The latest Maxima 5.34.1 does not have numeric/interpol : tht's the first problem for all viewers.
Maxima cspline is an horrible monkey business probably incompatible with Smath, WHY ?
On the first count: Smath is not a 'scalar' system, only discrete.
Thus it might be impossible to built a scalar cspline that can be assigned as a function
as a function analytical up to the 2nd order derivative.
On the 2nd count: the former Maxima cspline is archaic in the displaying the segments,
just figure splining a data set of small 50 pairs. Again not exportable.
More confusing: Smath f(x) has linterp, ainterp [Akima spline], cinterp
these 3 are LOCAL interpolating functions, i.e: nothing else to do with
except populate data set for export.
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The Lagrange interpolation is totally useless. From a data set of length 'n' you can get
an nth order polynomial that will do exactly what your Lagrange interpolation does.
If your data set is like noisy or not so regular [they are always noisy or not very regular
from experimental sampling], the the polynomial fit can be or les order than the 'n' data.
Thus you benefit some smoothing. The polynomial fit need not be of integer monomials
x, x^2, x^3 ... the x's may be of decimal exponents, it may help the fit.
Polynomial fit is just few line of Smath simple coding.
A much, much, much more powerful fitter is the Padé rational fraction, in Mathcad 11, it works
by clicking the fingers. BTW, all [if not all] approximation of functions in computers
are Padé rational fractions [collected in Hart et al.]
jmgiraud@bell.net