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identfor-mat_trace-matrix-sum-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

sum(sum(strain(u)[i][...

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

B: matrix([1/La,0],[0...

invert(s*identfor(A)-A);

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

B: matrix([1/La,0],[0...

sol1: invert(s*identf...

Calculate

identfor-mat_trace-matrix-sum-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

sum(sum(strain(u)[i][...

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(R);

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

B: matrix([1/La,0],[0...

sol1: simplify(invert...

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

B: matrix([1/La,0],[0...

sol1: invert(s*identf...

Calculate

identfor-matrix

A: matrix([-Ra/La,-k/...

B: matrix([1/La,0],[0...

(s*identfor(A)-A)^-1;

Calculate

identfor-invert-matrix

A: matrix([-Ra/La,-k/...

B: matrix([1/La,0],[0...

sol1: invert(s*identf...

Calculate

identfor-mat_trace-matrix-sum-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

sum(sum(strain[i][j] ...

Calculate

identfor

Run Example
(%i1)A: matrix([-Ra/La,-k/La],[k/O,0]);
                                [   Ra    k  ]
                                [ - --  - -- ]
                                [   La    La ]
(%o1)                           [            ]
                                [  k         ]
                                [  -     0   ]
                                [  O         ]
(%i2) B: matrix([1/La,0],[0,1/O]);
                                   [ 1     ]
                                   [ --  0 ]
                                   [ La    ]
(%o2)                              [       ]
                                   [     1 ]
                                   [ 0   - ]
                                   [     O ]
(%i3) invert(s*identfor(A)-A);
              [           s                        k            ]
              [   -----------------    - ---------------------- ]
              [     2                          2                ]
              [    k            Ra            k            Ra   ]
              [   ---- + s (s + --)      La (---- + s (s + --)) ]
              [   La O          La           La O          La   ]
              [                                                 ]
(%o3)         [                                    Ra           ]
              [                                s + --           ]
              [           k                        La           ]
              [ ---------------------     -----------------     ]
              [    2                        2                   ]
              [   k            Ra          k            Ra      ]
              [ (---- + s (s + --)) O     ---- + s (s + --)     ]
              [  La O          La         La O          La      ]
(%i4) 
Run Example
T: matrix([-lambda, lambda], [mu, -mu]);
                             [ - lambda  lambda ]
(%o1)                        [                  ]
                             [    mu      - mu  ]
(%i2) p0: [1, 0];
(%o2)                               [1, 0]
(%i3) A: s*identfor(T) - T;
                           [ lambda + s  - lambda ]
(%o3)                      [                      ]
                           [    - mu      s + mu  ]
(%i4) Ps: p0.invert(A);
      [              s + mu                             lambda               ]
(%o4) [ ---------------------------------  --------------------------------- ]
      [ (s + mu) (lambda + s) - mu lambda  (s + mu) (lambda + s) - mu lambda ]
(%i5) Pf: partfrac(Ps, s);
               [             lambda                      mu        ]
(%o5)  Col 1 = [ ------------------------------- + --------------- ]
               [ (lambda + mu) (lambda + s + mu)   s (lambda + mu) ]
                          [     lambda                    lambda              ]
                  Col 2 = [ --------------- - ------------------------------- ]
                          [ s (lambda + mu)   (lambda + mu) (lambda + s + mu) ]
(%i6) p0t: ilt(Pf[1,1], s, t);
                            - t (lambda + mu)
                   lambda %e                        mu
(%o6)              -------------------------- + -----------
                          lambda + mu           lambda + mu
(%i7) p1t: ilt(Pf[1,2], s, t);
                                          - t (lambda + mu)
                     lambda      lambda %e
(%o7)              ----------- - --------------------------
                   lambda + mu          lambda + mu
(%i8) declare(lambda, [constant, real, scalar]);
(%o8)                                done
(%i9) assume(lambda >
 0, lambda <
= 1);
(%o9)                    [0 < lambda, lambda - 1 <= 0]
(%i10) declare(mu, [constant, real, scalar]);
(%o10)                               done
(%i11) assume(mu >
 0, mu <
= 1);
(%o11)                       [0 < mu, mu - 1 <= 0]
(%i12) p0SS: limit(p0t, t, inf);
                                      mu
(%o12)                            -----------
                                  lambda + mu
(%i13) p0SS, lambda=1, mu=1, numer;
(%o13)                                0.5
(%i14) p1SS: limit(p1t, t, inf);
                                    lambda
(%o14)                            -----------
                                  lambda + mu
(%i15) p1SS, lambda=1, mu=1, numer;
(%o15)                                0.5
(%i16) for irow: 1 thru length(T) do (T[irow][length(T)]: 1);
(%o16)                               done
(%i17) b: zeromatrix (1, length(T));
(%o17)                             [ 0  0 ]
(%i18) b[1, length(T)]: 1;
(%o18)                                 1
(%i19) pSS: b.invert(T);
                     [        mu             lambda     ]
(%o19)               [ - -------------  - ------------- ]
                     [   - lambda - mu    - lambda - mu ]
(%i20) ratsimp(pSS);
                         [     mu         lambda    ]
(%o20)                   [ -----------  ----------- ]
                         [ lambda + mu  lambda + mu ]
(%i21) 
Run Example
A: matrix([-Ra/La,-k/La],[k/O,0]);
                                [   Ra    k  ]
                                [ - --  - -- ]
                                [   La    La ]
(%o1)                           [            ]
                                [  k         ]
                                [  -     0   ]
                                [  O         ]
(%i2) B: matrix([1/La,0],[0,1/O]);
                                   [ 1     ]
                                   [ --  0 ]
                                   [ La    ]
(%o2)                              [       ]
                                   [     1 ]
                                   [ 0   - ]
                                   [     O ]
(%i3) sol1: invert(s*identfor(A)-A);
              [           s                        k            ]
              [   -----------------    - ---------------------- ]
              [     2                          2                ]
              [    k            Ra            k            Ra   ]
              [   ---- + s (s + --)      La (---- + s (s + --)) ]
              [   La O          La           La O          La   ]
              [                                                 ]
(%o3)         [                                    Ra           ]
              [                                s + --           ]
              [           k                        La           ]
              [ ---------------------     -----------------     ]
              [    2                        2                   ]
              [   k            Ra          k            Ra      ]
              [ (---- + s (s + --)) O     ---- + s (s + --)     ]
              [  La O          La         La O          La      ]
(%i4) sol2: sol1b.B;
                                       [ 1     ]
                                       [ --  0 ]
                                       [ La    ]
(%o4)                          sol1b . [       ]
                                       [     1 ]
                                       [ 0   - ]
                                       [     O ]
(%i5) 

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