From fe6837f6dcf852ca55921c6dca4ca3d57917a4b4 Mon Sep 17 00:00:00 2001
From: David Manura <dm.git@math2.org>
Date: Wed, 22 Sep 2010 21:41:53 -0400
Subject: [PATCH] import version 0.2.9, 2008-08-26 	- decoupled symbol
 class from matrix class: 	-   matrix.replace has new semantics, applying
 a function to each element. 	      For old behavior: mtx =
 mtx:replace(matrix.symbol.makereplacer(...)) 	-   replaced mtx:gsub(a,b)
 with mtx = mtx:replace(symbol.gsub,a,b) 	-   replaced
 matrix.tosymbol(mtx) with mtx = mtx:replace(symbol) 	- eliminated
 dependency on complex: 	-   replaced matrix.tocomplex(mtx) with mtx =
 mtx:replace(complex) 	-   replaced matrix.conjugate(mtx) with mtx =
 mtx:replace(complex.conjugate) 	-   mulnum and divnum no longer can
 take num of type string 	-   complex table no longer returned on module
 load 	- renamed remcomplex to elementstostrings and changed it to return new
 	    matrix rather than doing in-place modification 	- fixed
 matrix.numround (numround variable mispelled). 	    Reported by Goeff
 Richards.

---
 LICENSE.txt                                   |  35 ++
 README.txt                                    |  22 +
 .../complex_changelog.txt                     |   5 +-
 fit_changelog.txt => doc/fit_changelog.txt    |   0
 .../matrix_changelog.txt                      |  62 +-
 complex.lua => lua/complex.lua                |  16 +-
 matrix.lua => lua/matrix.lua                  | 530 ++++++++----------
 rockspec                                      |  31 +
 fit.lua => samples/fit.lua                    |   3 +-
 test_fit.lua                                  |  22 -
 tests/test.lua                                |   8 +
 test_complex.lua => tests/test_complex.lua    |  10 +-
 tests/test_fit.lua                            |  25 +
 test_matrix.lua => tests/test_matrix.lua      |  80 +--
 14 files changed, 448 insertions(+), 401 deletions(-)
 create mode 100644 LICENSE.txt
 create mode 100644 README.txt
 rename complex_changelog.txt => doc/complex_changelog.txt (96%)
 rename fit_changelog.txt => doc/fit_changelog.txt (100%)
 rename matrix_changelog.txt => doc/matrix_changelog.txt (85%)
 rename complex.lua => lua/complex.lua (97%)
 rename matrix.lua => lua/matrix.lua (78%)
 create mode 100644 rockspec
 rename fit.lua => samples/fit.lua (96%)
 delete mode 100644 test_fit.lua
 create mode 100644 tests/test.lua
 rename test_complex.lua => tests/test_complex.lua (96%)
 create mode 100644 tests/test_fit.lua
 rename test_matrix.lua => tests/test_matrix.lua (77%)

diff --git a/LICENSE.txt b/LICENSE.txt
new file mode 100644
index 0000000..cce010c
--- /dev/null
+++ b/LICENSE.txt
@@ -0,0 +1,35 @@
+LuaMatrix License
+-----------
+
+LuaMatrix ( http://luamatrix.luaforge.net/ ) is licensed under the
+same terms as Lua (MIT license) reproduced below.  This means that
+LuaMatrix is free software and can be used for both academic and
+commercial purposes at absolutely no cost.
+
+For details and rationale, see http://www.lua.org/license.html .
+
+===============================================================================
+
+Copyright (C) 2007-2010 Michael Lutz.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+
+===============================================================================
+
+(end of COPYRIGHT)
diff --git a/README.txt b/README.txt
new file mode 100644
index 0000000..a0e8b2b
--- /dev/null
+++ b/README.txt
@@ -0,0 +1,22 @@
+== Description ==
+
+LuaMatrix - Matrices and matrix operations implemented in pure Lua.
+
+This supports operations on matrices and vectors whose elements are
+real, complex, or symbolic.  Implemented entirely in Lua as tables.
+Includes a complex number data type too.
+
+For details on use, see the comments in matrix.lua and complex.lua,
+as well as the test suite.
+
+To install, copy matrix.lua and complex.lua into your LUA_PATH.  The
+modules can alternately be installed via LuaRocks ("luarocks install
+luamatrix").
+
+== Project Page ==
+
+http://lua-users.org/wiki/LuaMatrix
+
+== License ==
+
+See the LICENSE.txt file for licensing details.
diff --git a/complex_changelog.txt b/doc/complex_changelog.txt
similarity index 96%
rename from complex_changelog.txt
rename to doc/complex_changelog.txt
index bd99662..372d0bb 100644
--- a/complex_changelog.txt
+++ b/doc/complex_changelog.txt
@@ -1,5 +1,8 @@
+complex changelog
 
-complex changelog:
+v 0.3.1: 2007-11-12
+	[ David Manura ]
+	rename mulconjugate to norm2
 
 v 0.3.0: 2007-08-26
 	- fixed print function
diff --git a/fit_changelog.txt b/doc/fit_changelog.txt
similarity index 100%
rename from fit_changelog.txt
rename to doc/fit_changelog.txt
diff --git a/matrix_changelog.txt b/doc/matrix_changelog.txt
similarity index 85%
rename from matrix_changelog.txt
rename to doc/matrix_changelog.txt
index fc9ee31..63d8b6a 100644
--- a/matrix_changelog.txt
+++ b/doc/matrix_changelog.txt
@@ -1,49 +1,21 @@
-matrix function list:
+matrix changelog
 
-matrix.add
-matrix.columns
-matrix.concath
-matrix.concatv
-matrix.conjugate
-matrix.copy
-matrix.cross
-matrix.det
-matrix.div
-matrix.divnum
-matrix.dogauss
-matrix.getelement
-matrix.gsub
-matrix.invert
-matrix.ipairs
-matrix.latex
-matrix.len
-matrix.mul
-matrix.mulnum
-matrix:new
-matrix.normf
-matrix.normmax
-matrix.pow
-matrix.print
-matrix.random
-matrix.remcomplex
-matrix.replace
-matrix.root
-matrix.rotl
-matrix.rotr
-matrix.round
-matrix.rows
-matrix.scalar
-matrix.setelement
-matrix.size
-matrix.solve
-matrix.sqrt
-matrix.sub
-matrix.subm
-matrix.tocomplex
-matrix.tostring
-matrix.tosymbol
-matrix.transpose
-matrix.type
+v 0.2.9: 2008-08-26
+	[ David Manura ]
+	- decoupled symbol class from matrix class:
+	-   matrix.replace has new semantics, applying a function to each element.
+	      For old behavior: mtx = mtx:replace(matrix.symbol.makereplacer(...))
+	-   replaced mtx:gsub(a,b) with mtx = mtx:replace(symbol.gsub,a,b)
+	-   replaced matrix.tosymbol(mtx) with mtx = mtx:replace(symbol)
+	- eliminated dependency on complex:
+	-   replaced matrix.tocomplex(mtx) with mtx = mtx:replace(complex)
+	-   replaced matrix.conjugate(mtx) with mtx = mtx:replace(complex.conjugate)
+	-   mulnum and divnum no longer can take num of type string
+	-   complex table no longer returned on module load
+	- renamed remcomplex to elementstostrings and changed it to return new
+	    matrix rather than doing in-place modification
+        - Fixed matrix.numround (numround variable mispelled).
+          Reported by Goeff Richards.
 
 v 0.2.8: 2007-08-26
 	[ Michael Lutz ]
diff --git a/complex.lua b/lua/complex.lua
similarity index 97%
rename from complex.lua
rename to lua/complex.lua
index c6dd552..86bfaea 100644
--- a/complex.lua
+++ b/lua/complex.lua
@@ -1,4 +1,4 @@
--- complex 0.3.0
+-- complex 0.3.1
 -- Lua 5.1
 
 -- 'complex' provides common tasks with complex numbers
@@ -15,8 +15,7 @@
 -- the access is faster than in a hash table
 -- the metatable is just a add on, when it comes to speed, one is faster using a direct function call
 
--- http://luaforge.net/projects/LuaMatrix
--- http://lua-users.org/wiki/ComplexNumbers
+-- http://luamatrix.luaforge.net
 
 -- Licensed under the same terms as Lua itself.
 
@@ -191,9 +190,10 @@ function complex.polardeg( cx )
 	return math.sqrt( cx[1]^2 + cx[2]^2 ), math.atan2( cx[2], cx[1] ) / math.pi * 180
 end
 
--- complex.mulconjugate( cx )
--- multiply with conjugate, function returning a number
-function complex.mulconjugate( cx )
+-- complex.norm2( cx )
+-- multiply with conjugate, function returning a scalar number
+-- norm2(x + i*y) returns x^2 + y^2
+function complex.norm2( cx )
 	return cx[1]^2 + cx[2]^2
 end
 
@@ -330,6 +330,10 @@ function complex.round( cx,idp )
 		math.floor( cx[2] * mult + 0.5 ) / mult }, complex_meta )
 end
 
+--// variables
+complex.zero = complex.new(0, 0)
+complex.one  = complex.new(1, 0)
+
 --// metatable functions
 
 complex_meta.__add = function( cx1,cx2 )
diff --git a/matrix.lua b/lua/matrix.lua
similarity index 78%
rename from matrix.lua
rename to lua/matrix.lua
index 8096097..96f3c03 100644
--- a/matrix.lua
+++ b/lua/matrix.lua
@@ -1,5 +1,5 @@
 --[[
-	matrix v 0.2.8
+	matrix v 0.2.9
 	
 	Lua 5.1 compatible
 	
@@ -30,10 +30,53 @@
 		where num will be a matrix with the result in mtx[1][1],
 		or use num = vec1:scalar( vec2 ), where num is a number
 		
-	Sites:
-		http://luaforge.net/projects/LuaMatrix
-		http://lua-users.org/wiki/SimpleMatrix
-		
+	Site: http://luamatrix.luaforge.net
+
+	matrix function list:
+
+	matrix.add
+	matrix.columns
+	matrix.concath
+	matrix.concatv
+	matrix.copy
+	matrix.cross
+	matrix.det
+	matrix.div
+	matrix.divnum
+	matrix.dogauss
+	matrix.elementstostring
+	matrix.getelement
+	matrix.gsub
+	matrix.invert
+	matrix.ipairs
+	matrix.latex
+	matrix.len
+	matrix.mul
+	matrix.mulnum
+	matrix:new
+	matrix.normf
+	matrix.normmax
+	matrix.pow
+	matrix.print
+	matrix.random
+	matrix.replace
+	matrix.root
+	matrix.rotl
+	matrix.rotr
+	matrix.round
+	matrix.rows
+	matrix.scalar
+	matrix.setelement
+	matrix.size
+	matrix.solve
+	matrix.sqrt
+	matrix.sub
+	matrix.subm
+	matrix.tostring
+	matrix.transpose
+	matrix.type
+
+	
 	Licensed under the same terms as Lua itself.
 	
 	Developers:
@@ -41,10 +84,6 @@
 		David Manura http://lua-users.org/wiki/DavidManura
 ]]--
 
--- for speed and clearer code load the complex function table
--- in there we define the complex number
-local complex = require "complex"
-
 --////////////
 --// matrix //
 --////////////
@@ -54,13 +93,6 @@ local matrix = {}
 -- access to the metatable we set at the end of the file
 local matrix_meta = {}
 
--- access to the symbolic metatable
-local symbol_meta = {}; symbol_meta.__index = symbol_meta
--- set up a symbol type
-local function newsymbol(o)
-	return setmetatable({tostring(o)}, symbol_meta)
-end
-
 --/////////////////////////////
 --// Get 'new' matrix object //
 --/////////////////////////////
@@ -124,7 +156,7 @@ setmetatable( matrix, { __call = function( ... ) return matrix.new( ... ) end }
 --// matrix 'matrix' functions //
 --///////////////////////////////
 
---// for real, complx and symbolic matrices //--
+--// for real, complex and symbolic matrices //--
 
 -- note: real and complex matrices may be added, subtracted, etc.
 --		real and symbolic matrices may also be added, subtracted, etc.
@@ -132,33 +164,35 @@ setmetatable( matrix, { __call = function( ... ) return matrix.new( ... ) end }
 --		since it is not clear which metatable then is used
 
 --// matrix.add ( m1, m2 )
--- Add 2 matrices; m2 may be of bigger size than m1
+-- Add two matrices; m2 may be of bigger size than m1
 function matrix.add( m1, m2 )
 	local mtx = {}
 	for i = 1,#m1 do
-		mtx[i] = {}
+		local m3i = {}
+		mtx[i] = m3i
 		for j = 1,#m1[1] do
-			mtx[i][j] = m1[i][j] + m2[i][j]
+			m3i[j] = m1[i][j] + m2[i][j]
 		end
 	end
 	return setmetatable( mtx, matrix_meta )
 end
 
 --// matrix.sub ( m1 ,m2 )
--- Subtract 2 matrices; m2 may be of bigger size than m1
+-- Subtract two matrices; m2 may be of bigger size than m1
 function matrix.sub( m1, m2 )
 	local mtx = {}
 	for i = 1,#m1 do
-		mtx[i] = {}
+		local m3i = {}
+		mtx[i] = m3i
 		for j = 1,#m1[1] do
-			mtx[i][j] = m1[i][j] - m2[i][j]
+			m3i[j] = m1[i][j] - m2[i][j]
 		end
 	end
 	return setmetatable( mtx, matrix_meta )
 end
 
 --// matrix.mul ( m1, m2 )
--- Multiply 2 matrices; m1 columns must be equal to m2 rows
+-- Multiply two matrices; m1 columns must be equal to m2 rows
 -- e.g. #m1[1] == #m2
 function matrix.mul( m1, m2 )
 	-- multiply rows with columns
@@ -177,7 +211,7 @@ function matrix.mul( m1, m2 )
 end
 
 --//  matrix.div ( m1, m2 )
--- Divide 2 matrices; m1 columns must be equal to m2 rows
+-- Divide two matrices; m1 columns must be equal to m2 rows
 -- m2 must be square, to be inverted,
 -- if that fails returns the rank of m2 as second argument
 -- e.g. #m1[1] == #m2; #m2 == #m2[1]
@@ -189,12 +223,9 @@ end
 
 --// matrix.mulnum ( m1, num )
 -- Multiply matrix with a number
--- num may be of type 'number','complex number' or 'string'
+-- num may be of type 'number' or 'complex number'
 -- strings get converted to complex number, if that fails then to symbol
 function matrix.mulnum( m1, num )
-	if type(num) == "string" then
-		num = complex.to(num) or newsymbol(num)
-	end
 	local mtx = {}
 	-- multiply elements with number
 	for i = 1,#m1 do
@@ -208,18 +239,16 @@ end
 
 --// matrix.divnum ( m1, num )
 -- Divide matrix by a number
--- num may be of type 'number','complex number' or 'string'
+-- num may be of type 'number' or 'complex number'
 -- strings get converted to complex number, if that fails then to symbol
 function matrix.divnum( m1, num )
-	if type(num) == "string" then
-		num = complex.to(num) or newsymbol(num)
-	end
 	local mtx = {}
 	-- divide elements by number
 	for i = 1,#m1 do
-		mtx[i] = {}
+		local mtxi = {}
+		mtx[i] = mtxi
 		for j = 1,#m1[1] do
-			mtx[i][j] = m1[i][j] / num
+			mtxi[j] = m1[i][j] / num
 		end
 	end
 	return setmetatable( mtx, matrix_meta )
@@ -251,6 +280,10 @@ function matrix.pow( m1, num )
 	return mtx
 end
 
+local function number_norm2(x)
+  return x * x
+end
+
 --// matrix.det ( m1 )
 -- Calculate the determinant of a matrix
 -- m1 needs to be square
@@ -261,8 +294,6 @@ end
 -- here we try to get the nearest element to |1|, (smallest pivot element)
 -- os that usually we have |mtx[i][j]/subdet| > 1 or mtx[i][j];
 -- with complex matrices we use the complex.abs function to check if it is bigger or smaller
-local fiszerocomplex = function( cx ) return complex.is(cx,0,0) end
-local fiszeronumber = function( num ) return num == 0 end
 function matrix.det( m1 )
 
 	-- check if matrix is quadratic
@@ -284,16 +315,10 @@ function matrix.det( m1 )
 	end
 	
 	--// no symbolic matrix supported below here
-	
-	local fiszero, abs
-	if matrix.type( m1 ) == "complex" then
-		fiszero = fiszerocomplex
-		abs = complex.mulconjugate
-	else
-		fiszero = fiszeronumber
-		abs = math.abs
-	end
-	
+	local e = m1[1][1]
+	local zero  = type(e) == "table" and e.zero or 0
+	local norm2 = type(e) == "table" and e.norm2 or number_norm2
+
 	--// matrix is bigger than 3x3
 	-- get determinant
 	-- using Gauss elimination and Laplace
@@ -313,12 +338,12 @@ function matrix.det( m1 )
 			-- if no subdet has been found
 			if not subdet then
 				-- check if element it is not zero
-				if not fiszero(e) then
+				if e ~= zero then
 					-- use element as new subdet
 					subdet,xrow = e,i
 				end
 			-- check for elements nearest to 1 or -1
-			elseif (not fiszero(e)) and math.abs(abs(e)-1) < math.abs(abs(subdet)-1) then
+			elseif e ~= zero and math.abs(norm2(e)-1) < math.abs(norm2(subdet)-1) then
 				subdet,xrow = e,i
 			end
 		end
@@ -335,7 +360,7 @@ function matrix.det( m1 )
 			for i = 1,rows-1 do
 				-- factor is the dividor of the first element
 				-- if element is not already zero
-				if not fiszero( mtx[i][j] ) then
+				if mtx[i][j] ~= zero then
 					local factor = mtx[i][j]/subdet
 					-- update all remaining fields of the matrix, with value from xrow
 					for n = j+1,#mtx[1] do
@@ -366,23 +391,23 @@ end
 
 -- locals
 -- checking here for the nearest element to 1 or -1; (smallest pivot element)
--- this way the factor of the evolving number division should be > 1 or the divided number itself,
--- what gives better results
-local setelementtosmallest = function( mtx,i,j,fiszero,fisone,abs )
+-- this way the factor of the evolving number division should be > 1 or the
+-- divided number itself, what gives better results
+local setelementtosmallest = function( mtx,i,j,zero,one,norm2 )
 	-- check if element is one
-	if fisone(mtx[i][j]) then return true end
+	if mtx[i][j] == one then return true end
 	-- check for lowest value
 	local _ilow
 	for _i = i,#mtx do
 		local e = mtx[_i][j]
-		if fisone(e) then
+		if e == one then
 			break
 		end
 		if not _ilow then
-			if not fiszero(e) then
+			if e ~= zero then
 				_ilow = _i
 			end
-		elseif (not fiszero(e)) and math.abs(abs(e)-1) < math.abs(abs(mtx[_ilow][j])-1) then
+		elseif (e ~= zero) and math.abs(norm2(e)-1) < math.abs(norm2(mtx[_ilow][j])-1) then
 			_ilow = _i
 		end
 	end
@@ -395,40 +420,28 @@ local setelementtosmallest = function( mtx,i,j,fiszero,fisone,abs )
 		return true
 	end
 end
-local cxfiszero = function( cx ) return complex.is(cx,0,0) end
-local cxfsetzero = function( mtx,i,j ) complex.set(mtx[i][j],0,0) end
-local cxfisone = function( cx ) return complex.abs(cx) == 1 end
-local cxfsetone = function( mtx,i,j ) complex.set(mtx[i][j],1,0) end
-local numfiszero = function( num ) return num == 0 end
-local numfsetzero = function( mtx,i,j ) mtx[i][j] = 0 end
-local numfisone = function( num ) return math.abs(num) == 1 end
-local numfsetone = function( mtx,i,j ) mtx[i][j] = 1 end
+
+local function copy(x)
+	return type(x) == "table" and x.copy(x) or x
+end
+
 -- note: in --// ... //-- we have a way that does no divison,
 -- however with big number and matrices we get problems since we do no reducing
 function matrix.dogauss( mtx )
-	local fiszero,fsetzero,fisone,fsetone,abs
-	if matrix.type( mtx ) == "complex" then
-		fiszero = cxfiszero
-		fsetzero = cxfsetzero
-		fisone = cxfisone
-		fsetone = cxfsetone
-		abs = complex.mulconjugate
-	else
-		fiszero = numfiszero
-		fsetzero = numfsetzero
-		fisone = numfisone
-		fsetone = numfsetone
-		abs = math.abs
-	end
+	local e = mtx[1][1]
+	local zero = type(e) == "table" and e.zero or 0
+	local one  = type(e) == "table" and e.one  or 1
+	local norm2 = type(e) == "table" and e.norm2 or number_norm2
+
 	local rows,columns = #mtx,#mtx[1]
 	-- stairs left -> right
 	for j = 1,rows do
 		-- check if element can be setted to one
-		if setelementtosmallest( mtx,j,j,fiszero,fisone,abs ) then
+		if setelementtosmallest( mtx,j,j,zero,one,norm2 ) then
 			-- start parsing rows
 			for i = j+1,rows do
 				-- check if element is not already zero
-				if not fiszero(mtx[i][j]) then
+				if mtx[i][j] ~= zero then
 					-- we may add x*otherline row, to set element to zero
 					-- tozero - x*mtx[j][j] = 0; x = tozero/mtx[j][j]
 					local factor = mtx[i][j]/mtx[j][j]
@@ -436,7 +449,7 @@ function matrix.dogauss( mtx )
 					-- yet with big matrices (since we do no reducing and other things)
 					-- we get too big numbers
 					--local factor1,factor2 = mtx[i][j],mtx[j][j] //--
-					fsetzero(mtx,i,j)
+					mtx[i][j] = copy(zero)
 					for _j = j+1,columns do
 						--// mtx[i][_j] = mtx[i][_j] * factor2 - factor1 * mtx[j][_j] //--
 						mtx[i][_j] = mtx[i][_j] - factor * mtx[j][_j]
@@ -459,15 +472,15 @@ function matrix.dogauss( mtx )
 		-- start parsing rows
 		for i = j-1,1,-1 do
 			-- check if element is not already zero			
-			if not fiszero(mtx[i][j]) then
+			if mtx[i][j] ~= zero then
 				local factor = mtx[i][j]
 				for _j = j+1,columns do
 					mtx[i][_j] = mtx[i][_j] - factor * mtx[j][_j]
 				end
-				fsetzero(mtx,i,j)
+				mtx[i][j] = copy(zero)
 			end
 		end
-		fsetone(mtx,j,j)
+		mtx[j][j] = copy(one)
 	end
 	return true
 end
@@ -481,27 +494,14 @@ function matrix.invert( m1 )
 	assert(#m1 == #m1[1], "matrix not square")
 	local mtx = matrix.copy( m1 )
 	local ident = setmetatable( {},matrix_meta )
-	if matrix.type( mtx ) == "complex" then
-		for i = 1,#m1 do
-			ident[i] = {}
-			for j = 1,#m1 do
-				if i == j then
-					ident[i][j] = complex.new( 1,0 )
-				else
-					ident[i][j] = complex.new( 0,0 )
-				end
-			end
-		end
-	else
-		for i = 1,#m1 do
-			ident[i] = {}
-			for j = 1,#m1 do
-				if i == j then
-					ident[i][j] = 1
-				else
-					ident[i][j] = 0
-				end
-			end
+	local e = m1[1][1]
+    local zero = type(e) == "table" and e.zero or 0
+    local one  = type(e) == "table" and e.one  or 1
+	for i = 1,#m1 do
+		local identi = {}
+		ident[i] = identi
+		for j = 1,#m1 do
+			identi[j] = copy((i == j) and one or zero)
 		end
 	end
 	mtx = matrix.concath( mtx,ident )
@@ -527,7 +527,8 @@ end
 -- local average error
 local function get_abs_avg( m1, m2 )
 	local dist = 0
-	local abs = matrix.type(m1) == "complex" and complex.abs or math.abs
+	local e = m1[1][1]
+	local abs = type(e) == "table" and e.abs or math.abs
 	for i=1,#m1 do
 		for j=1,#m1[1] do
 			dist = dist + abs(m1[i][j]-m2[i][j])
@@ -650,7 +651,7 @@ local tround = function( t,mult )
 end
 function matrix.round( mtx, idp )
 	local mult = 10^( idp or 0 )
-	local fround = matrix.type( mtx ) == "number" and numound or tround
+	local fround = matrix.type( mtx ) == "number" and numround or tround
 	for i = 1,#mtx do
 		for j = 1,#mtx[1] do
 			mtx[i][j] = fround(mtx[i][j],mult)
@@ -691,12 +692,10 @@ end
 --// matrix.type ( mtx )
 -- get type of matrix, normal/complex/symbol or tensor
 function matrix.type( mtx )
-	if type(mtx[1][1]) == "table" then
-		if complex.type(mtx[1][1]) then
-			return "complex"
-		end
-		if getmetatable(mtx[1][1]) == symbol_meta then
-			return "symbol"
+	local e = mtx[1][1]
+	if type(e) == "table" then
+		if e.type then
+			return e:type()
 		end
 		return "tensor"
 	end
@@ -766,7 +765,7 @@ function matrix.subm( m1,i1,j1,i2,j2 )
 end
 
 --// matrix.concath( m1, m2 )
--- Concatenate 2 matrices, horizontal
+-- Concatenate two matrices, horizontal
 -- will return m1m2; rows have to be the same
 -- e.g.: #m1 == #m2
 function matrix.concath( m1,m2 )
@@ -787,7 +786,7 @@ function matrix.concath( m1,m2 )
 end
 
 --// matrix.concatv ( m1, m2 )
--- Concatenate 2 matrices, vertical
+-- Concatenate two matrices, vertical
 -- will return	m1
 --					m2
 -- columns have to be the same; e.g.: #m1[1] == #m2[1]
@@ -838,59 +837,32 @@ function matrix.rotr( m1 )
 	return mtx
 end
 
--- local get_elemnts in string
-local get_tstr = function( t )
-	return "["..table.concat(t,",").."]"
-end
-local get_str = function( e )
-	return tostring(e)
-end
--- local get_elemnts in string and formated
-local getf_tstr = function( t,fstr )
+local function tensor_tostring( t,fstr )
+	if not fstr then return "["..table.concat(t,",").."]" end
 	local tval = {}
 	for i,v in ipairs( t ) do
 		tval[i] = string.format( fstr,v )
 	end
 	return "["..table.concat(tval,",").."]"
 end
-local getf_cxstr = function( e,fstr )
-	return complex.tostring( e,fstr )
-end
-local getf_symstr = function( e,fstr )
-	return string.format( fstr,e[1] )
-end
-local getf_str = function( e,fstr )
-	return string.format( fstr,e )
+local function number_tostring( e,fstr )
+	return fstr and string.format( fstr,e ) or e
 end
 
 --// matrix.tostring ( mtx, formatstr )
 -- tostring function
 function matrix.tostring( mtx, formatstr )
 	local ts = {}
-	local getstr
-	if formatstr then -- get str formatted
-		local mtype = matrix.type( mtx )
-		if mtype == "tensor" then getstr = getf_tstr
-		elseif mtype == "complex" then getstr = getf_cxstr
-		elseif mtype == "symbol" then getstr = getf_symstr
-		else getstr = getf_str end
-		-- iteratr
-		for i = 1,#mtx do
-			local tstr = {}
-			for j = 1,#mtx[1] do
-				tstr[j] = getstr(mtx[i][j],formatstr)
-			end
-			ts[i] = table.concat(tstr, "\t")
-		end
-	else
-		getstr = matrix.type( mtx ) == "tensor" and get_tstr or get_str
-		for i = 1,#mtx do
-			local tstr = {}
-			for j = 1,#mtx[1] do
-				tstr[j] = getstr(mtx[i][j])
-			end
-			ts[i] = table.concat(tstr, "\t")
+	local mtype = matrix.type( mtx )
+	local e = mtx[1][1]
+	local tostring = mtype == "tensor" and tensor_tostring or
+	      type(e) == "table" and e.tostring or number_tostring
+	for i = 1,#mtx do
+		local tstr = {}
+		for j = 1,#mtx[1] do
+			tstr[j] = tostring(mtx[i][j],formatstr)
 		end
+		ts[i] = table.concat(tstr, "\t")
 	end
 	return table.concat(ts, "\n")
 end
@@ -909,7 +881,7 @@ function matrix.latex( mtx, align )
 	--		\usepackage{dcolumn}; D{.}{,}{-1}; aligns number by . replaces it with ,
 	local align = align or "c"
 	local str = "$\\left( \\begin{array}{"..string.rep( align, #mtx[1] ).."}\n"
-	local getstr = matrix.type( mtx ) == "tensor" and get_tstr or get_str
+	local getstr = matrix.type( mtx ) == "tensor" and tensor_tostring or number_tostring
 	for i = 1,#mtx do
 		str = str.."\t"..getstr(mtx[i][1])
 		for j = 2,#mtx[1] do
@@ -1014,96 +986,29 @@ function matrix.len( m1 )
 	return math.sqrt( m1[1][1]^2 + m1[2][1]^2 + m1[3][1]^2 )
 end
 
---////////////////////////////////
---// matrix 'complex' functions //
---////////////////////////////////
 
---// matrix.tocomplex ( mtx )
--- we set now all elements to a complex number
--- also set the metatable
-function matrix.tocomplex( mtx )
-	assert( matrix.type(mtx) == "number", "matrix not of type 'number'" )
-	for i = 1,#mtx do
-		for j = 1,#mtx[1] do
-			mtx[i][j] = complex.to( mtx[i][j] )
+--// matrix.replace (mtx, func, ...)
+-- for each element e in the matrix mtx, replace it with func(mtx, ...).
+function matrix.replace( m1, func, ... )
+	local mtx = {}
+	for i = 1,#m1 do
+		local m1i = m1[i]
+		local mtxi = {}
+		for j = 1,#m1i do
+			mtxi[j] = func( m1i[j], ... )
 		end
+		mtx[i] = mtxi
 	end
 	return setmetatable( mtx, matrix_meta )
 end
 
 --// matrix.remcomplex ( mtx )
--- set the matrix elements to a number or complex number string
-function matrix.remcomplex( mtx )
-	assert( matrix.type(mtx) == "complex", "matrix not of type 'complex'" )
-	for i = 1,#mtx do
-		for j = 1,#mtx[1] do
-			mtx[i][j] = complex.tostring( mtx[i][j] )
-		end
-	end
-	return setmetatable( mtx, matrix_meta )
-end
-
---// matrix.conjugate ( m1 )
--- get the conjugate complex matrix
-function matrix.conjugate( m1 )
-	assert( matrix.type(m1) == "complex", "matrix not of type 'complex'" )
-	local mtx = {}
-	for i = 1,#m1 do
-		mtx[i] = {}
-		for j = 1,#m1[1] do
-			mtx[i][j] = complex.conjugate( m1[i][j] )
-		end
-	end
-	return setmetatable( mtx, matrix_meta )
-end
-
---/////////////////////////////////
---// matrix 'symbol' functions //
---/////////////////////////////////
-
---// matrix.tosymbol ( mtx )
--- set the matrix elements to symbolic values
-function matrix.tosymbol( mtx )
-	assert( matrix.type( mtx ) ~= "tensor", "cannot convert type 'tensor' to 'symbol'" )
-	for i = 1,#mtx do
-		for j = 1,#mtx[1] do
-			mtx[i][j] = newsymbol( mtx[i][j] )
-		end
-	end
-	return setmetatable( mtx, matrix_meta )
-end
-
---// matrix.gsub( m1, from, to )
--- perform gsub on all elements
-function matrix.gsub( m1,from,to )
-	assert( matrix.type( m1 ) == "symbol", "matrix not of type 'symbol'" )
-	local mtx = {}
-	for i = 1,#m1 do
-		mtx[i] = {}
-		for j = 1,#m1[1] do
-			mtx[i][j] = newsymbol( string.gsub( m1[i][j][1],from,to ) )
-		end
-	end
-	return setmetatable( mtx, matrix_meta )
-end
-
---// matrix.replace ( m1, ... )
--- replace one letter by something else
--- replace( "a",4,"b",7, ... ) will replace a with 4 and b with 7
-function matrix.replace( m1,... )
-	assert( matrix.type( m1 ) == "symbol", "matrix not of type 'symbol'" )
-	local tosub,args = {},{...}
-	for i = 1,#args,2 do
-		tosub[args[i]] = args[i+1]
-	end
-	local mtx = {}
-	for i = 1,#m1 do
-		mtx[i] = {}
-		for j = 1,#m1[1] do
-			mtx[i][j] = newsymbol( string.gsub( m1[i][j][1], "%a", function( a ) return tosub[a] or a end ) )
-		end
-	end
-	return setmetatable( mtx, matrix_meta )
+-- set the matrix elements to strings
+-- IMPROVE: tostring v.s. tostringelements confusing
+function matrix.elementstostrings( mtx )
+	local e = mtx[1][1]
+	local tostring = type(e) == "table" and e.tostring or tostring
+	return matrix.replace(mtx, tostring)
 end
 
 --// matrix.solve ( m1 )
@@ -1120,46 +1025,6 @@ function matrix.solve( m1 )
 	return setmetatable( mtx, matrix_meta )
 end
 
-function symbol_meta.__add(a,b)
-	return newsymbol(a .. "+" .. b)
-end
-
-function symbol_meta.__sub(a,b)
-	return newsymbol(a .. "-" .. b)
-end
-
-function symbol_meta.__mul(a,b)
-	return newsymbol("(" .. a .. ")*(" .. b .. ")")
-end
-
-function symbol_meta.__div(a,b)
-	return newsymbol("(" .. a .. ")/(" .. b .. ")")
-end
-
-function symbol_meta.__pow(a,b)
-	return newsymbol("(" .. a .. ")^(" .. b .. ")")
-end
-
-function symbol_meta.__eq(a,b)
-	return a[1] == b[1]
-end
-
-function symbol_meta.__tostring(a)
-	return a[1]
-end
-
-function symbol_meta.__concat(a,b)
-	return tostring(a) .. tostring(b)
-end
-
-function symbol_meta.abs(a)
-	return newsymbol("(" .. a[1] .. "):abs()")
-end
-
-function symbol_meta.sqrt(a)
-	return newsymbol("(" .. a[1] .. "):sqrt()")
-end
-
 --////////////////////////--
 --// METATABLE HANDLING //--
 --////////////////////////--
@@ -1232,7 +1097,7 @@ matrix_meta.__eq = function( m1, m2 )
 	if #m1 ~= #m2 or #m1[1] ~= #m2[1] then
 		return false
 	end
-	-- check normal,complex and symbolic
+	-- check elements equal
 	for i = 1,#m1 do
 		for j = 1,#m1[1] do
 			if m1[i][j] ~= m2[i][j] then
@@ -1259,8 +1124,107 @@ for k,v in pairs( matrix ) do
 	matrix_meta.__index[k] = v
 end
 
--- return the matrix and complex
-return matrix, complex
+
+--/////////////////////////////////
+--// symbol class implementation
+--/////////////////////////////////
+
+-- access to the symbolic metatable
+local symbol_meta = {}; symbol_meta.__index = symbol_meta
+local symbol = symbol_meta
+
+function symbol_meta.new(o)
+	return setmetatable({tostring(o)}, symbol_meta)
+end
+symbol_meta.to = symbol_meta.new
+
+-- symbol( arg )
+-- same as symbol.to( arg )
+-- set __call behaviour of symbol
+setmetatable( symbol_meta, { __call = function( _,s ) return symbol_meta.to( s ) end } )
+
+
+-- Converts object to string, optionally with formatting.
+function symbol_meta.tostring( e,fstr )
+	return string.format( fstr,e[1] )
+end
+
+-- Returns "symbol" if object is a symbol type, else nothing.
+function symbol_meta:type()
+	if getmetatable(self) == symbol_meta then
+		return "symbol"
+	end
+end
+
+-- Performs string.gsub on symbol.
+-- for use in matrix.replace
+function symbol_meta:gsub(from, to)
+	return symbol.to( string.gsub( self[1],from,to ) )
+end
+
+-- creates function that replaces one letter by something else
+-- makereplacer( "a",4,"b",7, ... )(x)
+-- will replace a with 4 and b with 7 in symbol x.
+-- for use in matrix.replace
+function symbol_meta.makereplacer( ... )
+	local tosub = {}
+	local args = {...}
+	for i = 1,#args,2 do
+		tosub[args[i]] = args[i+1]
+    end
+	local function func( a ) return tosub[a] or a end
+	return function(sym)
+		return symbol.to( string.gsub( sym[1], "%a", func ) )
+	end
+end
+
+-- applies abs function to symbol
+function symbol_meta.abs(a)
+	return symbol.to("(" .. a[1] .. "):abs()")
+end
+
+-- applies sqrt function to symbol
+function symbol_meta.sqrt(a)
+	return symbol.to("(" .. a[1] .. "):sqrt()")
+end
+
+function symbol_meta.__add(a,b)
+	return symbol.to(a .. "+" .. b)
+end
+
+function symbol_meta.__sub(a,b)
+	return symbol.to(a .. "-" .. b)
+end
+
+function symbol_meta.__mul(a,b)
+	return symbol.to("(" .. a .. ")*(" .. b .. ")")
+end
+
+function symbol_meta.__div(a,b)
+	return symbol.to("(" .. a .. ")/(" .. b .. ")")
+end
+
+function symbol_meta.__pow(a,b)
+	return symbol.to("(" .. a .. ")^(" .. b .. ")")
+end
+
+function symbol_meta.__eq(a,b)
+	return a[1] == b[1]
+end
+
+function symbol_meta.__tostring(a)
+	return a[1]
+end
+
+function symbol_meta.__concat(a,b)
+	return tostring(a) .. tostring(b)
+end
+
+matrix.symbol = symbol
+
+
+-- return matrix
+return matrix
 
 --///////////////--
 --// chillcode //--
diff --git a/rockspec b/rockspec
new file mode 100644
index 0000000..ad138a4
--- /dev/null
+++ b/rockspec
@@ -0,0 +1,31 @@
+package = "LuaMatrix"
+version = "[VERSION]"
+source = {
+   url = "[URL]",
+}
+description = {
+   summary    = "Matrices and matrix operations implemented in pure Lua.",
+   detailed   = [[
+      This supports operations on matrices and vectors whose elements are
+      real, complex, or symbolic.  Implemented entirely in Lua as tables.
+      Includes a complex number data type too.
+   ]],
+   license    =  "MIT/X11",
+   homepage   = "http://luamatrix.luaforge.net/",
+   maintainer = "David Manura <http://lua-users.org/wiki/DavidManura>",
+}
+dependencies = {
+   "lua >= 5.1",
+}
+build = {
+   type = "none",
+   install = {
+      lua = {
+         ["complex"] = "lua/complex.lua",
+         ["matrix"]  = "lua/matrix.lua",
+      }
+   },
+   copy_directories = {"doc", "samples", "tests"},
+}
+-- test: tests/test.lua
+
diff --git a/fit.lua b/samples/fit.lua
similarity index 96%
rename from fit.lua
rename to samples/fit.lua
index de58a38..a48e952 100644
--- a/fit.lua
+++ b/samples/fit.lua
@@ -8,8 +8,7 @@
 
 -- little add-on to the matrix module, to show some curve fitting
 
--- http://luaforge.net/projects/LuaMatrix
--- http://lua-users.org/wiki/SimpleFit
+-- http://luamatrix.luaforge.net
 
 -- Licensed under the same terms as Lua itself.
 
diff --git a/test_fit.lua b/test_fit.lua
deleted file mode 100644
index 80ccb84..0000000
--- a/test_fit.lua
+++ /dev/null
@@ -1,22 +0,0 @@
--- require fit
-local fit = require "fit"
-
-print( "Fit a straight line " )
--- x(i) = 2  | 3  | 4  | 5
--- y(i) = 5  | 9  | 15 | 21
--- model = y = a +  b * x
--- r(i) = y(i) - ( a + b * x(i) )
-local a,b = fit.linear(	{ 2,3, 4, 5 },
-								{ 5,9,15,21 } )
-print( "=>    y = ( "..a.." )  +  ( "..b.." ) * x")
-
-print( "Fit a parabola " )
-local a, b, c = fit.parabola(	{ 0,1,2,4,6 },
-											{ 3,1,0,1,4 } )
-print( "=>    y = ( "..a.." )  +  ( "..b.." ) * x  +  ( "..c.." ) * x²")
-
-print( "Fit exponential" )
-local a, b = fit.exponential( {1,  2,  3,  4,   5},
-										{1,3.1,5.6,9.1,12.9} )
-print( "=>    y = ( "..a.." )  *  x^( "..b.." )")
-	
\ No newline at end of file
diff --git a/tests/test.lua b/tests/test.lua
new file mode 100644
index 0000000..80b665a
--- /dev/null
+++ b/tests/test.lua
@@ -0,0 +1,8 @@
+-- test suite (run from parent directory).
+
+package.path = './lua/?.lua;' .. package.path
+
+dofile 'tests/test_complex.lua'
+dofile 'tests/test_matrix.lua'
+dofile 'tests/test_fit.lua'
+print 'ALL PASSED'
diff --git a/test_complex.lua b/tests/test_complex.lua
similarity index 96%
rename from test_complex.lua
rename to tests/test_complex.lua
index 0b1aa5c..d4d7fae 100644
--- a/test_complex.lua
+++ b/tests/test_complex.lua
@@ -82,9 +82,9 @@ local r,phi = complex.polardeg( {0,-3} )
 assert( r == 3 )
 assert( phi == -90 )
 
--- complex.mulconjugate( cx )
+-- complex.norm2( cx )
 cx = complex "2+3i"
-assert( complex.mulconjugate( cx ) == 13 )
+assert( complex.norm2( cx ) == 13 )
 
 -- complex.abs( cx )
 cx = complex "3+4i"
@@ -168,7 +168,7 @@ assert( cx:ln():round( 4 ) == complex "1.6094+0.9273i" )
 
 -- complex.exp( cx )
 cx = complex "2+3i"
-assert( cx:ln():exp() == complex "2+3i" )
+assert( cx.abs( cx:ln():exp() - complex "2+3i" ) < 1e-7 )
 
 -- complex.conjugate( cx )
 cx = complex "2+3i"
@@ -182,4 +182,6 @@ assert( cx+2 == complex "4+3i" )
 
 -- __unm
 cx = complex "2+3i"
-assert( -cx == complex "-2-3i" )
\ No newline at end of file
+assert( -cx == complex "-2-3i" )
+
+print 'PASSED'
diff --git a/tests/test_fit.lua b/tests/test_fit.lua
new file mode 100644
index 0000000..263f3d7
--- /dev/null
+++ b/tests/test_fit.lua
@@ -0,0 +1,25 @@
+-- require fit
+package.path = "samples/?.lua;" .. package.path
+local fit = require "fit"
+
+-- Fit a straight line
+-- x(i) = 2  | 3  | 4  | 5
+-- y(i) = 5  | 9  | 15 | 21
+-- model = y = a +  b * x
+-- r(i) = y(i) - ( a + b * x(i) )
+local a,b = fit.linear(	{ 2,3, 4, 5 }, { 5,9,15,21 } )
+assert(math.abs(a - -6.4) < 0.001)
+assert(math.abs(b - 5.4) < 0.001)
+
+-- Fit a parabola
+local a, b, c = fit.parabola(	{ 0,1,2,4,6 }, { 3,1,0,1,4 } )
+assert(math.abs(a - 2.8251599147122) < 0.001)
+assert(math.abs(b - -2.0490405117271) < 0.001)
+assert(math.abs(c - 0.3773987206823) < 0.001)
+
+-- Fit exponential
+local a, b = fit.exponential( {1,  2,  3,  4,   5}, {1,3.1,5.6,9.1,12.9} )
+assert(math.abs(a - 1.0077958966968) < 0.001)
+assert(math.abs(b - 1.5834684450364) < 0.001)
+
+print 'PASSED'
diff --git a/test_matrix.lua b/tests/test_matrix.lua
similarity index 77%
rename from test_matrix.lua
rename to tests/test_matrix.lua
index 1302bf2..021faf7 100644
--- a/test_matrix.lua
+++ b/tests/test_matrix.lua
@@ -1,4 +1,6 @@
-local matrix, complex = require "matrix"
+local matrix = require "matrix"
+local complex = require "complex"
+local symbol = matrix.symbol
 
 local mtx, m1,m2,m3,m4,m5, ms,ms1,ms2,ms3,ms4
 
@@ -24,42 +26,42 @@ m1 = matrix{{8,4,1},{6,8,3}}
 m2 = matrix{{-8,1,3},{5,2,1}}
 assert(m1 + m2 == matrix{{0,5,4},{11,10,4}})
 -- matrix.add; complex
-m1 = matrix{{10,"2+6i",1},{5,1,"4-2i"}}:tocomplex()
-m2 = matrix{{3,4,5},{"2+3i",4,"6i"}}:tocomplex()
-assert(m1 + m2 == matrix{{13,"6+6i",6},{"7+3i",5,"4+4i"}}:tocomplex())
+m1 = matrix{{10,"2+6i",1},{5,1,"4-2i"}}:replace(complex)
+m2 = matrix{{3,4,5},{"2+3i",4,"6i"}}:replace(complex)
+assert(m1 + m2 == matrix{{13,"6+6i",6},{"7+3i",5,"4+4i"}}:replace(complex))
 -- matrix.add; symbol
-m1 = matrix{{8,4,1},{6,8,3}}:tosymbol()
-m2 = matrix{{-8,1,3},{5,2,1}}:tosymbol()
-assert(m1 + m2 == matrix{{"8+-8","4+1","1+3"},{"6+5","8+2","3+1"}}:tosymbol())
+m1 = matrix{{8,4,1},{6,8,3}}:replace(symbol)
+m2 = matrix{{-8,1,3},{5,2,1}}:replace(symbol)
+assert(m1 + m2 == matrix{{"8+-8","4+1","1+3"},{"6+5","8+2","3+1"}}:replace(symbol))
 
 -- matrix.sub; number
 m1 = matrix{{8,4,1},{6,8,3}}
 m2 = matrix{{-8,1,3},{5,2,1}}
 assert(m1 - m2 == matrix{{16,3,-2},{1,6,2}})
 -- matrix.sub; complex
-m1 = matrix{{10,"2+6i",1},{5,1,"4-2i"}}:tocomplex()
-m2 = matrix{{3,4,5},{"2+3i",4,"6i"}}:tocomplex()
-assert(m1 - m2 == matrix{{7,"-2+6i",-4},{"3-3i",-3,"4-8i"}}:tocomplex())
+m1 = matrix{{10,"2+6i",1},{5,1,"4-2i"}}:replace(complex)
+m2 = matrix{{3,4,5},{"2+3i",4,"6i"}}:replace(complex)
+assert(m1 - m2 == matrix{{7,"-2+6i",-4},{"3-3i",-3,"4-8i"}}:replace(complex))
 -- matrix.sub; symbol
-m1 = matrix{{8,4,1},{6,8,3}}:tosymbol()
-m2 = matrix{{-8,1,3},{5,2,1}}:tosymbol()
-assert(m1 - m2 == matrix{{"8--8","4-1","1-3"},{"6-5","8-2","3-1"}}:tosymbol())
+m1 = matrix{{8,4,1},{6,8,3}}:replace(symbol)
+m2 = matrix{{-8,1,3},{5,2,1}}:replace(symbol)
+assert(m1 - m2 == matrix{{"8--8","4-1","1-3"},{"6-5","8-2","3-1"}}:replace(symbol))
 
 -- matrix.mul; number
 m1 = matrix{{8,4,1},{6,8,3}}
 m2 = matrix{{3,1},{2,5},{7,4}}
 assert(m1 * m2 == matrix{{39,32},{55,58}})
 -- matrix.mul; complex
-m1 = matrix{{"1+2i","3-i"},{"2-2i","1+i"}}:tocomplex()
-m2 = matrix{{"i","5-i"},{2,"1-i"}}:tocomplex()
-assert( m1*m2 == matrix{{"4-i","9+5i"},{"4+4i","10-12i"}}:tocomplex() )
+m1 = matrix{{"1+2i","3-i"},{"2-2i","1+i"}}:replace(complex)
+m2 = matrix{{"i","5-i"},{2,"1-i"}}:replace(complex)
+assert( m1*m2 == matrix{{"4-i","9+5i"},{"4+4i","10-12i"}}:replace(complex) )
 -- matrix.mul; symbol
-m1 = matrix{{8,4,1},{6,8,3}}:tosymbol()
-m2 = matrix{{3,1},{2,5},{7,4}}:tosymbol()
+m1 = matrix{{8,4,1},{6,8,3}}:replace(symbol)
+m2 = matrix{{3,1},{2,5},{7,4}}:replace(symbol)
 assert(m1 * m2 == matrix{
   {"(8)*(3)+(4)*(2)+(1)*(7)", "(8)*(1)+(4)*(5)+(1)*(4)"},
   {"(6)*(3)+(8)*(2)+(3)*(7)", "(6)*(1)+(8)*(5)+(3)*(4)"}
-}:tosymbol())
+}:replace(symbol))
 
 -- matrix.div; number, same for complex, not for symbol
 m1 = matrix {{1,2},{3,4}}
@@ -72,9 +74,9 @@ assert( m2/2 == matrix{{2,2.5},{3,3.5}} )
 mtx = matrix {{3,5,1},{2,4,5},{1,2,2}}
 assert( 2 / mtx == matrix{{4,16,-42},{-2,-10,26},{0,2,-4}} )
 -- matrix.mulnum; symbol
-m1 = m1:tosymbol()
-assert( m1*2 == matrix{{"(1)*(2)","(2)*(2)"},{"(3)*(2)","(4)*(2)"}}:tosymbol() )
-assert( m1/2 == matrix{{"(1)/(2)","(2)/(2)"},{"(3)/(2)","(4)/(2)"}}:tosymbol() )
+m1 = m1:replace(symbol)
+assert( m1*2 == matrix{{"(1)*(2)","(2)*(2)"},{"(3)*(2)","(4)*(2)"}}:replace(symbol) )
+assert( m1/2 == matrix{{"(1)/(2)","(2)/(2)"},{"(3)/(2)","(4)/(2)"}}:replace(symbol) )
 
 -- matrix.pow; number, same complex
 mtx = matrix{{3,5,1},{2,4,5},{1,2,2}}
@@ -94,8 +96,8 @@ assert(select(2, pcall(function() return mtx^-1 end))
 mtx = matrix {{1,4,3,2},{2,1,-1,-1},{-3,2,2,-2},{-1,-5,-4,1}}
 assert( mtx:det() == 78 )
 -- matrix.det; complex
-m1 = matrix{{"1+2i","3-i"},{"2-2i","1+i"}}:tocomplex()
-m2 = matrix{{"i","5-i"},{2,"1-i"}}:tocomplex()
+m1 = matrix{{"1+2i","3-i"},{"2-2i","1+i"}}:replace(complex)
+m2 = matrix{{"i","5-i"},{2,"1-i"}}:replace(complex)
 m3 = m1*m2
 -- (checked in maple)
 assert( m3:det() == complex "12-114i" )
@@ -104,7 +106,7 @@ mtx = {{"2+3i","1+4i","-2i",3,2},
 	{3,"-2i",6,"4+5i",0},
 	{1,"1+2i",3,5,7},
 	{"-3+3i","3+3i",3,-8,2}}
-matrix(mtx):tocomplex()
+mtx = matrix(mtx):replace(complex)
 -- (checked in maple)
 assert( mtx:det():round(10) == complex "5527+2687i" )
 
@@ -123,7 +125,7 @@ mtx = {
 {3,"-1+5i",-3},
 {4,0,7},
 }
-matrix.tocomplex( mtx )
+mtx = matrix.replace( mtx, complex )
 local mtxinv = mtx^-1
 local mtxinvcomp = {
 {"0.13349-0.07005i","0.14335+0.03609i","0.04237+0.02547i"},
@@ -131,7 +133,7 @@ local mtxinvcomp = {
 {"-0.07628+0.04003i","-0.08192-0.02062i","0.11865-0.01456i"},}
 mtxinvcomp = matrix( mtxinvcomp )
 mtxinv:round( 5 )
-mtxinv:remcomplex()
+mtxinv = mtxinv:elementstostrings()
 assert( mtxinvcomp == mtxinv  )
 
 -- matrix.sqrt; number
@@ -140,7 +142,7 @@ local m2 = m1*m1
 local msqrt = m2:sqrt()
 assert((m2 - msqrt^2):normmax() < 1E-12)
 -- matrix.sqrt; complex
-local m1 = matrix{{4,"2+i",1},{1,5,"4-2i"},{1,"5+3i",2}}:tocomplex()
+local m1 = matrix{{4,"2+i",1},{1,5,"4-2i"},{1,"5+3i",2}}:replace(complex)
 local m2 = m1*m1
 local msqrt = m2:sqrt()
 assert((m2 - msqrt^2):normmax() < 1E-12)
@@ -152,7 +154,7 @@ local m2 = m1^p
 local mroot = m2:root(p)
 assert((m2 - mroot^p):normmax() < 1E-7)
 -- matrix.root; complex
-local m1 = matrix{{4,"2+i",1},{1,5,"4-2i"},{1,"5+3i",2}}:tocomplex()
+local m1 = matrix{{4,"2+i",1},{1,5,"4-2i"},{1,"5+3i",2}}:replace(complex)
 local m2 = m1^p
 local mroot = m2:root(p)
 assert((m2 - mroot^p):normmax() < 1E-7)
@@ -160,16 +162,16 @@ assert((m2 - mroot^p):normmax() < 1E-7)
 -- matrix.normf
 mtx = matrix{{2,3},{-2,-3}}
 assert(mtx:normf() == math.sqrt(2^2+3^2+2^2+3^2))
-mtx = matrix{{'2i','3'},{'-2i','-3'}}:tocomplex()
+mtx = matrix{{'2i','3'},{'-2i','-3'}}:replace(complex)
 assert(mtx:normf() == math.sqrt(2^2+3^2+2^2+3^2))
-mtx = matrix{{'a','b'},{'c','d'}}:tosymbol()
+mtx = matrix{{'a','b'},{'c','d'}}:replace(symbol)
 assert(tostring(mtx:normf()) == "(0+((a):abs())^(2)+((b):abs())^(2)+((c):abs())^(2)+((d):abs())^(2)):sqrt()")
 
 -- matrix.normmax
 -- note: symbolic matrices not supported
 mtx = matrix{{2,3},{-2,-4}}
 assert(mtx:normmax() == 4)
-mtx = matrix{{'2i','3'},{'-2i','-4i'}}:tocomplex()
+mtx = matrix{{'2i','3'},{'-2i','-4i'}}:replace(complex)
 assert(mtx:normmax() == 4)
 
 -- matrix.transpose
@@ -187,7 +189,7 @@ assert( m1:rotr() == matrix{{6,4,2},{7,5,3}} )
 mtx = matrix{{4,2,-3},{3,-5,2}}
 assert(tostring(mtx) == "4\t2\t-3\n3\t-5\t2" )
 -- matrix.tostring; complex
-mtx = matrix{{4,"2+i"},{"3-4i",5}}:tocomplex()
+mtx = matrix{{4,"2+i"},{"3-4i",5}}:replace(complex)
 assert(tostring(mtx) == "4\t2+i\n3-4i\t5" )
 -- matrix.tostring; tensor
 local mt = matrix {{{1,2},{3,4}},{{5,6},{7,8}}}
@@ -216,14 +218,14 @@ assert( vx:scalar( v2 ) == 0 )
 assert( v2:len() == math.sqrt( 3^2+4^2 ) )
 
 --// test symbolic
-ms = matrix {{ "a",1 },{2,"b"}}:tosymbol()
-ms2 = matrix {{ "a",2 },{"b",3}}:tosymbol()
+ms = matrix {{ "a",1 },{2,"b"}}:replace(symbol)
+ms2 = matrix {{ "a",2 },{"b",3}}:replace(symbol)
 ms3 = ms2+ms
-ms3 = ms3:replace( "a",4,"b",2 )
+ms3 = ms3:replace( symbol.makereplacer( "a",4,"b",2 ) )
 ms3 = ms3:solve()
 assert( ms3 == matrix {{8,3},{4,5}} )
 ms4 = ms2*ms
-ms4 = ms4:replace( "a",4,"b",2 )
+ms4 = ms4:replace( symbol.makereplacer( "a",4,"b",2 ) )
 ms4 = ms4:solve()
 assert( ms4 == matrix {{20,8},{14,8}} )
 
@@ -255,4 +257,6 @@ end
 table.sort( t )
 for i,v in ipairs( t ) do
 	--print( "matrix."..v )
-end
\ No newline at end of file
+end
+
+print 'PASSED'