Subject: Substituting values into differentiated function
From: Andrew Martin
Date: Wed, 15 Aug 2012 17:58:57 +0100
Hi,
I'm trying to reproduce the steps from this paper:
http://www.doc.gold.ac.uk/~mas02mb/sdp/download/Myatt2004Convergence.pdf
I can do the first few steps:
1) Define the function "g".
g(c,a,b) := ((1-a)/a)*c+(1-b)*(1-(c/a));
2) Define the function "f".
f(c,a,b) := a*(c+ g(c,a,b)*c);
3) Differentiate f with respect to c
fWRTc(c,a,b) := diff(f(c,a,b),c);
I'm not confident my syntax in step 3) is correct. If I type
"fWRTc(0.1,0.8,0.1);" I get this error:
> diff: second argument must be a variable; found 0.1
> #0: fWRTc(c=0.1,a=0.8,b=0.1)"
I think it's because it's substituting c=0.1 in diff(f(c,a,b),c) and
so it's trying to differentiate with respect to 0.1.
My problems are:
1) Displaying the result of diff(f(c,a,b),c) as a*(2-b) - 2*c*(a-b)
2) The syntax for calculating a when c=0 and fWRTc(c,a,b) = 1.
In the linked paper they show that a = 1/(2-b) when df/dc = 1 and c = 0.
Can you help me find the correct functions to display these results?
Thank you,
Andrew
--
Andrew Owen Martin
PhD Cand. at Goldsmiths, University of London (ma901am)
Investigating Enactivism with Sensory Substitution
M: 07901 65 35 28
http://aomartin.co.uk