From "compass and ruler" to computer

Some notes about calculations on computer

I use the word "function" with both meanings:
  • real and complex functions with mathematical meaning, in Japanese, I use "函数 (Hánshù)".
  • command function with computational meaning, in Japanese, I use "関数 (Guān shù)".
GeoGebra is a Dynamic Geometry Software (DGS).
  • DGS is a computer program which allows one to create geometric constructions with emulated compass and ruler.
  • What is the merit of computer program? accuracy, reproducibility, repeatability, interactivity, encapsulability, ...
In the sense of numerical computing, there are some errors on floating point arithmetics. When you use a computer algebra system, we can expect exact calculus. But, in drawing, in many cases, we don't need accuracy?