LinearSystemMatrixPackage(F, Row, Col, M)

solvelin.spad line 1 [edit on github]

• F: Field

• Row: Join(FiniteLinearAggregate F, shallowlyMutable)

• Col: Join(FiniteLinearAggregate F, shallowlyMutable)

• M: MatrixCategory(F, Row, Col)

This package solves linear system in the matrix form AX = B.

hasSolution?: (M, Col) -> Boolean

hasSolution?(A, B) tests if the linear system AX = B has a solution.

particularSolution: (M, Col) -> Union(Col, failed)

particularSolution(A, B) finds a particular solution of the linear system AX = B.

rank: (M, Col) -> NonNegativeInteger

rank(A, B) computes the rank of the complete matrix (A|B) of the linear system AX = B.

solve: (M, Col) -> Record(particular: Union(Col, failed), basis: List Col)

solve(A, B) finds a particular solution of the system AX = B and a basis of the associated homogeneous system AX = 0.

solve: (M, List Col) -> List Record(particular: Union(Col, failed), basis: List Col)

solve(A, LB) finds a particular soln of the systems AX = B and a basis of the associated homogeneous systems AX = 0 where B varies in the list of column vectors LB.