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D.15.23.5 createGroup
Procedure from library multigrading.lib (see multigrading_lib).
- Usage:
- createGroup(S, L); S, L are integer matrices
- Purpose:
- create the group of the form (S+L)/L, i.e.
S specifies generators, L specifies relations.
- Return:
- group
Example:
| | LIB "multigrading.lib";
intmat S[3][3] =
1, 0, 0,
0, 1, 0,
0, 0, 1;
intmat L[3][2] =
1, 1,
1, 3,
1, 5;
def G = createGroup(S, L); // (S+L)/L
printGroup(G);
==> Generators:
==> 1 0 0
==> 0 1 0
==> 0 0 1
==> Relations:
==> 1 1
==> 1 3
==> 1 5
kill S, L, G;
/////////////////////////////////////////////////
intmat S[2][3] =
1, -2, 1,
1, 1, 0;
intmat L[2][1] =
0,
2;
def G = createGroup(S, L); // (S+L)/L
printGroup(G);
==> Generators:
==> 1 -2 1
==> 1 1 0
==> Relations:
==> 0
==> 2
kill S, L, G;
// ----------- extreme case ------------ //
intmat S[1][3] =
1, -1, 10;
// Torsion:
intmat L[1][1] =
0;
def G = createGroup(S, L); // (S+L)/L
printGroup(G);
==> Generators:
==> 1 -1 10
==> Relations:
==> 0
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