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D.11.2.7 leftInverse
Procedure from library control.lib (see control_lib).
- Usage:
- leftInverse(M); M a module
- Return:
- module
- Purpose:
- computes such a matrix L, that LM = 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[2][1] = 1,x2z;
print(M);
==> 1,
==> x2z
print( leftInverse(M) );
==> 1,0
kill r;
// derived from the example TwoPendula:
ring r=(0,m1,m2,M,g,L1,L2),Dt,dp;
matrix U[3][1];
U[1,1]=(-L2)*Dt^4+(g)*Dt^2;
U[2,1]=(-L1)*Dt^4+(g)*Dt^2;
U[3,1]=(L1*L2)*Dt^4+(-g*L1-g*L2)*Dt^2+(g^2);
module M = module(U);
module L = leftInverse(M);
print(L);
==> (L1^2)/(g^2*L1-g^2*L2),(-L2^2)/(g^2*L1-g^2*L2),1/(g^2)
// check
print(matrix(L)*matrix(M));
==> 1
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