linalg7 http://www.openmath.org/cd/linalg7.ocd 2005-00-00 experimental 2003-03-22 1 0 alg1 arith1 interval1 linalg1 linalg4 list1 logic1 mathmltypes quant1 relation1 set1 A CD of structured vectors zero The zero symbol represents the zero vector, it takes one parameter which should be the length (dimension in some terminology) of the vector. If M is an n*m matrix and V is a zero vector of length m then V*M = V2 where V2 is a zero vector of length n If M is an n*m matrix and V is a zero vector of length n then M*V = V2 where V2 is a zero vector of length m If V is a zero vector of length n and V2 is a vector of length n then V+V2 = V2+V = V2 If V is a zero vector of length n and i is in the integral interval [1,n] then V.i = 0 constant The constant symbol represents the constant vector. It takes two parameters, the length (dimension) of the vector and the constant value, which all the elements are equal to. If V is a constant vector of length n, with constant value c and i is in the integral interval [1,n] then V.i = c sparse The sparse symbol is a constructor for sparse vectors, it is (n+1)-ary, where the first parameter is the length (dimension) of the vector, and every following parameter specifies a possibly non-zero element in the following way. The parameter is a list which should have length two. The first element in the list is the position (one based), whilst the second element in the list is the value. Every other element of the vector is implicitly zero. This example shows a representation of the sparse matrix $$\left (\begin{array}[c]1\\0\\0\\0\\0\end{array}\right$$ 5 1