I'm having problems transforming equations, again...
Setting up the functions b(a) and c(b) works. Inserting them into each other also works to get from a temperature to a current c(b(a)). But now I want to flip it around a(c). The result should be like this a(c):= (c-(4`mA))*(25`degC)/(4`mA); But it's not working even with the ''-trick.
(%i1) load(ezunits);
(%o1) "C:/maxima-5.44.0/share/maxima/5.44.0/share/ezunits/ezunits.mac"
(%i7) a0: 0`degC;
am: 100`degC;
b0: 0`mV;
bm: 4`mV;
c0: 4`mA;
cm: 20`mA;
(a0) 0 ` degC
(am) 100 ` degC
(b0) 0 ` mV
(bm) 4 ` mV
(c0) 4 ` mA
(cm) 20 ` mA
(%i8) b(a):= (bm-b0)/(am-a0)*(a-a0)+b0;
(%o8) b(a):=(bm-b0)/(am-a0)*(a-a0)+b0
(%i9) c(b):= (cm-c0)/(bm-b0)*(b-b0)+c0;
(%o9) c(b):=(cm-c0)/(bm-b0)*(b-b0)+c0
(%i10) c(b(50`degC));
(%o10) 12 ` mA
(%i11) a(c):= dimensionally(solve(c(b(T)), T));
(%o11) a(c):=dimensionally(solve(c(b(T)),T))
(%i12) a(12`mA);
(%o12) [T=(-25) ` degC]
(%i13) a(c):= ''(dimensionally(solve(c(b(T)), T)));
(%o13) a(c):=[T=(-25) ` degC]
(%i14) a(12`mA);
(%o14) [T=(-25) ` degC]
(%i15) oi: T, dimensionally(solve(c(b(T)), T));;
(oi) (-25) ` degC
(%i16) a(c):= (c-(4`mA))*(25`degC)/(4`mA);
(%o16) a(c):=((c-4 ` mA)*(25 ` degC))/4 ` mA
(%i17) a(12`mA);
(%o17) 50 ` degC
-->
It looks like you have omitted the specific value of c from solve(c(b(T)), T) -- what I mean is you need something like solve(c(b(T)) = c1, T) where c1 is the input value such as 12 ` mA.
This definition seems to work --
a(c1):= dimensionally(solve(c(b(T)) = c1, T));
Then I get
(%i22) a(12`mA);
(%o22) [T = 50 ` degC]
When you omit the ... = c1, you are effectively solving for ... = 0, that's why you get T = (- 25) ` degC.
The other variation a(c1) := ''(...) should also work, although I didn't try it.
You can write a(c) := dimensionally(solve(c(b(T)) = c, T)), i.e., using the same name for the variable c and the function c, but it's easy to get mixed up, and also I am hoping the change that behavior in the near future (with the implementation of lexical scope of symbols) which will make that not work anymore.