genericMatrix should be row major

[mahrud]

It was pointed out during the workshop that the output of genericMatrix should be row major instead of column major because this makes no sense:

i1 : R = QQ[x_(1,1) .. x_(2,5)];

i2 : genericMatrix(R, 2, 5)

o2 = | x_(1,1) x_(1,3) x_(1,5) x_(2,2) x_(2,4) |
     | x_(1,2) x_(1,4) x_(2,1) x_(2,3) x_(2,5) |

             2      5
o2 : Matrix R  <-- R

[d-torrance]

This was bugging me the other day, too. I wonder how much code it would break if we changed it? For example, permanents fixes the problem by doing this:

M1:= transpose genericMatrix(R1,xxX_(1,1),c,r);

[mahrud]

I personally think it's a change worth trying, and if we find that it breaks way too many things we can just add genericMatrix' which does the transpose.

[mikestillman]

I agree that the proposed way is better, but I'm afraid it will break alot of code. Not code in the system so much, but in particular, for personal code of mine for different projects of mine.

[pzinn]

I remember this as being one of the first things that annoyed me when I started using M2 twenty years ago. And adding transpose is not great because the degree shift becomes visible

i2 : transpose genericMatrix(QQ[m_(1,1)..m_(2,2)],2,2)

o2 = {-1} | m_(1,1) m_(1,2) |
     {-1} | m_(2,1) m_(2,2) |

                            2                     2
o2 : Matrix (QQ[m   ..m   ])  <-- (QQ[m   ..m   ])
                 1,1   2,2             1,1   2,2

[mahrud]

This is also bad:

i4 : R = QQ[x_(1,1)..x_(2,3)];

i5 : reshape(R^2, R^3, vars R)

o5 = | x_(1,1) x_(1,3) x_(2,2) |
     | x_(1,2) x_(2,1) x_(2,3) |

             2      3
o5 : Matrix R  <-- R

[pzinn]

maybe add an option RowMajor to genericMatrix? also at some point I experimented with an alternative syntax R=QQ[m_(1,1)...m_(5,5)]; M=genericMatrix m where M2 figures out on its own the correct shape.

[mahrud]

I just have a genericMatrix' in my scripts that does the right thing, but an option is fine too.