A long time ago, there was a discussion about the legality of using 
Mathematica with the notebook (providing access via a webserver).  Here 
is the relevant section from the license agreement I see with MMA 7:

Note that item 7 now specifies that the prohibited use is allowing 
*others* to access MMA through a webserver.  Hence, I think using the 
notebook to access MMA for personal use is now a non-issue.

There was also question about how the examples were inconsistent with 
the license agreement in that the examples indicated that mathematica 
functions could and should be modified, while the license agreement 
forbade it.  However, this new license agreement explicitly grants 
permission to modify portions of Mathematica written in MMA code.

Jason

PROHIBITED USES

All uses of the Software and other elements of the Product not 
specifically stated in the Permitted Uses and Installations section of 
this Agreement are prohibited, including without limitation:

    1. running more Controlling Processes or Computational Processes 
concurrently than the maximum specified on Your License Certificate, 
allowing access to a single Controlling Process by multiple computers or 
terminals;
    2. installing or running the Software on a computer associated with 
a Product Class greater than the Product Class specified on Your License 
Certificate;
    3. decompiling, disassembling, or reverse engineering the Software;
    4. modifying the Software in any manner, except those portions 
written in the Mathematica language and included as examples;
    5. distributing, publishing, transferring, sublicensing, lending, 
leasing, renting, or otherwise making available the Product or any 
portion of the Software including collections of data;
    6. copying or allowing copying of the Product or any elements of the 
Product, except as permitted for the maintenance of an archival copy of 
the Software as allowed by the Permitted Uses and Installations section 
of this Agreement;
    7. allowing access to the Product by any user other than Licensee, 
including without limitation, access to the Product via a web server, 
which is only allowed pursuant to a valid webMathematicaTM license 
agreement;
    8. removing any copyright, trademark, or other proprietary notices 
from the Product; and
    9. Installing separate components of each Controlling Process or 
Computation Process on separate computers, with the exception that the 
Front End of a Controlling Process can be on a separate computer from 
the associated Kernel.




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