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NoetherianOperators :: InterpolatedDiffOp

InterpolatedDiffOp -- differential operator with interpolated coefficients

Description

A type of DiffOp returned by interpolation based methods, such as numericalNoetherianOperators. Because of this, users are not expected to create instances of this type.

If the interpolation of any coefficient fails, the numerator and denominator will be replaced by the string "?".

Assuming the interpolation was successful, the method evaluate(InterpolatedDiffOp,Point) will convert an InterpolatedDiffOp to a specialized differential operators of type DiffOp by evaluating each numerator and denominator at a point.

i1 : R = CC[x,y]

o1 = R

o1 : PolynomialRing
i2 : D = new InterpolatedDiffOp from {x => (x+y, pi*ii*x^2*y), y => (x, 1.3_R)}

          x + y           x
o2 = --------------*dx + ---*dy
                 2       1.3
     3.14159*ii*x y

o2 : InterpolatedDiffOp
i3 : D' = evaluate(D, point{{1.2, 2+ii}})

o3 = (- .0530516 - .327152*ii)dx + .923077*dy

o3 : DiffOp

See also

Methods that use an object of class InterpolatedDiffOp :

For the programmer

The object InterpolatedDiffOp is a type, with ancestor classes DiffOp < HashTable < Thing.