satisfiesDegreeCondition1 -- Does the semigroup ideal of L satisfies the degree condition for the 3rd respectively 2nd syzgy matrix?

i1 : L = {6,9,13,16}

o1 = {6, 9, 13, 16}

o1 : List

i2 : satisfiesDegreeCondition1 L

o2 = true

i3 : satisfiesDegreeCondition2 L

o3 = true

i4 : displaySyzygyMatrices L;
+----------------------------------------------------------------------+
|{-18} | x_3^2-x_0^3 -y    -w    0    0    x_0^5 0      0      0      ||
|{-22} | x_3y-wx_0   x_3   x_0^2 -w   yx_0 -y2   0      0      -x_0^6 ||
|{-25} | x_3w-yx_0^2 x_0   x_3   y    -w   0     -y2    -x_0^5 0      ||
|{-32} | w2-y2x_0    0     0     -x_0 x_3  0     0      0      -y2    ||
|{-39} | y3-x_3x_0^5 0     0     0    0    x_3   -x_0^2 -w     -yx_0  ||
|{-42} | y2w-x_0^7   0     0     0    0    -x_0  x_3    y      w      ||
|{0}   | 0           w     -y    x_3  x_0  0     0      0      0      ||
|{0}   | 0           0     x_0^5 -y2  0    w     -y     x_3    x_0    ||
|{0}   | 0           x_0^6 0     0    y2   yx_0  -w     x_0^2  x_3    ||
+----------------------------------------------------------------------+
|(13, | 13  16 20 23 30 33 37 40 |, | 16  33 36 |)                     |
|     | 9   12 16 19 26 29 33 36 |  | 13  30 33 |                      |
|     | 6   9  13 16 23 26 30 33 |  | 9   26 29 |                      |
|     | -1  2  6  9  16 19 23 26 |  | 6   23 26 |                      |
|     | -8  -5 -1 2  9  12 16 19 |  | -1  16 19 |                      |
|     | -11 -8 -4 -1 6  9  13 16 |  | -4  13 16 |                      |
|                                   | -8  9  12 |                      |
|                                   | -11 6  9  |                      |
+----------------------------------------------------------------------+

i5 : L = {6,15,17,20}

o5 = {6, 15, 17, 20}

o5 : List

i6 : displaySyzygyMatrices L;
+--------------------------------------------------------------------------+
|{-30} | x_3^2-x_0^5 -y    -w    0      0     x_0^6  0      0      0      ||
|{-32} | x_3y-wx_0^2 x_3   x_0^3 -w     yx_0  -y2    0      0      -x_0^7 ||
|{-35} | x_3w-yx_0^3 x_0^2 x_3   y      -w    0      -y2    -x_0^6 0      ||
|{-40} | w2-y2x_0    0     0     -x_0^2 x_3   0      0      0      -y2    ||
|{-51} | y3-x_3x_0^6 0     0     0      0     x_3    -x_0^3 -w     -yx_0  ||
|{-54} | y2w-x_0^9   0     0     0      0     -x_0^2 x_3    y      w      ||
|{0}   | 0           w     -y    x_3    x_0^2 0      0      0      0      ||
|{0}   | 0           0     x_0^6 -y2    0     w      -y     x_3    x_0^2  ||
|{0}   | 0           x_0^7 0     0      y2    yx_0   -w     x_0^3  x_3    ||
+--------------------------------------------------------------------------+
|(18, | 17 20 22 25 36 39 41 44 |, | 20 39 42 |)                           |
|     | 15 18 20 23 34 37 39 42 |  | 17 36 39 |                            |
|     | 12 15 17 20 31 34 36 39 |  | 15 34 37 |                            |
|     | 7  10 12 15 26 29 31 34 |  | 12 31 34 |                            |
|     | -4 -1 1  4  15 18 20 23 |  | 1  20 23 |                            |
|     | -7 -4 -2 1  12 15 17 20 |  | -2 17 20 |                            |
|                                  | -4 15 18 |                            |
|                                  | -7 12 15 |                            |
+--------------------------------------------------------------------------+

i7 : satisfiesDegreeCondition1 L

o7 = false