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D.15.13.4 getLattice
Procedure from library multigrading.lib (see multigrading_lib).
- Usage:
- getLattice([R[,opt]])
- Purpose:
- get associated grading group matrix, i.e. generators (cols) of the grading group
- Return:
- intmat, the grading group matrix, or
its hermite normal form if an optional argument ("hermiteNormalForm") is given or
smith normal form if an optional argument ("smith") is given
Example:
| | LIB "multigrading.lib";
ring R = 0, (x, y, z), dp;
// Weights of variables
intmat M[3][3] =
1, 0, 0,
0, 1, 0,
0, 0, 1;
// Torsion:
intmat L[3][2] =
1, 1,
1, 3,
1, 5;
// attaches M & L to R (==basering):
setBaseMultigrading(M, L); // Grading: Z^3/L
// Torsion is accessible via "getLattice()":
getLattice() == L;
==> 1
// its hermite NF:
print(getLattice("hermite"));
==> 1 0
==> 1 2
==> 1 4
kill L, M;
// ----------- isomorphic multigrading -------- //
// Weights of variables
intmat M[2][3] =
1, -2, 1,
1, 1, 0;
// Torsion:
intmat L[2][1] =
0,
2;
// attaches M & L to R (==basering):
setBaseMultigrading(M, L); // Grading: Z + (Z/2Z)
// Torsion is accessible via "getLattice()":
getLattice() == L;
==> 1
// its hermite NF:
print(getLattice("hermite"));
==> 0
==> 2
kill L, M;
// ----------- extreme case ------------ //
// Weights of variables
intmat M[1][3] =
1, -1, 10;
// Torsion:
intmat L[1][1] =
0;
// attaches M & L to R (==basering):
setBaseMultigrading(M); // Grading: Z^3
// Torsion is accessible via "getLattice()":
getLattice() == L;
==> 1
// its hermite NF:
print(getLattice("hermite"));
==> 0
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