#!perl -w -I..
my
(
$a
,
$b
,
$x
,
$y
,
$i
,
$c2
,
$c3
) = symbols(
qw(a b x y i 2 3)
);
ok(
sin
(
$x
)**2 +
cos
(
$x
)**2 == 1,
'Pythagoras'
);
ok( (
$x
**8 - 1) / (
$x
**4+1) ==
$x
**4-1,
'Polynomial division'
);
ok( (
$x
**2 - 1) == (
$x
-1) * (
$x
+1),
'Polynomial multiplication'
);
ok(
abs
(!(
$x
+
$y
*$i
)*!(
$a
+
$b
*$i
)) == 1,
'Length of product of units'
);
ok( (
$x
+
$x
*$x
)
*$y
/(
$x
*$y
) == 1+
$x
);
ok( (2
*$x
*$y
**20) / (4
*$y
**19+4
*$y
**19) == (
$x
*$y
)/4);
ok( (4
*$b
+4
*$a
*$b
)/(4
*$b
+4
*$a
*$b
) == 1/(
$a
+1)
*$a
+1/(
$a
+1));
ok( (
sqrt
(
$c2
)+
sqrt
(
$c3
))**4 == 10*(
sqrt
(
$c2
)+
sqrt
(
$c3
))**2 - 1);
ok( (
$x
**16-1)/(
$x
**8-1) ==
$x
**8+1);
ok( (
$x
+1)**11 / (1+
$x
)**12 == 1/(
$x
+1));
ok( (
$x
**2 +
$y
**2)/(
$x
**2 +
$y
**2) == 1);
ok( (
$x
**2 + 2
*$x
*$y
+
$y
**2) / (
$x
+
$y
) ==
$x
+
$y
);
ok( ((
$x
**2-1)/((
$x
+1)*(
$x
-1))) == 1);
exit
(0);