ae415815-55e3-44ee-8d12-50eb717aa2e9 27 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Solving coefficients for "a" Frobenius example

V C 1 el 1 ≡ C 2 el 1 ≡ C 3 el 1 ≡ C 4 el 1 ≡ C 5 el 1 ≡ C 6 el 1 ≡ C 7 el 1 ≡ C 8 el 1 ≡ C 9 el 1 ≡ 19 mat transpose :

C F C 1 el 1 ≡ 3 C 2 el * C 1 el + 10 C 3 el * 6 C 2 el * + 112 / C 1 el * + 15 C 3 el * 21 C 4 el * + 92 / C 2 el * + 36 C 5 el * 28 C 4 el * + 232 / C 3 el * + 55 C 6 el * 532 / C 4 el * + 45 C 5 el * + 78 C 7 el * 66 C 6 el * + 992 / C 5 el * + 91 C 7 el * 105 C 8 el * + 1612 / C 6 el * + 136 C 9 el * 120 C 8 el * + 2392 / C 7 el * + 91 mat :

C F V FindRoot 1 0.3333 - 0.35 - 0.3214 0.1382 - 0.0418 - 0.1231 0.0746 - 0.0423 - 91 mat

C1 1 0.3333 - 0.35 - 0.3214 0.1382 - 0.0418 - 0.1231 0.0746 - 0.0423 - 91 mat :

C coeff C F V FindRoot :

Q C coeff :

'C' is now replaced by the results and excludes re-using 'C' unless cleared.

Q transpose 1 0.3333 - 0.35 - 0.3214 0.1382 - 0.0418 - 0.1231 0.0746 - 18 mat

Explain the "shadow in the context"

"shadow in the context" is Mathematica 4.0 for unsolved code incompatibility. In this example, 'C' was used above and CAN NOT be re-used for this new set of coefficents. The solver does not allocate the computed coefficients as a result. It replaces the calculated 'C' to itself, thus excluding the solver to re-initialise itself. 'C' must be cleared or otherwise named. Many more instances of "shadow in the context" have been identified in Smath. The Smath Designers didn't envisage the chain construction, otherwise each new re-use would have been coded "new" as a clearing instruction for next "Jo Blo" [TI-58/59 NoOp]. And there is more "persistent shadow in the context" : Observe FindRoot(Q(any),U), FindRoot(Q(JoBlo),U) ...etc. But NOT FindRoot(Q(C),U) ... Unlike Smath, Mathcad is auto-clear as demonstrated by the snippets.

C C Clear :

C 1

'C' register is now cleared of the result above and free to be re-allocated for the next => FindRoot(Q(JoBlo),U)

U C 1 el 1 ≡ C 2 el 1 ≡ C 3 el 1 ≡ C 4 el 1 ≡ C 5 el 1 ≡ C 6 el 1 ≡ C 7 el 1 ≡ C 8 el 1 ≡ C 9 el 1 ≡ 19 mat transpose :

C Q C 1 el 1 - C 2 el 13 / + C 3 el 1 - 10 C 3 el * 15 C 4 el * + 4 C 2 el * + 28 C 5 el * 21 C 4 el * + 7 C 3 el * + 45 C 6 el * 18 C 4 el * + 36 C 5 el * + 66 C 7 el * 55 C 6 el * + 37 C 5 el * + 91 C 8 el * 78 C 7 el * + 64 C 6 el * + 105 C 8 el * 120 C 9 el * + 99 C 7 el * + 91 mat :

JoBlo Q U FindRoot 1 0.3333 - 1 0.5778 - 0.1833 0.0844 0.1731 - 0.089 0.065 91 mat

======== This more natural coding =========

C C Clear :

C 1

Clear does nothing for this simpler code. MUST rename the solver 'λ' or else user.

U λ 1 el 1 ≡ λ 2 el 1 ≡ λ 3 el 1 ≡ λ 4 el 1 ≡ λ 5 el 1 ≡ λ 6 el 1 ≡ λ 7 el 1 ≡ λ 8 el 1 ≡ λ 9 el 1 ≡ 19 mat transpose :

Ω λ 1 el 1 - λ 2 el 13 / + λ 3 el 1 - 10 λ 3 el * 15 λ 4 el * + 4 λ 2 el * + 28 λ 5 el * 21 λ 4 el * + 7 λ 3 el * + 45 λ 6 el * 18 λ 4 el * + 36 λ 5 el * + 66 λ 7 el * 55 λ 6 el * + 37 λ 5 el * + 91 λ 8 el * 78 λ 7 el * + 64 λ 6 el * + 105 λ 8 el * 120 λ 9 el * + 99 λ 7 el * + 91 mat :

Copy/paste to isolate/export Ω U FindRoot 1 0.3333 - 1 0.5778 - 0.1833 0.0844 0.1731 - 0.089 0.065 91 mat

Extract coefficients FrobeniusC2 Ω U FindRoot :

FrobeniusC2 1 0.3333 - 1 0.5778 - 0.1833 0.0844 0.1731 - 0.089 0.065 91 mat