Some mutableMatrix updates

[d-torrance]

A few semi-related things that all grew out of fixing the first thing:

Rank errors

According to mutable-matrix.h:

/**
   returns the rank of the matrix M.  If 'rank' is not defined on this type of
   matrix, then returns -1 (and an error message is given).
 */
long rawLinAlgRank(MutableMatrix *M);

However, no such error message is given, and we just get -1!

i1 : rank mutableMatrix(ZZ/101, {{1}}, Dense => false)

o1 = -1

So I added a little check in the interpreter -- if we get -1, return the last engine error instead, so now we have:

i1 : rank mutableMatrix(ZZ/101, {{1}}, Dense => false)
stdio:1:4:(3):[1]: error: 'rank' not implemented for this kind of matrix over this ring

Constructor methods

While testing the above, I was sad that I had to type {{ and }}' when constructing a $1\times 1$ mutable matrix and wanted the Number/RingElement constructors we have for immutable matrices. So I'm proposing 6 new methods:

i1 : mutableMatrix 2 -- mutableMatrix(Number)

o1 = | 2 |

o1 : MutableMatrix

i2 : mutableMatrix(QQ, 2) -- mutableMatrix(Ring, Number)

o2 = | 2 |

o2 : MutableMatrix

i3 : mutableMatrix(RR, 2) -- mutableMatrix(RingFamily, Number)

o3 = | 2 |

o3 : MutableMatrix

i4 : R = QQ[x]; mutableMatrix x -- mutableMatrix(RingElement)

o5 = | x |

o5 : MutableMatrix

i6 : mutableMatrix(R[y], x) -- mutableMatrix(Ring, RingElement)

o6 = | x |

o6 : MutableMatrix

There's also mutableMatrix(RingFamily, RingElement), which won't do anything now except raise errors about promoting. But it might work in the future (e.g., after adding $p$-adics to the engine).

Documentation updates

When I went to document the new constructor methods, I saw that a bunch of the mutable matrix docs were in the old format and in the poorly named doc3.m2 file. So I moved them and had Claude update them to SimpleDoc format.

AfterPrint method

While writing this pull request description, I realized that mutable matrices don't tell us the size or what ring we're working over like we get for immutable matrices. That's a great use for AfterPrint methods so we just use the Matrix one:

i1 : mutableMatrix(QQ[x,y,z,w], 6, 7)

o1 = 0

                                6                  7
o1 : MutableMatrix (QQ[x..z, w])  <-- (QQ[x..z, w])

🤖 AI Disclosure 🤖

I wrote the actual d and m2 code, but got lazy and had Claude do the boring stuff (documentation and tests) lol.