> 
> with(linalg):
> W:=matrix(20,20,[[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
> [1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
> [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0,0,0,0,0],
> [1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
> [1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0],
> [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
> [1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0,0,0],
> [1,1/2,0,0,0,0,0,0,1/4,0,0,0,0,0,0,0,0,0,0,0],
> [1,1,1/2,0,1/2,0,0,0,1,1/4,0,1/2,0,1/4,0,0,0,0,0,0],
> [1,1/2,1,0,1/2,0,0,0,1/4,1,0,1/4,0,1/2,0,0,0,0,0,0],
> [1,0,1/2,0,0,0,0,0,0,1/4,0,0,0,0,0,0,0,0,0,0],
> [1,0,0,1/2,0,0,0,0,0,0,1/4,0,0,0,0,0,0,0,0,0],
> [1,1,0,1/2,0,0,1/2,0,1,0,1/4,0,1/2,0,0,1/4,0,0,0,0],
> [1,1,1,1/2,1,1/2,1/2,1/2,1,1,1/4,1,1/2,1,1/2,1/4,1/4,1/2,1/2,1/4],
> [1,0,1,1/2,0,1/2,0,0,0,1,1/4,0,0,0,1/2,0,1/4,0,0,0],
> [1,1/2,0,1,0,0,1/2,0,1/4,0,1,0,1/4,0,0,1/2,0,0,0,0],
> [1,1,1/2,1,1/2,1/2,1,1/2,1,1/4,1,1/2,1,1/4,1/4,1,1/2,1/2,1/4,1/2],
> [1,1/2,1,1,1/2,1,1/2,1/2,1/4,1,1,1/4,1/4,1/2,1,1/2,1,1/4,1/2,1/2],
> [1,0,1/2,1,0,1/2,0,0,0,1/4,1,0,0,0,1/4,0,1/2,0,0,0]]):
> 
> Inverse:=inverse(%):
> w:=matrix(1,20,[x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[9],x[10],x[1
> 1],x[12],x[13],x[14],x[15],x[16],x[17],x[18],x[19],x[20]]):
> y:=matrix(1,20,[a[1],a[2],a[3],a[4],a[5],a[6],a[7],a[8],a[9],a[10],a[1
> 1],a[12],a[13],a[14],a[15],a[16],a[17],a[18],a[19],a[20]]):
> Y:=transpose(linsolve(W,transpose(w))):
> X:=matrix(1,20,[1,xi,eta,zeta,xi*eta,eta*zeta,zeta*xi,xi*eta*zeta,
> xi^2,eta^2,zeta^2,xi^2*eta,xi^2*zeta,eta^2*xi,eta^2*zeta,zeta^2*xi,zet
> a^2*eta,xi^2*eta*zeta,eta^2*zeta*xi,zeta^2*xi*eta]):
> Formfunktionen:=multiply(transpose(Inverse),transpose(X)):
> N:=matrix(map(factor,%));

  N :=

        [(-1 + zeta) (-1 + eta) (-1 + xi) (2 xi + 2 eta + 2 zeta - 1)

        ]

        [xi (-1 + zeta) (-1 + eta) (-2 eta - 2 zeta - 1 + 2 xi)]

        [-xi eta (-1 + zeta) (2 eta - 2 zeta - 3 + 2 xi)]

        [-eta (-1 + zeta) (-1 + xi) (2 xi + 2 zeta - 2 eta + 1)]

        [-zeta (-1 + eta) (-1 + xi) (2 xi + 2 eta - 2 zeta + 1)]

        [-xi zeta (-1 + eta) (-2 eta + 2 zeta - 3 + 2 xi)]

        [xi eta zeta (2 eta + 2 zeta - 5 + 2 xi)]

        [eta zeta (-1 + xi) (2 xi - 2 zeta + 3 - 2 eta)]

        [-4 xi (-1 + zeta) (-1 + eta) (-1 + xi)]

        [4 xi eta (-1 + zeta) (-1 + eta)]

        [4 xi eta (-1 + zeta) (-1 + xi)]

        [-4 eta (-1 + zeta) (-1 + eta) (-1 + xi)]

        [-4 zeta (-1 + zeta) (-1 + eta) (-1 + xi)]

        [4 xi zeta (-1 + zeta) (-1 + eta)]

        [-4 xi eta zeta (-1 + zeta)]

        [4 eta zeta (-1 + zeta) (-1 + xi)]

        [4 xi zeta (-1 + eta) (-1 + xi)]

        [-4 xi eta zeta (-1 + eta)]

        [-4 xi eta zeta (-1 + xi)]

        [4 eta zeta (-1 + eta) (-1 + xi)]

> 
> 
