Top
Back: intprog_lib
Forward: modstd_lib
FastBack: integralbasis_lib
FastForward: modstd_lib
Up: intprog_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.4.9.1 solve_IP

Procedure from library intprog.lib (see intprog_lib).

Usage:
solve_IP(A,bx,c,alg); A intmat, bx intvec, c intvec, alg string.
solve_IP(A,bx,c,alg); A intmat, bx list of intvec, c intvec, alg string.
solve_IP(A,bx,c,alg,prsv); A intmat, bx intvec, c intvec, alg string, prsv intvec.
solve_IP(A,bx,c,alg,prsv); A intmat, bx list of intvec, c intvec, alg string, prsv intvec.

Return:
same type as bx: solution of the associated integer programming problem(s) as explained in

Toric ideals and integer programming.

Note:
This procedure returns the solution(s) of the given IP-problem(s) or the message `not solvable'.
One may call the procedure with several different algorithms:
- the algorithm of Conti/Traverso (ct),
- the positive variant of the algorithm of Conti/Traverso (pct),
- the algorithm of Conti/Traverso using elimination (ect),
- the algorithm of Pottier (pt),
- an algorithm of Bigatti/La Scala/Robbiano (blr),
- the algorithm of Hosten/Sturmfels (hs),
- the algorithm of DiBiase/Urbanke (du).
The argument `alg' should be the abbreviation for an algorithm as above: ct, pct, ect, pt, blr, hs or du.

`ct' allows computation of an optimal solution of the IP-problem directly from the right-hand vector b.
The same is true for its `positive' variant `pct' which may only be applied if A and b have nonnegative entries.
All other algorithms need initial solutions of the IP-problem.

If `alg' is chosen to be `ct' or `pct', bx is read as the right hand vector b of the system Ax=b. b should then be an intvec of size m where m is the number of rows of A.
Furthermore, bx and A should be nonnegative if `pct' is used. If `alg' is chosen to be `ect',`pt',`blr',`hs' or `du', bx is read as an initial solution x of the system Ax=b. bx should then be a nonnegative intvec of size n where n is the number of columns of A.

If `alg' is chosen to be `blr' or `hs', the algorithm needs a vector with positive coefficients in the row space of A.
If no row of A contains only positive entries, one has to use the versions of solve_IP which take such a vector prsv as an argument.

solve_IP may also be called with a list bx of intvecs instead of a single intvec.

Example:
 
See also: Integer programming; intprog_lib; toric_lib.


Top Back: intprog_lib Forward: modstd_lib FastBack: integralbasis_lib FastForward: modstd_lib Up: intprog_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.