I can show next signs for exterminating P. alpina and P. vulgaris if they are not in flowering time: http://www2.arnes.si/~sopjslat/mesojedke/mesojedk.htm (it is not in English but you will understand the pictures anyway ;).
You can see the roots of P. alpina (the left one), which are strong, yellow, with one redish main root. They are present at wintertime also. The plant on the right is P. vulgaris, the roots are pale white tufted roots, absent in winter.
When the plants stop flowering, you still can recognize P. alpina, its flower stalk is rough and in P. vulgaris is rounded.
It seems they don't care much about the soil type. They grow on sphagnum or silica sand or limestone equally. I prefer one exposition on travertine stone, which is always in water and is covered with mosses. This seems to be just right one as evaporation of water lower temperature in summertime. They get sunshine only to 10 o'clock in the morning, later they are in shadow. The main trouble are blackbirds (Tordus merula), they use the plants for nests or maybe they eat winter hibernacula.