# Question:How to obtain a symbolic set of solutions containing an interpolate function?

## Question:How to obtain a symbolic set of solutions containing an interpolate function?

Maple 17

Hello Maple-Primers!

I am trying to evaluate a system at many different points.  I would like to include an interpolation function in this system, but have thusfar been unsuccessful.

Usually, I solve a system symbolically by using eliminate and unapply:

eq[1] := A = M^3;
eq[2] := C = A*2;
eq[3] := D = N+3;
eq[4] := B = piecewise(A = 0, 0,C);
eq[5] := E = B*D;
elimsol:=eliminate(convert(eq,list),[A,B,C,D,E])[1];

unappsol:=unapply(elimsol,[N,M]);

unappsol(1,2);
{A = 8, B = 16, C = 16, D = 4, E = 64} <--- great!

Now, I want to include an interpolation function in the system of equations.  They look like this (see worksheet for actual interpolation function):

B_interp := (W,T) -> CurveFitting:-ArrayInterpolation([FC_Map_W,FC_Map_T],FC_Map,Array(1 .. 1, 1 .. 1, 1 .. 2, [[[W, T]]]),method=linear);

eq[5] := E = B_interp(N,M);

Error, (in CurveFitting:-ArrayInterpolation) invalid input: coordinates of xvalues must be of type numeric <-- bad!

Anyone have any ideas?  I've tried to use polynomials, but I can't seem to get a fit close enough for my purposes.

Maple_2D_Interpolate_FC.mw

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