Update 06/12/23

Version 0.2 of linearalgebra.mac

Remove the s_test_case for vec_convert that seems to be causing issues.

The convenience functions `c` and `r` throw errors regularly if non-conforming vectors are added/multiplied inappropriately, so the original solution of directly converting to matrix form was inappropriate. 

The solution is to keep `c` and `r` as inert functions and use `vec_convert` to remove these as needed. Correspondingly, `vec_convert` now uses `errcatch` and will return the original expression when errors arise. A new predicate function, `vec_convertedp`, will detect whether an expression was successfully converted to matrix form.

Whilst editing questions I have found that saving and loading has been very burdensome compared to normal and my theory is that it runs all tests on every save, and on every preview (perhaps with deployed variants this would stop). This file exists with no `s_test_case` lines to see if the load times are improved.

Declared `c` and `r` to be nonscalar so that they behave appropriately with other matrices in expressions.

Fixed the vector display functions; they now display the tex-formatted entries rather than just the plaintex (how did I miss this earlier??)

Prevented divide by zero errors in integerify

Fixed subspace_equiv
Added col_vecp and row_vecp

v0.2 of linearalgebra.mac features most of the functions I expect to use, and test cases for almost all of these functions.  It contains:
- Convenience functions for student vector input
- Various predicate functions for vector and matrix properties
- Functions to manipulate/extract parts of matrices
- Functions to convert collections of vectors into a locally standard form (currently preferring lists of lists or matrices)
- Functions to compare objects, typically checking for independence, or equivalence to subspaces.
- Functions to convert collection of vectors to a basis
- Extension of significantfigures to work for matrices
- Extension of norm and cond functions to use the 2-norm
- Extension of linsolve to accept matrix input and optionally use least squares
- A function to produce smallest integer vector parallel to given vector (useful for eigenproblems!)
- rowspace and nullTspace functions to pair with columnspace and nullspace
- Rayleigh quotient calculation
- Algebraic and geometric multiplicities of eigenvalues
- Computing various matrices and factorisations, including rectangular diagonal matrix, projection matrices, QR, Jordan form, (orthgonal) diagonalisation, SVD, and pseudoinverse.

Still to-do: 
- Possibly write some eigenvalue/eigenvector predicates (need to determine what is actually useful)
- Work on the disp_eqns function that produces nice LaTeX for displaying systems of linear equations. 
- More functions will likely get added (and possibly removed) as work continues on local linear algebra course.

Copy of linearalgebra.mac v0.2.3 (committed 8th May 2024) with the s_test_case lines removed.

Implemented old fix for integerify (missed in the upgrade to 0.2.3).

Implemented old fix to integerify (missed in upgrade to 0.2.3)

Following the fix to maths#1148: 

maths@a35ebc0

Deleting file with plan to rename `linearalgebra_no_test` to `linearalgebra`

Mostly a documentation update. 

Also added checks in lin_indp and subspace_equiv so that they don't throw errors when given lists of lists of unequal length.

- Added support for displaying augmented matrices easily using an inert function and texput. Also added `aug` and `de_aug` to convert matrices in and out of this mode.
- Reworked `triu`, `tril`, `get_diag`, `triup`, `trilp`, `diagp`, and `diag_entries`. These should be significantly more efficient now. Thanks for the `genmatrix` tip-off Georg Osang!
- Added `un_vec_convert` to change matrices into `c` and `r` form. Mostly intended for making teachers' answers the format we expect students to use.
- Added a line to `make_list_of_lists` that will take a single vector and make it a list of a list. e.g. `[1,2,k]` -> `[[1,2,k]]`.
- Edited `orthogonal_columnsp` and associated functions to forcibly expand the matrix before comparing. Thanks Georg! 
- Added support for eigenproblems. This includes
  - `eigenvaluep` and `eigenvectorp` which check whether a given value or vector is "eigen". Optionally checks them against a given vector or value respectively. 
  - `get_eigenvalue` and `get_eigenvector` to extract the corresponding one from a given. Much nicer than using `eigenvectors` when you only want one! Can also orthonormalise the basis if requested.
  - Moved `Rayleigh` up to be with these.
- Added support for vector parametric equations. It's a bit sparse, but these functions can check whether a given expression is of the desired form, and if so extract the useful bits (linear offset, direction vectors, parameters) and then format this nicely for TeX display. This is the only remaining TODO: add support for other vector input options, notably lists and ntuples. This will likely not happen in 2024. 
- Finished off `disp_eqns` and added `mat_disp_eqns` to do the same given `A` and `b` instead of a list of equations. 
- I've given up on PLU for now and have thus removed this section. I think that `rref`, `triangularize`, `echelon` and `lu_factor` do a good enough job, though it's still baffling to me that none of them do partial pivoting, nor do they avoid scaling rows unnecessarily.

Added test cases for v0.2.4

Added 
- rowscale and columnscale, intended as complements to rowop, rowswap, columnop and columnswap. It is odd that the third elementary row/column operation is not included by default.
- setrowmx, setcolmx, and setdiagmx, intended as complements to setelmx. Used to overwrite rows, columns or diagonals.

Added tests for new functions in linearalgebra

Changed the names of some functions per suggestions from others; added two more vector parametric equation functions to test whether a given point is in a given affine subspace and whether a given vector is in a given vector subspace.

Adjusted test cases for recent commit to linearalgebra.mac

Modify disp_eqns to support parameters

I didn't realise that vectors of constants were also considered constants, so one of the if-statements in make_list_of_lists wasn't behaving as intended. 

There may be a bug in point_in_affine_spacep; its 3rd test didn't work for me when running the whole bank of tests. I think that the problem is that I didn't declare local variables, so I have added that and I hope it fixes it.

%i is NOT the corresponding eigenvalue for matrix([0,-1],[1,0]) and c(1,%i), so the ta should be false.

get_eigenvector returns an empty list rather than false when given an incorrect eigenvalue, so the ta should be [] instead of false.

- Fixed a bug in disp_eqns where negative pivots were missing their minus sign when the pivot was not in the first column.
- Added tex1 into the format_as_coeff function as suggested by Georg Osang

TODO: Unit tests need updating.