summary of all solutions refer to ApCoCoAServer
 
  
 
------------------------------------
 
------------------------------------

Revision as of 13:53, 30 June 2009

Bertini.BSolve

Solves zero dimensional homogeneous or non-homogeneous polynomial system 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 M: List of polynomials in the system.

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

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 
M := [x^2+y^2-5, xy-2];
SysTyp := <quotes>Nhom</quotes>;

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

-- And we achieve a list of lists containing all finite solutions:
----------------------------------------
[[Vector(400000000000003/200000000000000, -3416759775755413/500000000000000000000000000000), 
Vector(9999999999999927/10000  000000000000, 8966048861359829/1000000000000000000000000000000)],
[Vector(2499999999999963/2500000000000000, 5007041073746  771/100000000000000000000000000000),
Vector(249999999999999/125000000000000, -1089183184148021/250000000000000000000000000  00)],
[Vector(-9999999999999969/10000000000000000, 191792591213411/125000000000000000000000000000),
Vector(-19999999999999  99/1000000000000000, 2443331461729629/2500000000000000000000000000000)],
[Vector(-250000000000001/125000000000000, 4347064  850996171/1000000000000000000000000000000),
Vector(-9999999999999943/10000000000000000, -2154842536286333/5000000000000000  00000000000000)]]

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 finite solutions:
----------------------------------------
[[2190685167348543/5000000000000000, 2190685167348543/5000000000000000, 2190685167348543/5000000000000000],
[1237092982347  763/5000000000000000, 1237092982347763/5000000000000000, -1237092982347763/5000000000000000],
[3235177805819999/1000000000  00000000000000000000, 9932123317905381/10000000000000000, 
621807549382663/5000000000000000000000000000], [30067693529  85381/100000000000000000000000000000,
1241515414738241/1250000000000000, 555981798431817/5000000000000000000000000000]]

------------------------------------



See also

Introduction to CoCoAServer

Bertini.BCMSolve

Bertini.BCSolve

Bertini.BMSolve

Bertini.BUHSolve