koeff[1,2]

koeff[1;1]

Polynom

Spline

zweiteAbleitungrechts = 0 (slider from -10 to 10, step 0.1)
A = (-12.953539278731997, 0.9126074842187561)
B = (-6.180162941435439, 2.45936926895747)
C = (1.954892178964583, -0.7240382520965148)
D = (10.317093637048123, 1.868675701129139)
E = (19.268937505637556, 1.986526335366668)
zweiteAbleitunglinks = 0 (slider from -10 to 10, step 0.1)
MatA: {{x(A)^(3.0), x(A)^(2.0), x(A), 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {x(B)^(3.0), x(B)^(2.0), x(B), 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, x(B)^(3.0), x(B)^(2.0), x(B), 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, x(C)^(3.0), x(C)^(2.0), x(C), 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, x(C)^(3.0), x(C)^(2.0), x(C), 1.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, x(D)^(3.0), x(D)^(2.0), x(D), 1.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, x(D)^(3.0), x(D)^(2.0), x(D), 1.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, x(E)^(3.0), x(E)^(2.0), x(E), 1.0}, {3.0 * x(B)^(2.0), 2.0 * x(B), 1.0, 0.0, -3.0 * x(B)^(2.0), -2.0 * x(B), -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 3.0 * x(C)^(2.0), 2.0 * x(C), 1.0, 0.0, -3.0 * x(C)^(2.0), -2.0 * x(C), -1.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.0 * x(D)^(2.0), 2.0 * x(D), 1.0, 0.0, -3.0 * x(D)^(2.0), -2.0 * x(D), -1.0, 0.0}, {6.0 * x(B), 2.0, 0.0, 0.0, -6.0 * x(B), -2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 6.0 * x(C), 2.0, 0.0, 0.0, -6.0 * x(C), -2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.0 * x(D), 2.0, 0.0, 0.0, -6.0 * x(D), -2.0, 0.0, 0.0}, {6.0 * x(A), 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 6.0 * x(E), 2.0, 0.0, 0.0}}
MatAInv = Invert(MatA)
v: {{y(A)}, {y(B)}, {y(B)}, {y(C)}, {y(C)}, {y(D)}, {y(D)}, {y(E)}, {0.0}, {0.0}, {0.0}, {0.0}, {0.0}, {0.0}, {zweiteAbleitunglinks}, {zweiteAbleitungrechts}}
koeff: MatAInv * v
A1 = Element(koeff, 1.0)
a1 = Element(Element[koeff, 1.0], 1.0)
b1 = Element(Element[koeff, 2.0], 1.0)
c1 = Element(Element[koeff, 3.0], 1.0)
d1 = Element(Element[koeff, 4.0], 1.0)
a2 = Element(Element[koeff, 5.0], 1.0)
b2 = Element(Element[koeff, 6.0], 1.0)
c2 = Element(Element[koeff, 7.0], 1.0)
d2 = Element(Element[koeff, 8.0], 1.0)
a3 = Element(Element[koeff, 9.0], 1.0)
b3 = Element(Element[koeff, 10.0], 1.0)
c3 = Element(Element[koeff, 11.0], 1.0)
d3 = Element(Element[koeff, 12.0], 1.0)
a4 = Element(Element[koeff, 13.0], 1.0)
b4 = Element(Element[koeff, 14.0], 1.0)
c4 = Element(Element[koeff, 15.0], 1.0)
d4 = Element(Element[koeff, 16.0], 1.0)
sp1 = Function(a1 * x^(3.0) + b1 * x^(2.0) + c1 * x + d1, x(A), x(B))
sp2 = Function(a2 * x^(3.0) + b2 * x^(2.0) + c2 * x + d2, x(B), x(C))
sp3 = Function(a3 * x^(3.0) + b3 * x^(2.0) + c3 * x + d3, x(C), x(D))
sp4 = Function(a4 * x^(3.0) + b4 * x^(2.0) + c4 * x + d4, x(D), x(E))
MatP: {{x(A)^(4.0), x(A)^(3.0), x(A)^(2.0), x(A), 1.0}, {x(B)^(4.0), x(B)^(3.0), x(B)^(2.0), x(B), 1.0}, {x(C)^(4.0), x(C)^(3.0), x(C)^(2.0), x(C), 1.0}, {x(D)^(4.0), x(D)^(3.0), x(D)^(2.0), x(D), 1.0}, {x(E)^(4.0), x(E)^(3.0), x(E)^(2.0), x(E), 1.0}}
vPoly: {{y(A)}, {y(B)}, {y(C)}, {y(D)}, {y(E)}}
MatPInv = Invert(MatP)
koeffP: MatPInv * vPoly
f = Polynomial({A, B, C, D, E})
g = Function(f(x), x(A), x(E))
a = false
b = true