Not as clean as Mathcad, but can be done terms by terms.
Smath 5346 does not recognise the dot product integration.
I might have missed some coding for solving algo style.

Jean

Symbolic Gram-Schmidt.sm (109,26 KiB) scaricato 1575 volta(e).

... read more in the attached Smath document. Work sheet renamed
for easier retrieval. Though Mathcad 8/11 is the champion for creating
orthogonal polynomials, Smath will do as well with a bit more sweat !
The summarised application is inductive of what it can do for you.
More can be done ... assume you have a noisy data set and the project
requires a trigonometric fit. It would be easy to fit a Fourier polynomial
sin/cos function cleaned of noise. This is not offered in the work sheet.

Maybe collabs will find a way to instruct Smath accept the "dot integrator",
something that wiil result "Mathcad style", usefull for next Smath release.

Jean

PolyOrtho [Gram-Schmidt].sm (132,05 KiB) scaricato 1364 volta(e).

some automation .







Best regards
Carlos

ortogonal_Jean_CBG.sm (9,45 KiB) scaricato 1570 volta(e).

A small improvement.

I correct , because the " dot " function does not work correctly




Best Regards

Carlos.


ortogonal_Jean_CBG_R2.sm (13,77 KiB) scaricato 1556 volta(e).

Thanks, Carlos: Your 2nd version is OK.
Still, can't export the reduced components in visible form.
Will work again tonight.

Cheers, Jean

Carlos,

Thanks again for your contribution. This "Reconciliation" is made a bit more
function style. Very interesting that Smath can build "kernel algo" like
Mathcad 8/11 [discovered after years !]. The symbolic expansion is not
convenient at all. Maple is not good companion in there ...
... thus PART 2 in the attached.

Jean

PolyOrtho [Gram-Schmidt, RECONCILIATION].sm (54,25 KiB) scaricato 1418 volta(e).

... final reconciliation ...
ASSUME:
1. The 'o' "Kernel algo" can build from any vector functions f(x).
2. That naturally the roots exist and can be found.
3. Then the 15 decimals Lagrange is adequate for applications.

Project done, nothng to be envious of Mathcad, just different.

Successful collaboration

Jean

PolyOrtho [Gram-Schmidt, Reconciliation].sm (61,57 KiB) scaricato 1354 volta(e).

Jean,

A small simplification in the manual part.


Best regards.

Carlos.

PolyOrtho [Gram-Schmidt, Reconciliation]_JEAN_CBG.sm (53,07 KiB) scaricato 1412 volta(e).

Thanks, Carlos.

Jean