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CharacteristicClasses :: CheckSmooth

CheckSmooth

Description

The option CheckSmooth is only used by the commands CSM and only when computing the CSM class of a toric variety. It is set to true by default. When true it will check if the toric variety is smooth before proceeding, if it is this will speed up computation; however checking for smoothness does take some time.

i1 : needsPackage "NormalToricVarieties"

o1 = NormalToricVarieties

o1 : Package
i2 : U = toricProjectiveSpace 7

o2 = normalToricVariety((({{-1, -1, -1, -1, -1, -1, -1}, {1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1}}(,({{0, 1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 4, 5, 7}, {0, 1, 2, 3, 4, 6, 7}, {0, 1, 2, 3, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 7}, {0, 1, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}} )))))

o2 : NormalToricVariety
i3 : time CSM U
     -- used 0.0392858 seconds

       7      6      5      4      3      2
o3 = 8x  + 28x  + 56x  + 70x  + 56x  + 28x  + 8x  + 1
       7      7      7      7      7      7     7

                                    ZZ[x , x , x , x , x , x , x , x ]
                                        0   1   2   3   4   5   6   7
o3 : -----------------------------------------------------------------------------------------------
     (x x x x x x x x , - x  + x , - x  + x , - x  + x , - x  + x , - x  + x , - x  + x , - x  + x )
       0 1 2 3 4 5 6 7     0    1     0    2     0    3     0    4     0    5     0    6     0    7
i4 : time CSM(U,CheckSmooth=>false)
     -- used 0.132094 seconds

       7      6      5      4      3      2
o4 = 8x  + 28x  + 56x  + 70x  + 56x  + 28x  + 8x  + 1
       7      7      7      7      7      7     7

                                    ZZ[x , x , x , x , x , x , x , x ]
                                        0   1   2   3   4   5   6   7
o4 : -----------------------------------------------------------------------------------------------
     (x x x x x x x x , - x  + x , - x  + x , - x  + x , - x  + x , - x  + x , - x  + x , - x  + x )
       0 1 2 3 4 5 6 7     0    1     0    2     0    3     0    4     0    5     0    6     0    7

Functions with optional argument named CheckSmooth :

For the programmer

The object CheckSmooth is a symbol.