Singular Manual: gitFan

| #### D.15.9.3 gitFan Procedure from library `gitfan.lib` (see gitfan_lib). Purpose: Returns the GIT-fan of the H-action defined by Q on V(a). An optional third parameter of type 'int' is interpreted as the number of CPU-cores you would like to use. Note that 'system("--cpus");' returns the number of cpu available in your system. Return: a fan. Example:
    LIB "gitfan.lib";
    intmat Q[3][4] =
    1,0,1,0,
    0,1,0,1,
    0,0,1,1;
    ring R = 0,T(1..4),dp;
    ideal a = 0;
    gitFan(a, Q);
    ==> cones found: 1
    ==> cones found: 2
    ==> cones found: 3
    ==> cones found: 4
    ==> _application PolyhedralFan
    ==> _version 2.2
    ==> _type PolyhedralFan
    ==>
    ==> AMBIENT_DIM
    ==> 3
    ==>
    ==> DIM
    ==> 3
    ==>
    ==> LINEALITY_DIM
    ==> 0
    ==>
    ==> RAYS
    ==> 0 1 0	# 0
    ==> 0 1 1	# 1
    ==> 1 0 0	# 2
    ==> 1 0 1	# 3
    ==> 1 1 1	# 4
    ==>
    ==> N_RAYS
    ==> 5
    ==>
    ==> LINEALITY_SPACE
    ==>
    ==> ORTH_LINEALITY_SPACE
    ==> -1 0 0	# 0
    ==> 0 -1 0	# 1
    ==> 0 0 -1	# 2
    ==>
    ==> F_VECTOR
    ==> 1 5 8 4
    ==>
    ==> SIMPLICIAL
    ==> 1
    ==>
    ==> PURE
    ==> 1
    ==>
    ==> CONES
    ==> {}	# Dimension 0
    ==> {0}	# Dimension 1
    ==> {1}
    ==> {2}
    ==> {3}
    ==> {4}
    ==> {0 1}	# Dimension 2
    ==> {0 2}
    ==> {1 3}
    ==> {0 4}
    ==> {1 4}
    ==> {2 3}
    ==> {2 4}
    ==> {3 4}
    ==> {0 1 4}	# Dimension 3
    ==> {0 2 4}
    ==> {1 3 4}
    ==> {2 3 4}
    ==>
    ==> MAXIMAL_CONES
    ==> {0 1 4}	# Dimension 3
    ==> {0 2 4}
    ==> {1 3 4}
    ==> {2 3 4}
    ==>
    ==> MULTIPLICITIES
    ==> 1	# Dimension 3
    ==> 1
    ==> 1
    ==> 1
    ==>
    // 2nd example //
    kill Q;
    intmat Q[3][6] =
    1,1,0,0,-1,-1,
    0,1,1,-1,-1,0,
    1,1,1,1,1,1;
    ring R = 0,T(1..6),dp;
    ==> // ** redefining R **
    ideal a = T(1)*T(6) + T(2)*T(5) + T(3)*T(4);
    int t = rtimer;
    fan F = gitFan(a, Q);
    ==> cones found: 1
    ==> cones found: 2
    ==> cones found: 3
    ==> cones found: 4
    ==> cones found: 5
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    t = rtimer - t;
    int tt = rtimer;
    fan F = gitFan(a, Q, 4);
    ==> // ** redefining F **
    ==> cones found: 1
    tt = rtimer - tt;
    t;
    ==> 0
    tt;
    ==> 0
    "--------";
    ==> --------
    kill R, Q, t, tt;
    // next example //
    ring R = 0,T(1..10),dp;
    ideal a = T(5)*T(10)-T(6)*T(9)+T(7)*T(8),
    T(1)*T(9)-T(2)*T(7)+T(4)*T(5),
    T(1)*T(8)-T(2)*T(6)+T(3)*T(5),
    T(1)*T(10)-T(3)*T(7)+T(4)*T(6),
    T(2)*T(10)-T(3)*T(9)+T(4)*T(8);
    bigintmat Q[4][10] =
    1,0,0,0,1,1,1,0,0,0,
    0,1,0,0,1,0,0,1,1,0,
    0,0,1,0,0,1,0,1,0,1,
    0,0,0,1,0,0,1,0,1,1;
    int t = rtimer;
    fan F = gitFan(a, Q);
    ==> // ** redefining F **
    ==> cones found: 1
    ==> cones found: 2
    ==> cones found: 3
    ==> cones found: 4
    ==> cones found: 5
    ==> cones found: 6
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    t = rtimer - t;
    int tt = rtimer;
    fan F = gitFan(a, Q, 4);
    ==> // ** redefining F **
    ==> cones found: 1
    ==> cones found: 2
    ==> cones found: 3
    ==> cones found: 4
    ==> cones found: 5
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    tt = rtimer - tt;
    t;
    ==> 1
    tt;
    ==> 1
    "--------";
    ==> --------
    kill R, Q, t, tt;
    // next example //
    ring R = 0,T(1..15),dp;
    ideal a =
    T(1)*T(10)-T(2)*T(7)+T(3)*T(6),
    T(1)*T(11)-T(2)*T(8)+T(4)*T(6),
    T(1)*T(12)-T(2)*T(9)+T(5)*T(6),
    T(1)*T(13)-T(3)*T(8)+T(4)*T(7),
    T(1)*T(14)-T(3)*T(9)+T(5)*T(7),
    T(1)*T(15)-T(4)*T(9)+T(5)*T(8),
    T(2)*T(13)-T(3)*T(11)+T(4)*T(10),
    T(2)*T(14)-T(3)*T(12)+T(5)*T(10);
    bigintmat Q[5][15] =
    1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,
    0,1,0,0,0,1,0,0,0,1,1,1,0,0,0,
    0,0,1,0,0,0,1,0,0,1,0,0,1,1,0,
    0,0,0,1,0,0,0,1,0,0,1,0,1,0,1,
    0,0,0,0,1,0,0,0,1,0,0,1,0,1,1;
    int t = rtimer;
    fan F = gitFan(a, Q);
    ==> // ** redefining F **
    ==> cones found: 1
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    t = rtimer - t;
    int tt = rtimer;
    fan F = gitFan(a, Q, 4);
    ==> // ** redefining F **
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    tt = rtimer - tt;
    t;
    ==> 62
    tt;
    ==> 63

User manual for Singular version 4-0-2, 2015, generated by texi2html.