IIUC "colspec" is used to control whether vertical lines appear in the 
table.  For example the default "{|T|T|T|}" gives vertical lines while 
"{TTT}" omits them.  In sphinx/writers/latex.py, Table.get_colspec() will 
use self.colspec, if set, as the column specification, but I can't figure 
out how to set that value from Python using docutils.  Hardcoding the value 
in latex.py to "{TTT}" does indeed get rid of the vertical lines.

Here's what I have at the moment:

self.table = nodes.table(classes=["prodn"], colspec="{TTT}")

widths = [1, 1, 100]

tgroup = nodes.tgroup(cols=len(widths), colspec="{TTT}")

for width in widths:

    tgroup += nodes.colspec(colwidth=width)

self.tbody = nodes.tbody(colspec="{TTT}")



        <table classes="prodn" colspec="{TTT}">
            <tgroup cols="3" colspec="{TTT}">
                <colspec colwidth="1"/>
                <colspec colwidth="1"/>
                <colspec colwidth="100"/>
                <tbody colspec="{TTT}">



For the horizontal lines, I don't even see an option to control this.  The 
"\hline"s appear to be hard coded.

Any suggestions?

I'd consider submitting a Spinx PR to support these, if necessary.  Provided 
it's not a large change.

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