-- -*- M2-comint -*- {* hash: 1424613957 *}

i1 : R = QQ[x,y,a..d,t,MonomialOrder=>{2,4,1}];

i2 : m = matrix{{x*a-d^2, a^3-1, x-a^100, a*b*d+t*c^3, t^3-t^2-t+1}}

o2 = | xa-d2 a3-1 x-a100 c3t+abd t3-t2-t+1 |

             1       5
o2 : Matrix R  <--- R

i3 : selectInSubring(1,m)

o3 = | a3-1 c3t+abd t3-t2-t+1 |

             1       3
o3 : Matrix R  <--- R

i4 : selectInSubring(2,m)

o4 = | t3-t2-t+1 |

             1       1
o4 : Matrix R  <--- R

i5 : S = QQ[a..d,MonomialOrder=>Lex];

i6 : m = matrix{{a^2-b, b^2-c, c^2-d, d^2-1}}

o6 = | a2-b b2-c c2-d d2-1 |

             1       4
o6 : Matrix S  <--- S

i7 : selectInSubring(1,m)

o7 = 0

             1
o7 : Matrix S  <--- 0

i8 : S = QQ[a..d,MonomialOrder=>{4:1}];

i9 : m = matrix{{a^2-b, b^2-c, c^2-d, d^2-1}}

o9 = | a2-b b2-c c2-d d2-1 |

             1       4
o9 : Matrix S  <--- S

i10 : selectInSubring(1,m)

o10 = | b2-c c2-d d2-1 |

              1       3
o10 : Matrix S  <--- S

i11 : selectInSubring(2,m)

o11 = | c2-d d2-1 |

              1       2
o11 : Matrix S  <--- S

i12 : selectInSubring(3,m)    

o12 = | d2-1 |

              1       1
o12 : Matrix S  <--- S

i13 :