linalg(deprecated)/intbasis - Help

linalg(deprecated)

 intbasis
 determine a basis for the intersection of spaces

 Calling Sequence intbasis(S1, S2, ..., Sn)

Parameters

 S[i] - vector, set of vectors, or list of vectors

Description

 • Important: The linalg package has been deprecated. Use the superseding packages LinearAlgebra[IntersectionBasis], instead.
 - For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
 • A basis for the intersection of the vector spaces spanned by the vectors in Si is returned.
 • A basis for the zero-dimensional space is an empty set or list.
 • The command with(linalg,intbasis) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding packages LinearAlgebra[IntersectionBasis], instead.

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $\mathrm{v1}≔\mathrm{vector}\left(\left[1,0,1,0\right]\right)$
 ${\mathrm{v1}}{≔}\left[\begin{array}{cccc}{1}& {0}& {1}& {0}\end{array}\right]$ (1)
 > $\mathrm{v2}≔\mathrm{vector}\left(\left[0,1,0,1\right]\right)$
 ${\mathrm{v2}}{≔}\left[\begin{array}{cccc}{0}& {1}& {0}& {1}\end{array}\right]$ (2)
 > $\mathrm{v3}≔\mathrm{vector}\left(\left[1,2,1,1\right]\right)$
 ${\mathrm{v3}}{≔}\left[\begin{array}{cccc}{1}& {2}& {1}& {1}\end{array}\right]$ (3)
 > $\mathrm{v4}≔\mathrm{vector}\left(\left[-1,-2,1,0\right]\right)$
 ${\mathrm{v4}}{≔}\left[\begin{array}{cccc}{-1}& {-2}& {1}& {0}\end{array}\right]$ (4)
 > $\mathrm{intbasis}\left(\left\{\mathrm{v1},\mathrm{v2}\right\},\left\{\mathrm{v3},\mathrm{v4}\right\}\right)$
 ${\varnothing }$ (5)
 > $\mathrm{intbasis}\left(\left[\mathrm{v1},\mathrm{v2},\mathrm{v3}\right],\left[\mathrm{v3},\mathrm{v4}\right],\left[\mathrm{v2},\mathrm{v3}\right]\right)$
 $\left\{\left[\begin{array}{cccc}{1}& {2}& {1}& {1}\end{array}\right]\right\}$ (6)
 > $u≔\mathrm{evalm}\left(\mathrm{v1}-\mathrm{v2}\right)$
 ${u}{≔}\left[\begin{array}{cccc}{1}& {-1}& {1}& {-1}\end{array}\right]$ (7)
 > $v≔\mathrm{evalm}\left(\mathrm{v1}+\mathrm{v2}\right)$
 ${v}{≔}\left[\begin{array}{cccc}{1}& {1}& {1}& {1}\end{array}\right]$ (8)
 > $w≔\mathrm{evalm}\left(\mathrm{v1}-\mathrm{v3}\right)$
 ${w}{≔}\left[\begin{array}{cccc}{0}& {-2}& {0}& {-1}\end{array}\right]$ (9)
 > $\mathrm{intbasis}\left(\left\{u,v,w\right\},\left\{\mathrm{v1},\mathrm{v2},\mathrm{v3}\right\}\right)$
 $\left\{\left[\begin{array}{cccc}{-2}& {0}& {-2}& {0}\end{array}\right]{,}\left[\begin{array}{cccc}{0}& {2}& {0}& {1}\end{array}\right]{,}\left[\begin{array}{cccc}{-1}& {1}& {-1}& {1}\end{array}\right]\right\}$ (10)