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A couple of apps have appeared that offer some very compelling local typesetting for LaTeX documents, namely Texpad en Tex Writer. Both seem to be based on different principles, though the end results are the same. Both approaches avoid the need to keep servers in the air for remote compiling and it works perfectly fine for the majority of documents. Nevertheless, none of these apps come anywhere near the usability of Textastic in terms of, well, editing and sharing the actual files :).