solvingFlatteningRelations -- Solving the flatttening relations over QQ

i1 : L={7,8,17,19,20}

o1 = {7, 8, 17, 19, 20}

o1 : List

i2 : I=semigroupIdeal L;

               ZZ
o2 : Ideal of -----[x ..x , x , x ..x ]
              10007  0   1   3   5   6

i3 : (answer,J,comp)=testBound(L,12);
  # of coordinate linear subspace of the base = 21
  # of linear subsets which leading to a point =21

i4 : (base1,family1)=getParameterFamily J;

i5 : base=last decompose base1;

o5 : Ideal of QQ[a      , a      , a      , a      , a      , a      , a      ]
                  {1, 1}   {1, 2}   {3, 4}   {0, 1}   {0, 2}   {2, 3}   {1, 3}

i6 : family=family1%sub(base,ring family1);

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          10
o6 : Matrix (QQ[x ..x , x , x ..x , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a       , a      , a      , a      , a      , a      , a       , a       , a      , a      , a      , a      , a       , a       , a      , a      , a      , a       , a       , a       , a       , a      , a      , a      ])  <-- (QQ[x ..x , x , x ..x , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a      , a       , a      , a      , a      , a      , a      , a       , a       , a      , a      , a      , a      , a       , a       , a      , a      , a      , a       , a       , a       , a       , a      , a      , a      ])
                 0   1   3   5   6   {9, 0}   {8, 0}   {7, 0}   {6, 0}   {5, 0}   {4, 0}   {9, 1}   {7, 1}   {5, 1}   {4, 1}   {9, 3}   {9, 8}   {8, 7}   {6, 6}   {5, 5}   {4, 3}   {2, 2}   {1, 1}   {9, 9}   {8, 8}   {5, 6}   {4, 4}   {3, 3}   {1, 2}   {8, 9}   {7, 8}   {4, 5}   {3, 4}   {8, 10}   {7, 9}   {6, 8}   {5, 7}   {3, 5}   {0, 1}   {8, 11}   {7, 10}   {6, 9}   {5, 8}   {3, 6}   {0, 2}   {9, 14}   {6, 11}   {4, 8}   {3, 7}   {2, 3}   {9, 15}   {8, 14}   {6, 12}   {5, 11}   {4, 9}   {2, 4}   {1, 3}             0   1   3   5   6   {9, 0}   {8, 0}   {7, 0}   {6, 0}   {5, 0}   {4, 0}   {9, 1}   {7, 1}   {5, 1}   {4, 1}   {9, 3}   {9, 8}   {8, 7}   {6, 6}   {5, 5}   {4, 3}   {2, 2}   {1, 1}   {9, 9}   {8, 8}   {5, 6}   {4, 4}   {3, 3}   {1, 2}   {8, 9}   {7, 8}   {4, 5}   {3, 4}   {8, 10}   {7, 9}   {6, 8}   {5, 7}   {3, 5}   {0, 1}   {8, 11}   {7, 10}   {6, 9}   {5, 8}   {3, 6}   {0, 2}   {9, 14}   {6, 11}   {4, 8}   {3, 7}   {2, 3}   {9, 15}   {8, 14}   {6, 12}   {5, 11}   {4, 9}   {2, 4}   {1, 3}

i7 : (worked,fiber)=solvingFlatteningRelations(base,family,I)
  # of coordinate linear subspace of the base = 2
  # of linear subsets which leading to a point =2

o7 = (true, | x_1^3-x_0x_3+x_1+x_0 x_1x_5-x_0x_6+x_0^2+x_1-x_0
 x_0^4-x_1x_6+x_0x_1+x_0^2-x_1
 x_1^2x_3-x_0^2x_5-x_5+x_3+x_1^2+x_0x_1+x_0^2
 x_3^2-x_0^2x_6+x_0^3-x_6+x_1^2+2x_0x_1-x_0^2+x_0-2
 x_3x_5-x_1^2x_6+x_0x_1^2-x_6-x_5+x_3-x_1^2+x_0-2
 x_0^3x_1^2-x_3x_6+x_0x_3+x_0x_1^2+x_0^3+x_6-x_3+1
 x_0^3x_3-x_5^2+x_0^2x_1+x_0^3+x_6-x_0+2
 x_0^2x_1x_3-x_5x_6+x_0x_5+x_0x_1^2+x_0^2x_1+x_0^3+x_6-x_5+1
 x_0^3x_5-x_6^2+2x_0x_6+x_0x_5+x_0^3-2x_6-x_0^2+3x_0-1 |)

o7 : Sequence