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D.15.11.6 createQuotientGroup
Procedure from library multigrading.lib (see multigrading_lib).
- Usage:
- createGroup(L); L is an integer matrix
- Purpose:
- create the group of the form (I+L)/L,
where I is the square identity matrix of size nrows(L) x nrows(L)
- Note:
- L specifies relations between free generators of Z^nrows(L)
- Return:
- group
Example:
| | LIB "multigrading.lib";
intmat I[3][3] =
1, 0, 0,
0, 1, 0,
0, 0, 1;
intmat L[3][2] =
1, 1,
1, 3,
1, 5;
// The group Z^3 / L can be constructed as follows:
// shortcut:
def G = createQuotientGroup(L);
printGroup(G);
==> Generators:
==> 1 0 0
==> 0 1 0
==> 0 0 1
==> Relations:
==> 1 1
==> 1 3
==> 1 5
// the general way:
def GG = createGroup(I, L); // (I+L)/L
printGroup(GG);
==> Generators:
==> 1 0 0
==> 0 1 0
==> 0 0 1
==> Relations:
==> 1 1
==> 1 3
==> 1 5
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