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makeRange -- Make a range of degrees for getSmoothingFamily

Description

i1 : L={4,5,7}

o1 = {4, 5, 7}

o1 : List
 
i2 : congruences={4,6}

o2 = {4, 6}

o2 : List
 
i3 : range1=makeRange(L,{4,6})

o3 = {4, 6, 8, 12}

o3 : List
 
i4 : elapsedTime (smooth,fib, comps)=getSmoothingFamily(L,range1)
 -- .480826s elapsed

                    3           2 4      8     2    2    2 6   3    2    
o4 = (true, ideal (x  - x x  - x z  - x z , x x  - x  - x z , x  - x x  +
                    0    1 3    0      0     0 1    3    0     1    0 3  
     ------------------------------------------------------------------------
          4        6      8
     x x z  - x x z  + x z ), {0})
      0 3      0 1      3

o4 : Sequence

The range are degrees r which congruent 0 mod d for some d in the list congruences. To get a degree bound rane one can use the following.

i5 : range2=drop(makeRange(L,{1}),9)

o5 = {10, 11, 12, 13, 14, 15}

o5 : List
 
i6 : elapsedTime (smooth,fib, comps)=getSmoothingFamily(L,range2,Verbose=>1)
time to decompose J1 : 
 -- .000643579s elapsed

component number = 0
deformation weights = {{10}}
semigroup = {4, 5, 7}
 smoothing components numbers = {0}
 -- .000687288s elapsed
flat = true
 -- .421197s elapsed

                    3            2    2      10   3    2        10
o6 = (true, ideal (x  - x x , x x  - x  - x z  , x  - x x  - x z  ), {0})
                    0    1 3   0 1    3    0      1    0 3    1

o6 : Sequence

See also

Ways to use makeRange:

  • makeRange(List,List)

For the programmer

The object makeRange is a method function with options.

The source of this document is in WeierstrassSemigroups.m2:3211:0.