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 KiB) downloaded 97 time(s).

... 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 KiB) downloaded 73 time(s).

some automation .







Best regards
Carlos

ortogonal_Jean_CBG.sm (9 KiB) downloaded 64 time(s).

A small improvement.

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




Best Regards

Carlos.


ortogonal_Jean_CBG_R2.sm (13 KiB) downloaded 66 time(s).

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 KiB) downloaded 62 time(s).

... 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 KiB) downloaded 67 time(s).

Jean,

A small simplification in the manual part.


Best regards.

Carlos.

PolyOrtho [Gram-Schmidt, Reconciliation]_JEAN_CBG.sm (53 KiB) downloaded 82 time(s).

Thanks, Carlos.

Jean