The name Lygodium circinnatum is not listed in the Plant List website. Instead, Lygodium circinatum, a name with single "n" is available. The Royal Botanic Garden Edinburgh website on ferns in Thailand, Laos and Cambodia used the name with the double "n" and provide quite a good description of this fern. The other piece of information on this name was from the BP sponsored booklet titled "A Guide to the Ferns of Singapore", page 48. I am not exactly sure which is the correct scientific name or are the 3 names referring to the same fern but will keep to the one that is most used by others at the moment.
I was confused between Lygodium circinnatum and Lygodium longifolium until November 2014 when I had the chance to meet the real Lygodium circinnatum in the wild. In the past, I had the pictures of Lygodium longifolium named as Lygodium circinnatum. Based on the description in the Flora of China website, the margin of the pinnae of Lygodium longifolium is shallowly serrate (teeth-like arrangement) while that of Lygodium circinnatum entire (smooth). The picture on the left below is from Lygodium longifolium while the one on the right is from Lygodium circinnatum.
The fronds of this climbing fern is huge and really long when compared to the other few climbing ferns available here. The smaller climbing fern in the picture below is Lygodium flexuosum while the gigantic one is Lygodium circinnatum.