% Release Notes
% Version 2.1  (R11)
% Symbolic Math Toolbox
% Extended Symbolic Toolbox
% 11-Sep-1998
%
% V E R S I O N   2.1
%
% Version 2.1 of the Symbolic Math Toolboxes contains two significant new features:
% The incorporation of the Maple V, Release 5 (MathEdge 2) OEM kernel and
% a series of plotting commands that enable the user to graph symbolic expressions
% that represent planar and spatial curves, polar coordinates, surfaces, and
% contours.
%
% In particular, EZPLOT graphs curves of the form y = f(x), f(x,y) = 0
% (i.e., implicit functions), and x = x(t), y = y(t) (parametric planar curves).
% The utility EZPLOT3 graphs x = x(t), y = t(t), z = z(t) (parametric spatial curves)
% while EZPOLAR plots r = f(theta) in polar coordinates.  Finally, EZSURF, EZSURFC,
% EZMESH, and EZMESHC graph surfaces/combined surface-contour plots on symbolic
% expressions of the form z = f(x,y); EZCONTOUR gives a contour graph of z = f(x,y).
%
% Three new additional functions have been added:  HYPERGEOM, TEXLABEL, and
% TAYLORTOOL.  HYPERGEOM returns Gauss' hypergeometric functions of various
% orders; TEXLABEL converts a symbolic expression into its equivalent TeX form
% to be used in combination with title, xlabel, ylabel, and/or zlabel.  This
% provides titles and labels that resemble mathematical typesetting.
% TAYLORTOOL is a pedagogical tool that enables the user to visualize the
% convergence of a Taylor series to a given input function.
%
% DSOLVE has been made more robust and returns solutions to a wider variety
% of differential equation (especially nonlinear ODEs).  A new option to the
% SYMS function has been provided:
% syms a k positive
% creates positive real variables a and k.
%
% The new Maple V, Release 5 kernel corrects several errors in the computation
% of symbolic eigenvalues and differential equations as well as correcting the
% memory management problems of Maple V, Release 4.  
%
% Many bug fixes and internal architectural changes to the M-files have been
% effected to increase ease and robustness of use.
%
% V E R S I O N   2.0.1
%
% Version 2.0.1 of the Symbolic Math Toolboxes contains a new and more robust
% SUBS function.  More specifically, a complete re-write of sym/SUBS.M, which
% is the link between symbolic expressions and numeric expressions from within
% the Symbolic Math Toolbox, has been added. The new sym/SUBS.M will handle all
% substitutions (string, double, Maple, and multiple substitutions) available
% in the Toolbox.  While the syntax for SUBS remains the same (as in Version 1
% and Version 2.0), a change in output occurs for substitutions of class DOUBLE.
% For example, subs(x^2,x,2.1) now returns 4.4100,  In Version 2.0, 
% subs(x^2,x,2.1) returns 441/100. Similarly, the V 2.0.1 subs(x/y,{x,y},{2,3})
% returns 0.6667, whereas the V 2.0 subs(x/y,{x,y},{2,3}) returns 2/3. 
%
%    Moreover, several bugs that affected formatting, consistency of use, 
% stability, and error handling have been fixed.  In particular, changes to
% MAPLE.M and MAPLEINIT.M were made to eliminate Maple/MATLAB string
% incompatibilities.
%
%   The sym/COLON.M operator was altered to make it consistent with MATLAB.
% The V 2.0 command sym(2):0:4 returns 2 + NaN while the new V 2.0.1 command
% returns [ empty sym ].
%
%   Both sym/DOUBLE.M and sym/EVAL.M were altered to permit evaluation of
% symbolic matrices when floating point variables are in the workspace. The
% V 2.0 commands syms x; A = A = [cos(x), sin(x);-sin(x),cos(x)]; x = pi/2;
% eval(A) return an error.  In V 2.0.1, these commands now return the class
% DOUBLE matrix
%     0     1
%    -1     0
%
%   The files sym/DISP.M and sym/DISPLAY.M were changed to permit the
% compact option in FORMAT.
%
%   Finally, the integral transforms sym/FOURIER.M, IFOURIER.M, ILAPLACE.M,
% IZTRANS.M, LAPLACE.M, and ZTRANS.M were reworked so that the correct
% default variable would be selected.  That is, in V 2.0, the commands
% syms s w t a; f = cos(w*t)*exp(-a*t); laplace(f) return exp(-a*t)*s/(s^2+t^2)
% and laplace(f,t,s) returns (s+a)/((s+a)^2+w^2).  Now, in V 2.0.1, both
% laplace(f) and laplace(f,t,s) return (s+a)/((s+a)^2+w^2).  Similar comments
% hold for FOURIER, IFOURIER, etc.
%
% V E R S I O N   2.0
%
% Compatibility with Earlier Versions
% 
% The documentation for Version 1 of the Symbolic Math Toolboxes
% anticipated the changes envisioned for future versions:
% 
%   "These first versions of the Symbolic Math Toolboxes are designed to
%   work with version 4.0 or 4.1 of MATLAB and version V, release 2
%   of Maple.  The goal has been to provide access to most of Maple with 
%   a language syntax that is familiar to MATLAB users.  This has been
%   done without modifying either of the two underlying systems.
%   
%   However, it is not possible to provide completely seamless integration
%   without modifying MATLAB.  For example, if f and g are strings
%   representing symbolic expressions, we would prefer to use the notation
%   f+g for their sum, instead of symadd(f,g).  But f+g attempts to add
%   the individual characters in the two strings, rather than concatenate
%   them with a plus sign in between.  Similarly, if A is a matrix whose
%   elements are symbolic expressions, we would prefer to use A(i,j)
%   to access a individual expression, instead of sym(A,i,j).  But if A is
%   a matrix of strings, then A(i,j) is a single character, not a complete
%   expression.
%   
%   We intend to develop further versions of these toolboxes, to be used
%   with future versions of MATLAB and Maple.  As we do so, we will be
%   able to provide closer integration and better syntax.  In particular,
%   we expect that many of the functions whose names now involve "sym"
%   will eventually be replaced by more direct use of underlying MATLAB
%   notation."
%  
% Version 2 of the Symbolic Math Toolboxes makes extensive use of the
% new MATLAB object capabilities and is intended to work with a newer
% release, number 4, of Maple, version V.  Some degree of backward
% compatibility with Version 1 of the Toolbox is available, but complete
% compatibility is not possible.
% 
% The following functions continue to be available, but their usage
% is considered obsolete.
% 
%     determ      - Symbolic matrix determinant.
%     linsolve    - Solve simultaneous linear equations.
%     eigensys    - Symbolic eigenvalues and eigenvectors.
%     singvals    - Symbolic singular values and singular vectors.
%     numeric     - Convert symbolic matrix to numeric form.
%     symop       - Symbolic operations.
%     symadd      - Add symbolic expressions.
%     symsub      - Subtract symbolic expressions.
%     symmul      - Multiply symbolic expressions.
%     symdiv      - Divide symbolic expressions.
%     sympow      - Power of symbolic expression.
%     eval        - Evaluate a symbolic expression.
% 
% These functions accept both strings and symbolic objects as input arguments
% and produce symbolic objects as results.  Most of the functions now also 
% have counterparts with overloaded MATLAB operators or function names.
% 
% For example, the version 1 statements
% 
%     f = '1/(5+4*cos(x))'
%     g = int(int(diff(f,2)))
%     e = symsub(f,g)
%     simple(e)
% 
% continue to work with version 2.  With version 1, all three variables,
% f, g and e, are strings; with version 2, f is a string, but g and e are
% symbolic objects.  With version 2, the preferred approach is
% 
%     syms x
%     f = 1/(5+4*cos(x))
%     g = int(int(diff(f,2)))
%     e = f - g
%     simple(e)
% 
% The version 1 statements
%  
%     H = sym(hilb(3))
%     I = sym(eye(3))
%     X = linsolve(H,I)
%     t = sym(0)
%     for j = 1:3
%        t = symadd(t,sym(X,j,j))
%     end
%     t
%  
% continue to work with version 2.  With version 2, the preferred
% approach is
% 
% 
%     H = sym(hilb(3))
%     I = eye(3)
%     X = H\I
%     t = sum(diag(X))
% 
% The version 1 statement
% 
%     M = sym(3,3,'1/(i+j-t)')
% 
% uses the sym function in a way that is no longer available with version 2.
% The example must be changed to something like
% 
%     syms t
%     [J,I] = meshgrid(1:3)
%     M = 1./(I+J-t)
% 
% The version 1 usage of diff, int, solve and dsolve with string arguments
% continues to be available with version 2.  With version 2, the results
% are symbolic objects instead of strings.  For some computations, the
% new release of Maple produces results in a different format.  
% 
% For example, with version 1, the statement
% 
%     [x,y] = solve('x^2 + 2*x*y + y^2 = 4', 'x^3 + 4*y^3 = 1')
% 
% produces
% 
%     x =
%     [   -RootOf(_Z^3-2*_Z^2-4*_Z-3)-2]
%     [-RootOf(3*_Z^3+6*_Z^2-12*_Z+7)+2]
%  
%     y =
%     [   RootOf(_Z^3-2*_Z^2-4*_Z-3)]
%     [RootOf(3*_Z^3+6*_Z^2-12*_Z+7)]
% 
% The same statement works in version 2, but produces results with the
% "RootOf" expressions expanded to exhibit the multiple solutions.

% $Revision: 1.8 $
% Copyright (c) 1993-1999 The Mathworks, Inc. All Rights Reserved.
