# [Xy-pic] problems + operator after a change of basis

Vasiliev.B at forces.gc.ca Vasiliev.B at forces.gc.ca
Thu Jun 12 08:50:15 CEST 2003

Good day,

I have noticed a rather weird behaviour of xy-pic after change of basis.
The problem appears after I move or rotate the
"standard basis".  For some reason,  the addition operation fails to work as
expected.  Here is an example.

\begin{xy}
% set up standard basis: x0x1 is a horizontal vector of length 1cm, x0x2 is
a vertical vector
<0cm,0cm>;<1cm,0cm>:(0,0),
(0,0)*{x0}="x0", (1,0)*{x1}, (0,1)*{x2},
% test case for + operator : "a" should appear at (1,1) in the x-basis and
it does
"x0"+(1,1)*{a},
% shift the origin 5 cm to the right and display new basis: we get a copy of
the previous picture, except "x" is replaced by "y"
(5,0);(6,0):(0,0),
(0,0)*{y0}="y0", (1,0)*{y1}, (0,1)*{y2},
% test case for + operator: "b" should appear at (1,1) in the y-basis, but
it does not
"y0"+(1,1)*{b},
% however this works
(1,1)*{c}
\end{xy}

It appears in the expression "y0"+(1,1), (1,1) is a vector whose true
coordinates  are (5,1) where 5 is the shift from x to y basis.
Does anybody have a solution to this (other than scaling (1,1) appropriately
to get the necessary results?

By no means I fully understand the package; so, if there is a mistake in the