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 | + | <item>@param <em>M</em>: List of polynomials in the system.</item> |
| − | <item>@param <em>SysTyp</em>: Type of the system | + | <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: |
---------------------------------------- | ---------------------------------------- | ||
| − | + | [[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> | </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: |
---------------------------------------- | ---------------------------------------- | ||
| − | + | [[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]] | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
------------------------------------ | ------------------------------------ | ||
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
