-- -*- M2-comint -*- {* hash: -1363098370 *}

i1 : R = ZZ/101[a..d];

i2 : m = matrix{{a,b,c,d}};

             1       4
o2 : Matrix R  <--- R

i3 : f = schreyerOrder m

o3 = | a b c d |

             1       4
o3 : Matrix R  <--- R

i4 : g = syz f

o4 = {1} | -b 0  -c 0  0  -d |
     {1} | a  -c 0  0  -d 0  |
     {1} | 0  b  a  -d 0  0  |
     {1} | 0  0  0  c  b  a  |

             4       6
o4 : Matrix R  <--- R

i5 : leadTerm g

o5 = {1} | 0 0 0 0 0 0 |
     {1} | a 0 0 0 0 0 |
     {1} | 0 b a 0 0 0 |
     {1} | 0 0 0 c b a |

             4       6
o5 : Matrix R  <--- R

i6 : hf = map(source f, 1, {{d},{c},{b},{a}})

o6 = {1} | d |
     {1} | c |
     {1} | b |
     {1} | a |

             4       1
o6 : Matrix R  <--- R

i7 : hm = map(source m, 1, {{d},{c},{b},{a}})        

o7 = {1} | d |
     {1} | c |
     {1} | b |
     {1} | a |

             4       1
o7 : Matrix R  <--- R

i8 : leadTerm hf

o8 = {1} | 0 |
     {1} | 0 |
     {1} | b |
     {1} | 0 |

             4       1
o8 : Matrix R  <--- R

i9 : leadTerm hm

o9 = {1} | 0 |
     {1} | 0 |
     {1} | 0 |
     {1} | a |

             4       1
o9 : Matrix R  <--- R

i10 : schreyerOrder source m

o10 = 0

                     4
o10 : Matrix 0 <--- R

i11 : schreyerOrder source f

o11 = | a 0 0 0 |
      | 0 b 0 0 |
      | 0 0 c 0 |
      | 0 0 0 d |

              4       4
o11 : Matrix R  <--- R

i12 :