Update matrix.mac

Improvements to `aug` following suggestions from Marc Peterfi. The function behaves as it previously did when given a single matrix (that is, it will insert a vertical bar before the final column), but when given two or more matrices as arguments it will concatenate them with vertical bars between each. 

The original use case is to generate worked solutions for matrix inversion or similar, e.g. aug(A, ident(3)) → aug(rowop(A,2,1,A[2,1]/A[1,1]), rowop(ident(3),2,1,A[2,1]/A[1,1]) but could be used for more. 

aug(addcol(A,b)) and aug(A,b) are identical. 

Existing test cases will fail only because the vertical bar is now generated as a closing bracket instead of an opening one. This looks nicer, so I am treating this as a feature instead of a bug.

Author: LukeLongworth

stack/maxima/contrib/matrix.mac

@@ -28,39 +28,43 @@ stack_linear_algebra_declare(true)$
 /*******************************************************************************/
 /* A convenience function for displaying a matrix as an augmented matrix       */
 /*******************************************************************************/
-texput(aug_matrix, lambda([ex], block([M,ll,rr,m,n,A,b,simp],
-  simp:true,
-  M: apply(matrix,args(ex)),
-  ll: lmxchar,
-  if is(ll="[") then rr: "]"
-  else if is(ll="(") then rr: ")"
-  else if is(ll="") then (ll: ".", rr: ".")
-  else if is(ll="{") then (ll: "\\{", rr: "\\}")
-  else if is(ll="|") then rr: "|",
-  [m, n]: matrix_size(M),
-  A: submatrix(M,n),
-  b: col(M,n),
-  sconcat("\\left",ll,block([lmxchar],lmxchar:"",tex1(A)),"\\right|\\left.",block([lmxchar],lmxchar:"",tex1(b)),"\\right",rr)
-)));
+texput(aug_matrix, lambda([ex],
+  block([exl:args(ex),ii,ss,ll:lmxchar,rr,lmxchar],
+    if is(ll="[") then rr: "]"
+    else if is(ll="(") then rr: ")"
+    else if is(ll="") then (ll: ".", rr: ".")
+    else if is(ll="{") then (ll: "\\{", rr: "\\}")
+    else if is(ll="|") then rr: "|",
+    lmxchar: "",
+    ss: ["\\left",ll,tex1(exl[1])],
+    for ii: 2 thru length(exl) do block(
+      ii: ev(ii,simp),
+      ss: append(ss, ["\\left|",tex1(exl[ii]),"\\right."])
+    ),
+    ss: append(ss, ["\\right",rr]),
+    return(simplode(ss))
+  )
+));
 
 /**
  * Converts a matrix to an aug_matrix
  * aug_matrix is an inert function that is used for displaying a matrix as an augmented matrix
  * To convert back, use de_aug 
  *
- * @param[matrix] M The matrix you would like to display as an augmented matrix
+ * @param[matrix] M The matrix or matrices you would like to display as an augmented matrix
  * @return[aug_matrix] An augmented matrix
  */
-aug(M):= apply(aug_matrix,args(M));
+aug([M]):= if is(length(M)=1) then apply(aug_matrix,[submatrix(first(M),second(matrix_size(first(M)))),col(first(M),second(matrix_size(first(M))))]) else apply(aug_matrix,M);
 
 /**
  * Converts an aug_matrix to a matrix
  * aug_matrix is an inert function that is used for displaying a matrix as an augmented matrix
+ * Note: This always returns a single matrix constructed by concatenating the arguments of the original aug_matrix. 
  *
  * @param[matrix] M The aug_matrix you would like to treat as a regular matrix
  * @return[aug_matrix] A matrix
  */
-de_aug(M):= apply(matrix,args(M));
+de_aug(M):= apply(addcol, args(M));
 
 /*********************************************************************************/
 /* Functions to extract parts of matrices                                        */