I’ve written a simple graphing implementation in C#, and I can graph things by comparing each pixel to the position on the graph it represents and plugging that position into the function I have to see if it is on the curve. That’s all well and good.
The problem I’m having is USING a generated taylor polynomial. For example, I am able to create the nth taylor polynomial of a transcendent function f centered at c by doing
summation of this from 0 to to n with the counter variable being k = ((kth derivative of f(c)) * (x-c)^k)/k!
I am not sure how to do math markup on stackoverflow nor am I too competent with doing that on the web, but I hope that is understandable. The left side could be written as sigma _k=0 ^n or something like that with _ representing the section under sigma and the ^ representing the part above…
So I end up generating a Taylor polynomial of the 6th degree for cos(x) centered at 0(maclaurin, I know) that looks something like
“1 – x^2/2! + x^4/4! – x^6/6!”
This can be done through simple string manipulation in C#. I can just loop through and add the next term to the string.
I really can’t comprehend how I would actually be able to use the string as a function to compare to graph positions to see if that graph position is actually on this graph to therefore graph it. So essentially: How would I use a string as an actual mathematical function in C#, or is there a better way of doing this.
Really sorry if it’s confusing…really trying my best to explain it in a way that people can help.
You need a parser of string -> function. See MathParser for an example, that probably does everything you mentioned you need.