This utility ranks Smath to Mathcad/Mathsoft.
1. 1rst & 2nd derivatives ... exact integration.
2. Bonus: Golden ratio, root_Dichotomy.
3. very accurate ∫(f,a,b,n) Romberg kernel.
Enjoy ... Jean

Maths EDU Reconciliation [l_p_c_splines] Copy.sm (96 KiB) downloaded 67 time(s).

... augmented Akima.
Mathcad/Mathsoft is missing Akima ainterp(X,Y,x)
in lieu, we construct ~ Hermite cubic interpolation.

Maths EDU Reconciliation [l_p_c_splines] Copy.sm (103 KiB) downloaded 60 time(s).

... this document illustrates the 3 types cubic splines:
linear, parabolic, cubic for eventual end use.
1. Assume a physical project evaluates @ points.
2. Assume this project has become a STANDARD.
3. Assume it has been populated 'cubic linear'.
4. Assume your Smath project is OK but can't be
made scalar like in [1.]
5. @ this point if you can't populate 'cubic linear'
6. Then, your project does NOT meet the STANDARD.
An example is the Mathcad ODEsolve from linear cubic.
Native Smath can't render from cinterp.
Cheers ... Jean.

Maths EDU Reconciliation [l_p_c_splines] READ FIRST Copy.sm (125 KiB) downloaded 72 time(s).