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Assumption -> quadratic multivariate function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg47119] Assumption -> quadratic multivariate function
*From*: damir at 2d.com (Damir Herman)
*Date*: Fri, 26 Mar 2004 03:56:17 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
Is there a way to tell Mathematica to assume that a function of more
than one variable is at most quadratic in its arguments? I do not want
to specify the variables, so in that regard I think I have two
options: to use Dt on f or partial derivatives acting on Hold[f].
For instance, approach that works for a function of one variable
(1) f/: Dt[f, {x, 3}] = 0;
does not work for a function of two variables
(2) f/:Dt[f, {x, 3}] = 0;
(3) f/:Dt[f, {y,3}] = 0;
I don't understand that, because these are not conditions for a
particular x or y.
For example,
Clear[f];
SetAttributes[p, {Constant}];
Dt[f^p, {x, 4}, {y,4}]
seems to work for x only and does not care about y.
Note that Mathematica returns
In[79]:= Dt[Dt[f, {x, 3}], y]
Out[79]:= 0
however
In[80]:= Dt[f, {x,3}, y]
Out[80]:= Dt[f, {x,3}, y]
How do I make mathematica use the comutativity of these two
operations?
Thanks,
Damir
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