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D.4.22.3 graver4ti2
Procedure from library sing4ti2.lib (see sing4ti2_lib).
- Usage:
- graver4ti2(A[,i]);
A=intmat
i=int
- Assume:
- - A is a matrix with integer entries which describes the lattice
as ker(A), if second argument is not present,
as the left image Im(A) = {zA : z \in ZZ^k}, if second argument is a positive integer
- number of variables of basering equals number of columns of A
(for ker(A)) resp. of rows of A (for Im(A))
- Create:
- temporary files sing4ti2.mat, sing4ti2.lat, sing4ti2.gra
in the current directory (I/O files for communication with 4ti2)
- Note:
- input rules for 4ti2 also apply to input to this procedure
hence ker(A)={x|Ax=0} and Im(A)={xA}
- Return:
- toric ideal specified by Graver basis thereof
Example:
| LIB "sing4ti2.lib";
ring r=0,(x,y,z,w),dp;
matrix M[2][4]=0,1,2,3,3,2,1,0;
graver4ti2(M);
==> -------------------------------------------------
==> 4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
==> 4ti2 comes with ABSOLUTELY NO WARRANTY.
==> This is free software, and you are welcome
==> to redistribute it under certain conditions.
==> For details, see the file COPYING.
==> -------------------------------------------------
==>
==> Linear integer system to solve:
==>
==> + + + +
==> - - - -
==>
==> 0 1 2 3 = 0
==> 3 2 1 0 = 0
==>
==> Linear integer system of homogeneous equalities to solve:
==>
==> + + + +
==> - - - -
==>
==> 0 1 2 3 = 0
==> 3 2 1 0 = 0
==>
==>
==> Appending variable 1... Solutions: 4, Step: 0.00 secs, Time: 0.00 secs
==> Appending variable 2... Solutions: 4, Step: 0.00 secs, Time: 0.00 secs
==> Appending variable 3... Solutions: 8, Step: 0.00 secs, Time: 0.00 secs
==> Appending variable 4... Solutions: 10, Step: 0.00 secs, Time: 0.00 secs
==>
==> Final basis has 1 inhomogeneous, 10 homogeneous and 0 free elements.
==> Writing 5 vectors to graver file, with respect to symmetry.
==>
==> 4ti2 Total Time: 0.00 secs
==> _[1]=-y2+xz
==> _[2]=-y3+x2w
==> _[3]=-yz+xw
==> _[4]=-z2+yw
==> _[5]=-z3+xw2
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