Comparison of mathematical programs for data analysis

Author : Stefan Steinhaus (University of Frankfurt, Germany)
E-Mail / Homepage : stst@informatik.uni-frankfurt.de / http://www.uni-frankfurt.de/~stst/
Edition : 2.12
Date : September 8, 1997
Last modified : September 27, 1997
Location : http://www.uni-frankfurt.de/~stst/ncrunch.html


1. Introduction

This comparison should give an overview about the functionality, the availability for different operating systems and the speed of mathematical programs for analyzing huge or very huge data sets in mathematical, statistical or graphical ways. The focus of this test is therefor set to mathematical functions which are mainly used in economics, financial analysis, biology, chemistry, physics and some other subjects where the numerical analyze of data is very important.

In the first part of this test report you can find an overview over the mathematical functionality divided into different subsections, in the second part you can find an overview about the graphical functionality, in the third part you can find an overview about the programming environment, in the fourth part you can find a list of available export/import options, in the fifth part there is a list of operating systems for which the programs are available and in the sixth part you can find a speed comparison on these systems. In the seventh part there will be a final summarize to relate all the different parts of the test report. The relation between these six parts will be 38 : 10 : 8 : 5 : 2 : 37 but for those who want to have their own weighting I will describe detailed the calculation for the summarize so that you can easily calculate the result with your own weighting.

The actual tested programs are :

The following symbols have been used all over the whole testreport within the comparison tables :

+      -  Function is implemented in the program
m      -  Function is supported by an additional module
-      -  Function is not implemented


2. Comparison of the mathematical functionality

Actually there are a lot of different mathematical and statistical programs on the market which covers a huge amount of functions. The following table should give an overview about the functionality for analyzing data in numerical ways and should mark out which program does support which function and whether this functions are already implement in the base program or whether you need an additional module. The functions are sorted by the categories "Standard mathematics", "Linear algebra", "Analysis", "Numerical mathematics", "Stochastic", "Statistics" and "Other mathematics".

2.1. Standard mathematics

Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Trig. functions + + + + + + + + +
Gamma function + + + + + + - - +
Poly gamma - + + + - - - + -
Log-Gammafunc. + + + + + + + + +
Beta function - + + + + + + + -
Implemented functions 60.000%
(3/5)
100.000%
(5/5)
100.000%
(5/5)
100.000%
(5/5)
80.000%
(4/5)
80.000%
(4/5)
60.000%
(3/5)
80.000%
(4/5)
60.000%
(3/5)

2.2. Linear Algebra

Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Eigenvalues + + + + + + + + +
Eigenvectors + + + + + + + + +
Cholesky decomposition + + + + + + + + +
Crout decomposition + - - - - - - - -
LU decomposition + + + + + - - + +
Singular value decomposition + + + + + - + + +
Upper Hessenberg form + + - - + - - - -
Toeplitz matrix + + + m + - - - -
Schur form of quadratic matrix + + - + + - - - +
Optimization
(Unconstr. / Constr.)
m / m + / - + / - + / + m / m - / - + / + + / - + / +
Linear equation solver + + + + + + + + +
Non-linear equation solver m + + + m + + - +
Ordinary Differential Equation solver m + + + + + + - +
Partial Differential Equation solver - m + + m - - - -
Sparse matrices handling + + - + + - - - -
Moore-Penrose pseudo-inverse + + - + + - - + +
Implemented functions 94.118%
(16/17)
88.235%
(15/17)
64.706%
(11/17)
88.235%
(15/17)
94.118%
(16/17)
35.294%
(6/17)
52.941%
(9/17)
47.059%
(8/17)
70.588%
(12/17)

2.3. Analysis

Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Numerical integration + + + + + + + m +
Double integration + + + + + + + - -
Triple integration + + + + - + - - -
Numerical differentiation + + + + + + - + +
Fourier transf.
(1D / 2D /multidim.)
+ / + / + + / - / - + / - / - + / + / + + / + / + + / - / - + / + / - + / - / - + / + / +
Inverse Fourier transformation
(1D / 2D / multidim.)
+ / + / + + / - / - + / - / - + / + / + + / + / + + / - / - + / + / - + / - / - + / + / +
Implemented functions 100.000%
(10/10)
60.000%
(6/10)
60.000%
(6/10)
100.000%
(10/10)
90.000%
(9/10)
60.000%
(6/10)
60.000%
(6/10)
40.000%
(4/10)
60.000%
(6/10)

2.4. Numerical mathematics

Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Classical Interpolation - + + + + + + - +
Pade Interpolation m + + + - + + - -
k-Spline Interpolation + + + + m - + + +
B-Spline Interpolation - - + + m - - + +
Newton method for finding roots m + + + m + + - -
Bisection m + - m m - - - -
Runge Kutta method for solving ODE m + + + m - + - -
Implemented functions 71.429%
(5/7)
85.714%
(6/7)
85.714%
(6/7)
100.000%
(7/7)
85.714%
(6/7)
42.857%
(3/7)
71.429%
(5/7)
28.571%
(2/7)
42.857%
(3/7)

2.5. Stochastic

Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Markov models m + - - - - - - -
Mean + + + + + + + + +
Median + + + + + - + + +
Mode m - + + - + - - -
Variance + + + + + + + + +
Beta distribution
(Density / CDF / random num.)
m / + / + + / + / - + / + / + + / + / + m / m / m - / - / - - / - / - + / + / + + / + / +
Chi-squared distr.
(Density / CDF / random num.)
m / + / m + / + / - + / + / + + / + / + m / m / m - / - / - - / - / - + / + / + + / + / +
Gamma distr.
(Density / CDF / random num.)
m / + / + + / + / - + / + / + + / + / + m / m / m - / - / - - / - / - + / + / + + / + / +
Log-normal distr.
(Density / CDF / random num.)
+ / + / m + / + / - + / + / + + / + / + m / m / m - / - / - - / - / - - / - / - + / + / +
Normal distr.
(Density / CDF / random num.)
+ / + / + + / + / - + / + / + + / + / + + / + / + - / - / - - / + / + + / + / + + / + / +
Poisson distr.
(Density / CDF / random num.)
m / m / + + / + / - + / + / + + / + / + m / m / m - / - / - - / - / - - / - / + + / + / +
Uniform distr.
(Density / CDF / random num.)
m / m / + + / + / + + / + / + + / + / + + / + / + - / - / + - / - / + - / - / + + / + / +
More distr.
(Density / CDF / random num.)
+ / + / + + / + / - + / + / + + / + / + m / m / m - / - / - - / + / - + / + / + + / + / +
Implemented functions 100.000%
(29/29)
72.414%
(21/29)
96.552%
(28/29)
96.552%
(28/29)
93.103%
(27/29)
13.793%
(4/29)
24.138%
(7/29)
68.966%
(20/29)
93.103%
(27/29)

2.6. Statistics

Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Linear regression + + + + + - + + +
Polynomial regression m + + + + - + - +
Nonlinear Regression m + - + m - + - +
Loess regression + - - m + - - - +
LOGIT regression m - - - - - - - +
PROBIT regression m - - - - - - m +
PSN regression m - - - - - - - -
Event count models m - - - - - - - +
Duration models m - - - - - - - -
Goodness of fit test m - - - - - - - +
T-Test - - - + m - + - +
F-Test - - - + - - + - +
Q-Test m - - - - - - - -
Z-Test - - - - m - - - +
Maximum Likelihood
(Unconstr. / Constr.)
m / m - / - - / - - / - m / - - / - - / - - / - + / +
ARIMA m - - m m - - m +
Time series analysis
(Stationary / Non-stat.)
m / m - / - - / - m / m m / m - / - - / - + / m + / +
GARCH models
(Univariate / Multivar.)
m / m - / - - / - m / m - / - - / - - / - - / - m / m
Wavelets m - - m m - + - m
Cluster analysis - - - - - - - - +
Survival analysis - - - - - - - - +
Implemented functions 79.167%
(19/24)
12.500%
(3/24)
8.333%
(2/24)
50.000%
(12/24)
45.833%
(11/24)
0.000%
(0/24)
25.000%
(6/24)
20.833%
(5/24)
87.500%
(21/24)

2.7. Other mathematics

Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Cointegration models m - - - - - - + -
Black Scholes model - + + m m - - - -
Dynamic rational expectation models m - - - - - - - -
Linear rational expectation models m - - - m - - - -
Non-linear rational expectation models m - - - - - - - -
Social network models m - - - - - - - -
Kalman filter m - - m m - + m -
Neuronal networks m - - m m - - - -
Regressive-autore- 
gressive models
m - - m m - - - +
Portfolio analysis m - - m m - - - -
State-space models m - - m m - - m -
Implemented 
functions
90.909%
(10/11)
9.091%
(1/11)
9.091%
(1/11)
54.545%
(6/11)
63.636%
(7/11)
0.000%
(0/11)
9.091%
(1/11)
27.273%
(3/11)
9.091%
(1/11)

2.8. Summarizing the comparison of the mathematical functions

Altogether 103 functions have been listed in the tables above. The following table summarizes the results calculated in percentage with a weighting of 5% for 'Standard mathematics', 15% for 'Linear Algebra', 10% for 'Analysis', 10% for 'Numerical mathematics', 20% for 'Stochastic', 20% for 'Statistics' and 20% for 'Other mathematics'.
Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Standard mathematics (5%) 60.000% 100.000% 100.000% 100.000% 80.000% 80.000% 60.000% 80.000% 60.000%
Linear Algebra (15%) 94.118% 88.235% 64.706% 88.235% 94.118% 35.294% 52.941% 47.059% 70.588%
Analysis (10%) 100.000% 60.000% 60.000% 100.000% 90.000% 60.000% 60.000% 40.000% 60.000%
Numerical mathematics (10%) 71.429% 85.714% 85.714% 100.000% 85.714% 42.857% 71.429% 28.571% 42.857%
Stochastic (20%) 100.000% 72.414% 96.552% 96.552% 93.103% 13.793% 24.138% 68.966% 93.103%
Statistics (20%) 79.167% 12.500% 8.333% 50.000% 45.833% 0.000% 25.000% 20.833% 87.500%
Other mathematics (20%) 90.909% 9.091% 9.091% 54.545% 63.636% 0.000% 9.091% 27.273% 9.091%
Overall result
(100% = Best)
88.276%
(92/103)
51.608%
(57/103)
52.073%
(59/103)
78.455%
(83/103)
76.204%
(80/103)
22.338%
(23/103)
35.730%
(37/103)
41.330%
(46/103)
61.813%
(75/103)

100% would mean that all listed functions are implemented (103 of 103).


3. Comparison of the graphical functionality

Not only for presentation purposes it might very useful to visualize numerical data (source or resulting data) by using graphical routines. Therefor it is in the way of scientific representation often very necessary to have not only the typical graphic types like curve plots or histograms but also represent the data in statistical graphic types like like i.e. dendograms, cluster graphs, multivariate plots or just to add additional graphical information on standard plots like error bars for example. Some of the tested programs (most especially CAS) include a really huge amount of graphical functions and graphic types but as my testreport has a high weighting on statistical, econometrical functions I will nearly only mention these type of graphic functions.
The following table shows a list of supported graphic types.
 
Functions
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
2D-Graphics
Bar charts + + + + + - + - +
Other charts + - - + + - + - +
Error bars - - - + + - + - +
High-Low-Average Plot - - - m m - - - +
Histograms + + + + + - + + +
Log Plot + + + + + - + - +
Log-log Plot + + + + + - + - +
Polar Plot + + + + + + + - +
XY Plot + + + + + + + + +
3D-Graphics
Charts - - - + + - - - +
Contour Plot + + + + + + + - +
Error bars - - - - - - - - -
Height colors + + + + + + + - +
Surface Plot + + + + + + + - +
XYZ Plot + + + + + + + - +
Special graphic types and functions
Animations - + + + + + - - -
Bollinger bands - - - m m - - - -
Box & Whisker Plots + - + m m - - - +
Candlestick charts - - - m m - - - -
Cluster graphs - - - - - - - - m
Dendograms - - - - - - - - m
Periodograms - - - - - - - + +
QQ Plot - - + - m - - + +
Overall result
(100% = Best)
52.174%
(12/23)
47.826%
(11/23)
56.522%
(13/23)
78.261%
(18/23)
82.609%
(19/23)
30.435%
(7/23)
52.174%
(12/23)
17.391%
(4/23)
82.609%
(19/23)

4. Functionality of the programming environment

For a lot of scientists it is very important to define complex models and to do simulations on them or to define complex mathematical problems as a standalone, ready to use application so that even non trained person can solve their problems. For these type users it is not only essential to have the facilities of a mathematical program but also a powerful programming environment which provides development tools and interface functionality like debuggers, tracing routines, foreign language interfaces etc.
The following table should give an overview about the supported programming environment.
 
 
Programming facilities GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Editing features
Built-in editor + + + + + + + + +
External editor configurable + - + + + - - - +
Source code formatting m + - - + - - - +
Syntax  highlighting - - - - + - - m -
Debugging
Breakpoints + + + - + + + - +
Function Tracer - + + + - + - - -
Line Tracing + - - - + + + - +
Profiler - + + m + + + - -
Stack inspection + + - + + + + - +
Variable inspection + + - + + + + - +
Language features
API-interface + - - + + - + + m
DDE support - - - - + + - - +
GUI programming - - - + + - + - +
N-dimensional arrays (> 3) - + + + + + - + +
Object oriented programming - - - + + + + + +
OLE support - - + + + + - - +
P code compiling + + - + + - - + -
Language interfaces
Assembler + - - + - - - + -
C/C++ + - - + + - - + +
FORTRAN + - + + + - - + +
GAUSS + - - - - - - + -
Macsyma - + - - - - - - -
Maple m - + - m - - - -
Mathematica - - - + m - - - -
Matlab - + - m + - - - -
MuPAD - - - - - + - - -
O-Matrix - - - - - - + - -
Ox - - - - - - - + -
S-Plus - - - - - - - - +
DLL-Calls + - - + + - + + +
Overall result
(100% = Best)
50.000%
(15/30)
36.667%
(11/30)
30.000%
(9/30)
60.000%
(18/30)
73.333%
(22/30)
40.000%
(12/30)
36.667%
(11/30)
40.000%
(12/30)
56.667%
(17/30)
The final result is display in percent, 100% means that every programming facility has been supported.


5. Data import/export options

For statistical and mathematical analysis it is essential to have access possibilities to the data which should be analyzed. Therefor it is necessary to have interfaces between your mathematical program and the database or spreadsheet program where you have the original data. In most mathematical programs you have the possibility to import and export ASCII-based data which of course supposes that you have to convert your original data file into this general format. It would be much easier to have direct access to your original data. The following table should give an overview of which direct import/export possibilities the tested mathematical programs do have.
 
 
Data import/export
possibilities
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
ACCESS - - - m - - - - +
Applixware - - - - m - - - -
ASCII + + + + + + + + +
AutoCAD - + - + - - - - -
Binary + - + + + + + + -
dBase m - - - - - - - +
Excel m - - m m - - + +
FoxPro m - - - - - - - +
GAUSS + - - - - - - + +
Hypercard - - - m - - - - -
Informix - - - m - - - - -
Labview - - - m - - - - -
Lotus 1-2-3 m - - - + - - + +
Lotus Symphony m - - - - - - - +
Matlab - - - m + - + - +
ODBC-connections - - - - - - - - +
Ox - - - - - - - + -
Paradox m - - - - - - - +
Quattro Pro m - - - - - - - +
SAS - - - - - - - - +
SigmaPlot - - - - - - - - +
S-Plus - - - - - - - - +
SPSS - - - - - - - - +
STATA - - - - - - - - +
Systat - - - - - - - - +
Transform - - - m - - - - -
Overall result
(100% = Best)
38.462%
(10/26)
7.692%
(2/26)
7.692%
(2/26)
38.462%
(10/26)
23.077%
(6/26)
7.692%
(2/26)
11.538%
(3/26)
23.077%
(6/26)
69.231%
(18/26)
The final result is display in percent, 100% means that every import/export format has been supported.


6. Available operating systems

Due to the fact that different kind of problems need different kind of performances especially if we have huge data sets, complex simulations or just because we have computer pools we contain different kind of hardware or operating system platforms, it might be also interesting to have the same mathematical program available on different platforms. Beside this it is of course also very important to have the possibility to run the programs from one platform without any or only with small changes on the other platform as well which means that each mathematical programs should be compatible on its different kind of platforms. The following list gives an overview about the availability of each mathematical program for several platforms.
 
 
Platform
(Version)
GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Convex - - + + - + - - -
DEC
(Linux / UNIX / VMS)
- / + / + - / - / + - / + / - - / + / + - / + / + + / + / + - / - / - - / + / - - / + / -
HP 9000
(HP-UX / NextStep)
+ / - + / - + / - + / + + / - + / - - / - + / - + / -
IBM RISC
(IBM AIX)
+ + + + + + - + +
Intel (DOS) + - + - - + - + -
Intel (OS/2) + - + + - + - - -
Intel
(Win. 3.1x / 95,NT)
- / + + / + + / + - / + - / + - / + + / + + / + + / +
Intel (Linux) + - + + + + - + -
Intel
(Solaris x86/NextStep)
+ / - - / - - / - - / + - / - + / + - / - - / - - / -
Motorola
(MAC OS / NextStep)
- / - - / - + / + + / + + / - + / - - / - - / - - / -
SGI (SGI IRIX) + + + + + + - + +
SUN (Solaris) + + + + + + - + +
Total amount 61.111%
(11/18)
33.333%
(6/18)
72.222%
(13/18)
77.778%
(14/18)
50.000%
(9/18)
83.333%
(15/18)
11.111%
(2/18)
50.000%
(9/18)
38.889%
(7/18)
(The above mentioned list marks out every OS-platform which is supported by the software producers but due to some development delays it might be possible that some programs are not available for all listed platforms in the newest version. i.e. Maple for Linux, Mathematica for OS/2...)

The assessment for this part of the test report is also calculated by the key amount of available platforms divided by the total amount of listed platforms and will be displayed in percentage.


7. Speed comparison

The following speed comparison have been performed on a PENTIUM PC with 90 MHz and 96 MB RAM running under Windows NT 4.0 with Windows versions of the programs (all timings are displayed in seconds).
 
 
Functions GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
400 x 400 random matrix^1000 16.476 136.747 > 1h 30.023 5.468 > 1h 0.400 1.011 1.260
Eigenvalues of a 300 x 300 random matrix 44.670 9.984 > 1h 45.626 48.760 > 1h 11.937 41.202 49.830
Inverse of a 500 x 500 random matrix 27.476 149.014 > 1h 142.054 27.504 * 26.678 26.969 99.280
Sorting of 500000 random values 8.202 434.013 *** 108.550 33.782 54.58 11.877 8.258 5.150
Creation of a 800 x 800 Toeplitzmatrix 1.718 1660.788 207.748 187.289 2.009 > 1h 37.735 0.307 13.160
Cholesky decomposition of a 500 x 500 random matrix 4.100 ** > 1h 927.624 3.939 ** 134.453 4.089 9.750
Creation of a 500 x 500 cross-product matrix 28.265 > 1h > 1h 59.366 24.423 > 1h 7.621 13.205 35.320
FFT over 100000 random values 6.940 2103.384 **** 23.054 2.686 46.76 1.502 5.651 3.180
Gaussian error function over a 500 x 500 random matrix 4.048 966.599 > 1h 55.74 15.790 > 1h 1.572 1.228 -
Gamma function on a 600 x 600 random matrix 2.715 > 1h > 1h 94.946 27.886 > 1h 6.138 6.723 6.600
Linear regression over a 500 x 500 random matrix 22.184 2017.682 77.702 > 1h 10.886 - 7.661 16.941 29.770
Overall performance 49.937% 10.971% 0.013% 7.674% 39.975% 1.658% 70.799% 66.207% 37.176%
* Program crashed with memory allocation problems
** Matrices need to be Hermitian and positive definit;to create such a type of random matrix takes too much time
*** Function doesn't work due to technical problems dependent on the size of the model
**** Function is too restrictive to use in this benchmark test

The overall performance will be calculated in the following way :

The best timing result of a benchmark function makes 100%; for calculating the results for each function I'll take the fastest timing and divide it by the timing of the tested program (the formula will look MIN(A1;A2;...)/A2 for example) and that makes the ranking in percentage. To calculate the final "Overall performance" I'll than sum the percentage values for each tested program and divide by the amount of tested functions (in the moment 12) which will make the result in percentage again.


8. Summary

The summary should set the results of the speed comparison, the functionality of the programming environment, the data import/export facilities and the availability for different platforms in relation to the results of the comparison of the functionality. The relation between these four tests is 39:2:5:8:46.
 
 
Test GAUSS Mac-
syma
Maple Mathe-
matica
Mat-
lab
Mu-
PAD
O-
Matrix
Ox S-
Plus
(3.2.29) (2.2.1) (V4) (3.0.1) (5.1) (1.3.0) (3.2) (1.11) (V4)
Comparison of the mathematical functionality (38%) 88.276% 51.608% 52.073% 78.455% 76.204% 22.338% 35.730% 41.330% 61.813%
Comparison of the graphical functionality (10%) 52.174% 47.826% 56.522% 78.261% 82.609% 30.435% 52.174% 17.391% 82.609%
Functionality of the programming environment (8%) 50.000% 36.667% 30.000% 60.000% 73.333% 40.000% 36.667% 40.000% 56.667%
Data import/export (5%) 38.462% 7.692% 7.692% 38.462% 23.077% 7.692% 11.538% 23.077% 69.231%
Available platforms (2%) 61.111% 33.333% 72.222% 77.778% 50.000% 83.333% 11.111% 50.000% 38.889%
Speed comparison (37%) 49.937% 10.971% 0.013% 7.674% 39.975% 1.658% 70.799% 66.207% 37.176%
Overall result 64.384% 32.437% 29.674% 48.757% 60.029% 17.397% 48.723% 47.295% 54.277%

Note : The overall results of some tested programs are pretty bad due to the specific weighting of this testreport. I would like to mention that this does of course not mean that the software is bad but that the programs are maybe not perfect for the specific usage mentioned in the testreport, for other weightings/usages they might be much better or even leading.

Pricing : Another important point to mention is also that I have not reported the prices for each software product nor the additional modules which might make some products quiete expensive. Summarizing I would like to notice that the programs MuPAD, the lightversion of O-Matrix and Ox are available free of charge for educational and academic usage. The other software products are varying very strongly in their prices and in their license politics. 


Appendix A : Benchmark tests for downloading

  • GAUSS Benchmark test (ASCII)
  • Macsyma Benchmark test (ASCII)
  • Maple Benchmark test (ASCII)
  • Mathematica Benchmark test (ASCII)
  • Matlab Benchmark test (ASCII)
  • MuPAD Benchmark test (ASCII)
  • O-Matrix Benchmark test (ASCII)
  • Ox Benchmark test (ASCII)
  • S-Plus Benchmark test (ASCII)

  • Appendix B : References

    The following persons helped to transfer the benchmark test and support information about their mathematical programs :
  • GAUSS : Stefan Steinhaus, University of Frankfurt (Germany)
  • Macsyma : Robert H. Berman, Macsyma Inc. (USA)
  • Macsyma : Gregory Kapsias, Scientific Software Service (Germany)
  • Macsyma : Richard Petti, Macsyma Inc. (USA)
  • Maple : Stefan Steinhaus, University of Frankfurt (Germany)
  • Mathematica : Brett H. Barnhart, Wolfram Research (USA)
  • Mathematica : Nicolas Hollis, Wolfram Research (England)
  • Mathematica : Roman Mäder, MathConsult (Switzerland)
  • Mathematica : Stefan Steinhaus, University of Frankfurt (Germany)
  • Matlab : Cleve Moler, The Mathworks Inc. (USA)
  • Matlab : Jim Tung, The Mathworks Inc. (USA)
  • MuPAD : Andreas Sorgatz, University of Paderborn (Germany)
  • MuPAD : Stefan Wehmeier, University of Paderborn (Germany)
  • O-Matrix : Beau Paisley, Harmonic Software Inc. (USA)
  • Ox : Jurgen Doornik, Nuffield College (England)
  • S-Plus : Tim Hesterberg, MathSoft Inc. (USA)
  • S-Plus : Charles Roosen, MathSoft Inc. (USA)
  • S-Plus : Reinhard Sy, GraS GmbH (Germany)
  • S-Plus : Matthew Todd, MathSoft Inc. (England)

  • 1997 by Stefan Steinhaus, stst@informatik.uni-frankfurt.de