The results (the files created with Maple's command "save"):
12tp-approx1.sav
12tp-approx2.sav
12tp-approx3.sav
12tp-approx4.sav
12tp-approx5.sav
12tp-approx6.sav
12tp-approx7.sav

The Maple code that verifies that the triple points are preserved with the announced precision (up to O(u^9) for approx7):
12tp-check-approx1.txt
12tp-check-approx2.txt
12tp-check-approx3.txt
12tp-check-approx4.txt
12tp-check-approx5.txt
12tp-check-approx6.txt
12tp-check-approx7.txt