Merge pull request #1745 from maths/aug_improvement

Aug improvement

Author: sangwinc

doc/en/Topics/Linear_algebra/Matrix_library.md

@@ -83,11 +83,15 @@ The last three predicates above will all accept an optional argument, `sp`, that
 
 It is sometimes convenient to be able to display an augmented matrix. `matrix.mac` adds some limited support for this. 
 
-Perhaps you have a question in which students are asked to solve the matrix equation \(A\underline{\mathbf{x}} = \underline{\mathbf{b}}\) using Gaussian elimination and you wanted to display this problem as an augmented matrix. Then, with matrix `A` and right hand side vector (really a matrix) `b` already defined, you could use `aug(addcol(A,b))` to display
+Perhaps you have a question in which students are asked to solve the matrix equation \(A\underline{\mathbf{x}} = \underline{\mathbf{b}}\) using Gaussian elimination and you wanted to display this problem as an augmented matrix. Then, with matrix `A` and right hand side vector (really a matrix) `b` already defined, you could use `aug(A,b)` to display
 
-\[{\left[\begin{array}{cc} 1 & 2 \\ 4 & 5 \end{array}\right|\left.\begin{array}{c} 3 \\ 6 \end{array}\right]}\]
+\[\left[\begin{array}{cc} 1 & 2 \\ 4 & 5 \end{array}\right|\left.\begin{array}{c} 3 \\ 6 \end{array}\right]\]
 
-Really what is happening here is that `aug` is converting a matrix with concatenated columns `A` and `b` to an `aug_matrix`, which then displays as a matrix with its final column separated by a vertical bar. `aug_matrix` is an inert function that exists only in this library for display purposes. You can save this to a variable, perhaps `Ab`, but Maxima doesn't know that this is a matrix at all and so matrix operations won't work on it. To turn it back into a matrix, you can use `de_aug(Ab)`. 
+Really what is happening here is that `aug` is converting a matrix with concatenated columns `A` and `b` to an `aug_matrix`, which then displays as a matrix with its final column separated by a vertical bar. `aug_matrix` is an inert function that exists only in this library for display purposes. You can save this to a variable, perhaps `Ab`, but Maxima doesn't know that this is a matrix at all and so matrix operations won't work on it. To turn it back into a matrix, you can use `de_aug(Ab)`. `de_aug` concatenates the input matrices instead of returning a list, so if you need more control you may prefer to programme your row operations separately and display `aug(A1,b1)`, `aug(A2,b2)` etc. manually.  
+
+This can generalise to as many inputs as needed. For instance, `aug(matrix([1,2,3],[4,5,6],[7,8,9]), matrix([1],[1],[1]), ident(3))` will display as
+
+\[\left[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\left|\begin{array}{c} 1 \\ 1 \\ 1 \end{array}\right.\left|\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right.\right]\]
 
 ### Systems of equations
 

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                                        */

stack/maxima/contrib/matrix_test.mac

@@ -30,6 +30,15 @@
 
 s_test_case(aug(matrix([1,2,3,1],[4,5,6,1],[7,8,9,1])),aug_matrix([1,2,3,1],[4,5,6,1],[7,8,9,1]));
 s_test_case(de_aug(aug_matrix([1,2,3,1],[4,5,6,1],[7,8,9,1])),matrix([1,2,3,1],[4,5,6,1],[7,8,9,1]));
+s_test_case(de_aug(aug(ident(4),matrix([1],[2],[3],[4]),ident(4))),matrix([1,0,0,0,1,1,0,0,0],[0,1,0,0,2,0,1,0,0],[0,0,1,0,3,0,0,1,0],[0,0,0,1,4,0,0,0,1]));
+
+lmxchar: "[";
+s_test_case(tex1(aug(matrix([1,2,3],[4,5,6],[7,8,9]),matrix([1],[1],[1]))),"\\left[\\begin{array}{ccc} 1 & 2 & 3 \\\\ 4 & 5 & 6 \\\\ 7 & 8 & 9 \\end{array}\\left|\\begin{array}{c} 1 \\\\ 1 \\\\ 1 \\end{array}\\right.\\right]");
+s_test_case(tex1(aug(matrix([1,2,3,1],[4,5,6,1],[7,8,9,1]))),"\\left[\\begin{array}{ccc} 1 & 2 & 3 \\\\ 4 & 5 & 6 \\\\ 7 & 8 & 9 \\end{array}\\left|\\begin{array}{c} 1 \\\\ 1 \\\\ 1 \\end{array}\\right.\\right]");
+s_test_case(tex1(aug(matrix([1,2,3],[4,5,6],[7,8,9]),matrix([1],[1],[1]),matrix([3,2,1,0],[6,5,4,3],[9,8,7,6]))),"\\left[\\begin{array}{ccc} 1 & 2 & 3 \\\\ 4 & 5 & 6 \\\\ 7 & 8 & 9 \\end{array}\\left|\\begin{array}{c} 1 \\\\ 1 \\\\ 1 \\end{array}\\right.\\left|\\begin{array}{cccc} 3 & 2 & 1 & 0 \\\\ 6 & 5 & 4 & 3 \\\\ 9 & 8 & 7 & 6 \\end{array}\\right.\\right]");
+lmxchar: "{";
+s_test_case(tex1(aug(matrix([1,2,3],[4,5,6],[7,8,9]),matrix([1],[1],[1]))),"\\left\\{\\begin{array}{ccc} 1 & 2 & 3 \\\\ 4 & 5 & 6 \\\\ 7 & 8 & 9 \\end{array}\\left|\\begin{array}{c} 1 \\\\ 1 \\\\ 1 \\end{array}\\right.\\right\\}");
+lmxchar: "[";
 
 s_test_case(triu(matrix([1,2,3],[4,5,6],[7,8,9])),matrix([1,2,3],[0,5,6],[0,0,9]));
 s_test_case(triu(matrix([1,2,3],[4,5,6],[7,8,9],[10,11,12])),matrix([1,2,3],[0,5,6],[0,0,9],[0,0,0]));