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