Graphics Reference
In-Depth Information
v
T
= the column vector form (n ¥ 1 matrix) of the row vector
v
(1
¥ n matrix)
GL
(n,k)
= the linear group of nonsingular n ¥ n matrices over k =
R
or
C
O
(n)
= the group of real orthogonal n ¥ n matrices
SO
(n)
= the group of real special orthogonal n ¥ n matrices
ker h
= kernel of a homomorphism
im h
= image of a homomorphism
V(f)
= set of zeroes of f (see pages 468, 675, and 676)
<a,b, . . .>
= ideal generated by elements a, b, . . . in a ring
= the radical of an ideal I
I
R(f,g) = R
X
(f,g)
= the resultant of polynomials f(X) and g(X)
k[V]
= ring of polynomial function on
V
k(V)
= field of rational functions on
V
tr
k
(K)
= transcendence degree of field K over k
= the complex conjugate of the complex number z
z
1
X
= the identity map on the set
X
c
A
= the characteristic function of a set
A
as a subset of a given
larger set
X
f
-1
(y)
= {x | f(x) = y}
a | b
= a divides b
Sign(x)
=+1 if x ≥ 0 and -1 otherwise (returns an
integer
)
Sign(s)
= sign of permutation s
=+1 if s is an even permutation, -1 if s is an odd permutation
atan2(y,x)
= undefined, if x = y = 0,
p/2, if x = 0 and y > 0,
-p/2, if x = 0 and y < 0,
0,
if y = 0 and x > 0,
p,
if y = 0 and x < 0, and
q,
where -p<q<p, tan q=y/x, and q lies in the same
quadrant
as (x,y).
atan2(y,x) is closely related to the ordinary arctangent tan
-1
(y/x). However,
the ordinary arctangent, which is a function of one variable, is not able
to keep track of the quadrant in which (x,y) lies, whereas atan2 does. For
example,
Note:
3
4
p
p
(
)
=-
(
)
=
atan
233
--
,
,
but
atan
233
,
.
4
= e
x
exp(x)
L(
V
,
W
)
= vector space of linear (see page 873)
L
k
(
V
1
,
V
2
,...,
V
k
;
W
)
= Vector space of multilinear maps (see page 875)
t
M
= tangent bundle of manifold
M
n
M
= normal bundle of manifold
M
