Re: Multi-variable Integration

• To: mathgroup at smc.vnet.net
• Subject: [mg79758] Re: Multi-variable Integration
• From: gravmath at yahoo.com
• Date: Fri, 3 Aug 2007 06:35:59 -0400 (EDT)
• References: <f8pjji\$2ae\$1@smc.vnet.net><f8s3c6\$37o\$1@smc.vnet.net>

```Jens,

Thank you for the response but, with all due respect, you miss my
point.  In the example you cite, the expression a*b*c*d*e*x*y is only
'discovered' to be a function of x by virtue of the differentiation
that is carried out in the first step.  However, it is not clear what
a, b, c, d, e, and y are.  One might respond to this point by saying
'surely a, b, c, d, and e are parameters and y is another variable'
but it is not all obvious that this should be so.  Consider, for
example, the concept of variation of parameters, in which symbols in
an expresson that are not originally regarded as independent variables
are regarded as such for the sake of some particular calculation.  We
humans can work in this contextual way, switching meaning when it
suits us, and in doing so can clearly distinguish each situation (at
least sometimes).

What I was aiming for was something deeper.  How can I let
Mathematica know that I am working in a 2-dimensional space, that is
to say with 2 independent variables.  Mathematically, I want to regard
the f[] as depending on x, y and in doing so I have specified the
context explicitly.  I then want to know if Mathematica can understand
that Integrate[D[f[x,y],x],x] could (and I would argue should) yield
f[x,y] + g[y], in which g[y] is not a constant of integration but a
function of the other independent variable.  This may not be possible
as a built-in feature and I have an idea of how to program this,
however, why should I do so if Mathematica can do it.  Said another
way, what I am looking for is akin the 'depends' (if memory serves)
concept in Maxima but within the Mathematica framework.

Regards,

> Hi,
>
> form the mathematical point of view the general convention
> is that the integration constant for indefinite integration
> is zero ... otherwise
>
> Integrate[D[a*b*c*d*e*x*y,x],x]
>
> would be
>
> a*b*c*d*e*x*y+arbitaryConstant[a,b,c,d,e,y]
>
> clearly this would made the system unusable because it would
> quickly grow the complexity of the expression.
>
> In the dedicated cases, where you wish to violate the
> convention about the integration constant, you must do
> it by hand.
>
> Regards
>    Jens
>

```

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