Solutions of Systems of Linear Equations

IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng

Given a matrix A belonging to M_n(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 particular solution v;
• The kernel K of A so that (v + k) * A = w for k in K.

IsConsistent(A, W) : ModMatRngElt, [ ModTupRng ] -> BoolElt, [ ModTupRngElt ], ModTupRng

Given a matrix A belonging to M_n(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 solution sequence V;
• The kernel K of A so that (V[i] + k) * A = W[i] for k in K.

Solution(A, w) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng

Given a matrix A belonging to M_n(R) and a vector v belonging to the tuple module R^((n)), solve the system of linear equations v * A = w. The function returns two values:

• A particular solution v;
• The kernel K of A so that (v + k) * A = w for k in K.

Solution(A, W) : ModMatRngElt, [ ModTupRng ] -> [ ModTupRngElt ], ModTupRng

Given a matrix A belonging to M_n(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 solution sequence V;
• The kernel K of A so that (V[i] + k) * A = W[i] for k in K.