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D.15.14.20 preimageLattice

Procedure from library multigrading.lib (see multigrading_lib).

Usage:
preimageLattice(P, B); intmat P, intmat B

Purpose:
compute an integral basis for the preimage of B under the homomorphism of lattices defined by the intmat P.

Returns:
intmat

Example:
 
LIB "multigrading.lib";
intmat P[2][3] =
2,6,10,
4,8,12;
intmat B[2][1] =
1,
0;
// should be a (3x2)-matrix with columns e.g. [1,1,-1] and [0,3,-2] (the generated lattice should be identical)
print(preimageLattice(P,B));
==>      1     0
==>      1     3
==>     -1    -2
// another example
intmat W[3][3] =
1,0,0,
0,1,1,
0,2,0;
intmat Z[3][2] =
1,0,
0,1,
0,0;
// should be a (3x2)-matrix with columns e.g. [1,0,0] and [0,0,-1] (the generated lattice should be identical)
print(preimageLattice(W,Z));
==>      1     0
==>      0     0
==>      0     1