Add TaylorSeriesRationalFunction and improve Derivative for univariate rational functions
#4104
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hulpke
added
kind: new feature
topic: library
release notes: not needed
fingolfin
changed the title
fingolfin
added
release notes: to be added
|
This is a new documented feature, so it does need release notes. I've changed the PR title to a suitable candidate for the release notes entry. |
fingolfin
approved these changes
Sep 3, 2020
Comment on lines
+1128
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| t:=Zero(f); | ||
| for i in [0..deg] do | ||
| if i>0 then | ||
| f:=Derivative(f); | ||
| fi; | ||
| t:=t+Value(f,at)*(x-at)^i/Factorial(i); | ||
| od; |
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Assuming we require deg >= 0 (which is not clear to me from the description of the function), could also do this
Suggested change
| t:=Zero(f); | |
| for i in [0..deg] do | |
| if i>0 then | |
| f:=Derivative(f); | |
| fi; | |
| t:=t+Value(f,at)*(x-at)^i/Factorial(i); | |
| od; | |
| t:=Value(f,at)*x^0; | |
| for i in [1..deg] do | |
| f:=Derivative(f); | |
| t:=t+Value(f,at)*(x-at)^i/Factorial(i); | |
| od; |
There was a problem hiding this comment.
I think this is a wash in terms of cost or code readability, so I left it out. (Added test for deg\ge0)
PaulaHaehndel
added
release notes: added
fingolfin
changed the title
TaylorSeriesRationalFunction and improve Derivative for univariate rational functions
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Includes better method for derivative of rational function.
Taylor series coefficients may be useful for Molien series or Growth series