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Solutions of Systems of Linear Equations
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.
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