Singular Manual: getGradingGroup

| #### D.15.12.3 getGradingGroup Procedure from library `multigrading.lib` (see multigrading_lib). Usage: getGradingGroup([R]) Purpose: get associated grading group Return: group, the grading group 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
    def G = getGradingGroup();
    printGroup( G );
    ==> Generators:
    ==>      1     0     0
    ==>      0     1     0
    ==>      0     0     1
    ==> Relations:
    ==>      1     1
    ==>      1     3
    ==>      1     5
    G[1] == M; G[2] == L;
    ==> 1
    ==> 1
    kill L, M, G;
    // ----------- 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)
    def G = getGradingGroup();
    printGroup( G );
    ==> Generators:
    ==>      1    -2     1
    ==>      1     1     0
    ==> Relations:
    ==>      0
    ==>      2
    G[1] == M; G[2] == L;
    ==> 1
    ==> 1
    kill L, M, G;
    // ----------- 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
    def G = getGradingGroup();
    printGroup( G );
    ==> Generators:
    ==>      1    -1    10
    ==> Relations:
    ==>      0
    G[1] == M; G[2] == L;
    ==> 1
    ==> 1
    kill L, M, G;

User manual for Singular version 4.3.2, 2023, generated by texi2html.