Software Requirements

• Install SageMath:

  • 8.2 version (released on 2018-05-05) is needed. (http://www.sagemath.org/)

• Install ore_algebra: follow the instructions in http://www.kauers.de/software.html

How to Run Codes

• go to 'code' folder.

• run SageMath using the command line

~/Downloads/SageMath/sage

• When SageMath is running, load the script. For example

load("D-finite-core.sage")

• Instructions for codes and functions are available in 'D-finite-core.sage' file. Users can construct their examples and test them.

How to Run Example Scripts

• go to 'code/examples' folder.

type the command line

~/Downloads/SageMath/sage expExample.sage

to execute the scripts

• or in 'code/examples' folder, run sage by the command line

~/Downloads/SageMath/sage

When the sage is running, load the script. For example

load("expExample.sage")

• Scripts in 'code/examples' folder.
  • err-2equations-comparison.sage : compare alpha theory, Krawczyk method based tests on the system with 2 error functions.(example in section 5.1)
  • mixed-2equations.sage : computes gamma value using maximum value of a Bessel function and an error function.(example in section 5.2)
  • expExample.sage : comparison between 'alphaCertified' on the system with an exponential function.(example in section 5.3)
  • ellipseExp-alpha.sage : maximization problem with two ellipses certified by alpha theory (example in section 5.4)
  • ellipseExp-Krawczyk.sage : maximization problem with two ellipses certified by Krawczyk method (example in section 5.4)