Thank you for the proofs. Here are our comments.

On p. 3, line 1. The text "These side conditions apply:" that starts a line is
slightly indented, with a space. Please remove the space. It wasn't there in
the authors' manuscript.

On p. 7, line 5 from the bottom: "we must apply the substitution {F⃗ → f⃗}". The
curly braces { } are very large. Would it be possible to use normal-sized
braces?

On p. 9, line 4 of text (ignoring the displayed table). The text "In this
example" that starts a line is slightly indented, with a space. Please remove
the space. It wasn't there in the authors' manuscript.

On p. 10, line 8: "Every resulting recurrence P (M⃗ , ⃗S)". The parentheses ( )
are very large. Would it be possible to use normal-sized parentheses?

On p. 10, line 9: "P (aM⃗ + ⃗b, S⃗) σf + σe = 0 of σf where we have collected".
The parentheses ( ) are very large. Would it be possible to use normal-sized
parentheses?

On p. 10, line 8 from the bottom: The text "Now σ maps the lowest four
recurrences" that starts a line is slightly indented, with a space. Please
remove the space. It wasn't there in the authors' manuscript.

On p. 10, line 3 from the bottom: The text "The next step is to propagate to
the summation" that starts a line is slightly indented, with a space. Please
remove the space. It wasn't there in the authors' manuscript.

On p. 12, line 4, there is too much space between "Hence, in total we have" and
the displayed material below it. The vertical space should be the same above
and below the display. Right now it is larger above than below.

On p. 15, line 2 from the bottom, there is a displayed equation. The vertical
space should be the same above and below the display. Right now it is larger
above than below.

On p. 16, line 4, there is a pair of displayed equations. The vertical space
should be the same above and below the display. Right now it is larger above
than below.

On p. 17, line 6: Please replace "anonmyous" by "anonymous". This typo is our
own fault, but we would be grateful if you could fix it.
