I'm using sage for data analysis and number crunching in my physical
chemistry class and stumbled on a curiosity while replacing the
variables that are used by find_fit:
When replacing variables like 'a, b ,c' for 'c1, c2, c3' on a 11th
degree polynomial the whole find_fit-function goes nuts and the former
nicely fitting function doesn't fit at all anymore.
Example:
While the following code works perfectly:
var('a b c d f g j h k l n o')
model(x) = a*x
+b*x^(2)+c*x^(3)+d*x^(4)+f*x^(5)+g*x^(6)+h*x^(7)+j*x^(8)+k*x^(9)+l*x^(10)+n*x^(11)+o
m=find_fit(V,model)
Temp(x)=model(a=m[0].rhs(),b=m[1].rhs(),c=m[2].rhs(),d=m[3].rhs(),f=m[4].rhs(),g=m[5].rhs(),h=m[6].rhs(),j=m[7].rhs(),k=m[8].rhs(),l=m[9].rhs(),n=m[10].rhs(),o=m[11].rhs())
The following code does not (replaced only 'a' by 'k1') and Temp(x)
shoots off to infinity at some point:
var('k1 b c d f g j h k l n o')
model(x) = k1*x
+b*x^(2)+c*x^(3)+d*x^(4)+f*x^(5)+g*x^(6)+h*x^(7)+j*x^(8)+k*x^(9)+l*x^(10)+m*x^(11)+o
m=find_fit(V,model)
Temp(x)=model(k1=m[0].rhs(),b=m[1].rhs(),c=m[2].rhs(),d=m[3].rhs(),f=m[4].rhs(),g=m[5].rhs(),h=m[6].rhs(),j=m[7].rhs(),k=m[8].rhs(),l=m[9].rhs(),n=m[10].rhs(),o=m[11].rhs())
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