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Astronomical Applications Department, U.S. Naval Observatory - Sensitivity Integral (Page 18)

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Astronomical Applications Department, U.S. Naval Observatory - Sensitivity Integral
:=
denoms
{ };
p
expr
for
in
do
(
)
hastype
,
p `^`
if
then
(
)
type
,
p `^`
if
then
fi
<
(
)
op
,
2 p
0
:=
denoms
union
{
}
(
)
op
,
1 p
denoms
if
then
:=
denoms
union
denoms
( )
procname p
else
fi
fi
od;
denoms
end
:=
denoms
(
)
get_denoms indef
denoms
+ -
2 s
r
r g s
+ +
2 s
r
r g r
- -
2 s
r
r g
+
s
r
- +
2 s
r
r g
- +
1
g g
+
s
r g
-
s
r
, ,
, ,
,
,
,
, ,
,
,
{
:=
-
s
r g
+
1
g
,
}
:=
blowups
{ };
for
in
do
od
p
denoms
:=
blowups
union
blowups
(
)
solve { }
p
;
:=
blowups
minus
blowups
{
}
,
,
=
s
s
=
r
r
=
g
g
:=
blowups
(
)
map
,
factor blowups
blowups
=
s
1
2
r (
)
- +
1
g
=
g
1
=
g
0
=
r
0
=
s
0
=
r
s
=
s
1
2
r (
)
+
1
g
=
s
-
1
2
r (
)
- +
1
g
,
,
,
,
,
,
,
,
{
:=
=
g
-1
=
s
-
1
2
r (
)
+
1
g
=
s
r g
=
s
-
r g
=
r
-
s
,
,
,
,
}
Expansions of the integral kernel
integrand
0
(
)
sin s x
2
(
)
-
(
)
sin r x
(
)
sin r g x
2
across the singular surfaces are
p
blowups
for
in
do
:=
q
(
)
series
, ,
integrand
0
p 2 ;
if
then
fi
=
(
)
convert
,
% polynom
0
:=
q
(
)
series
, ,
integrand
0
p 3
;
( )
print q
od




sin
1
2
r (
)
- +
1
g x
2
(
)
-
(
)
sin r x
(
)
sin r g x
2
+
2




sin
1
2
r (
)
- +
1
g x




cos
1
2
r (
)
- +
1
g x x (
)
-
(
)
sin r x
(
)
sin r g x
2




-
s
1
2
r (
)
- +
1
g
+




O




-
s
1
2
r (
)
- +
1
g
2
+
(
)
sin s x
2
(
)
cos r x
2
r
2
x
2
(
)
- +
1
g
2
(
)
O (
)
- +
1
g
3
Page 18

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