Version 5.0 The LEDA User Manual

at vector&
rat vector
rat vector&
v += const rat vector& w addition plus assignment.
const rat vector& v − const rat vector& w
subtracts cartesian coordinates.
v −= const rat vector& w subtraction plus assignment.
rat vector −v returns -v.
3.4 Input and Output
ostream&
istream&
ostream& O ≪ const rat vector& v
istream& I ≫ rat vector& v
writes v’s homogeneous coordinates
componentwise to the output stream
O.
reads v’s homogeneous coordinates componentwise
from the input stream I. The operator
uses the current dimension of v.
3.5 Linear Hull, Dependence and Rank
bool contained in linear hull(const array& A,
const rat vector& x)
determines whether x is contained in the linear
hull of the vectors in A.
int linear rank(const array& A)
bool linearly independent(const array& A)
array linear base(const array& A)
4. Implementation
computes the linear rank of the vectors in A.
decides whether the vectors in A are linearly
independent.
computes a basis of the linear space spanned
by the vectors in A.
Vectors are implemented by arrays of integers as an item type. All operations like creation,
initialization, tests, vector arithmetic, input and output on an vector v take time
O(v.dim( )). dim( ), coordinate access and conversions take constant time. The operations
for linear hull, rank and independence have the cubic costs of the used matrix
operations. The space requirement is O(v.dim( )).