Friday, 14 June 2019


Taylored Polynomials

Differentiating f(x)^g(x)
The Differentiator
Graphing Derivatives
The Complexities Of The Simplifier
Formula Translation: The Error Function
Expression Parser
Note: As always, the latest ToyGraf code can be found at

What better use for a graphing differentiator, than to generate Taylor polynomials for arbitrary functions, in the fewest possible keystrokes?

  • Run ToyGraf;
  • Press F2 (or click the green + button) to add a new function;
  • Type sin x + cos x
  • Click the little yellow pencil in the top row to bring up the Trace Properties dialog;
  • Type Alt+T, or click the big friendly Taylor Polynomial... button;
  • Use the spin edit to select the desired degree of your polynomial, then click OK.
The Legend Box that appears will obscure most of the new graph, while the Property Table hides the rest. But that's your own fault for selecting such a ridiculously high degree of polynomial. There are both menu options and toolbar buttons to control both if and where stuff like the toolbar, legend and property table appear - have a hunt for them!

Save some files in the ToyGraf .tgf format, then open them in Notepad++ to read what they contain. Don't worry, you won't injure yourself on the sharp brackets, they're not XML (thanks to my code reviewer and tester Stuart for convincing me JSON was the way to go).

Next time: Using ToyGraf to make real analysis demo animations...