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D.11.2.8 rightInverse
Procedure from library control.lib (see control_lib).
- Usage:
- rightInverse(M); M a module
- Return:
- module
- Purpose:
- computes such a matrix L, that ML = Id
- Note:
- exists only in the case when M is free submodule
Example:
| | LIB "control.lib";
// a trivial example:
ring r = 0,(x,z),dp;
matrix M[1][2] = 1,x2+z;
print(M);
==> 1,x2+z
print( rightInverse(M) );
==> 1,
==> 0
kill r;
// derived from the TwoPendula example:
ring r=(0,m1,m2,M,g,L1,L2),Dt,dp;
matrix U[1][3];
U[1,1]=(-L2)*Dt^4+(g)*Dt^2;
U[1,2]=(-L1)*Dt^4+(g)*Dt^2;
U[1,3]=(L1*L2)*Dt^4+(-g*L1-g*L2)*Dt^2+(g^2);
module M = module(U);
module L = rightInverse(M);
print(L);
==> (L1^2)/(g^2*L1-g^2*L2),
==> (-L2^2)/(g^2*L1-g^2*L2),
==> 1/(g^2)
// check
print(M*L);
==> 1
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