Solutions of Systems of Linear Equations

IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng
Given a matrix A belonging to Mn(R) and a vector w belonging to the tuple module R(n), return true iff the system of linear equations v * A = w is consistent. If the system is consistent, then the function will also return:
(a)
A particular solution v;
(b)
The kernel K of A so that (v + k) * A = w for k∈K.
IsConsistent(A, W) : ModMatRngElt, [ ModTupRng ] -> BoolElt, [ ModTupRngElt ], ModTupRng
Given a matrix A belonging to Mn(R) and a sequence W of vectors belonging to the tuple module R(m), return true iff the system of linear equations V[i] * A = W[i] for each i is consistent. If the systems are all consistent, then the function will also return:
(a)
A solution sequence V;
(b)
The kernel K of A so that (V[i] + k) * A = W[i] for k∈K.
Solution(A, w) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng
Given a matrix A belonging to Mn(R) and a vector w belonging to the tuple module R(n), solve the system of linear equations v * A = w. The function returns two values:
(a)
A particular solution v;
(b)
The kernel K of A so that (v + k) * A = w for k∈K.
Solution(A, W) : ModMatRngElt, [ ModTupRng ] -> [ ModTupRngElt ], ModTupRng
Given a matrix A belonging to Mn(R) and a sequence W of vectors belonging to the tuple module R(n), solve the system of linear equations V[i] * A = W[i] for each i. The function returns two values:
(a)
A solution sequence V;
(b)
The kernel K of A so that (V[i] + k) * A = W[i] for k∈K.
V2.28, 13 July 2023