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MathGroup Archive 2004

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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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