European Research in Mathematics Education I - Fakultät für ...

European Research in Mathematics Education I: Group 2 273
Let us test the function TetrTest(M) with matrix M(regular case) and singular matrix
given directly (lines #3 - #6):
#3: TetrTest(M),
#4: «Tetrahedron is defined»
#5: TetrTest([[1,0,0,0], [0,1,0,0], [0,0,1,0], [1,1,1,0]]) ,
#6: «Tetrahedron isn’t defined»
The auxiliary function System(i) returns the system obtained from the original
system avoiding i th equation. The function TetrVertices returns the vector of vertices of
the tetrahedron defined by the four planes (given by matrix M) in the form [[x=x 1,y=y 1,
z=z 1],..,[x=x 4,y=y 4,z=z 4]].
#7: System(i):=vector((element(M,mod(i+k,4)+1).[x,y,z,1]=0,k,0,2)
#8: TetrVertices(M):=vector(solve(system((i),[x,y,z],i,1,4)
Let us test the function TetrVertices(M):
#9: TetrVertices(M),
#10: [[x=1,y=0,z=0], [x=0,y=1,z=0], [x=0,y=0,z=1], [x=0,y=0,z=0]]
Remark that the way in which the vertices are represented in line #10 not always
suitable (for example if we want to use them in further calculations with Derive).
The function TetrVert below returns the set of vertices of the tetrahedron in the
form of the vector of vectors: [[x 1,y 1,z 1],..,[x 4,y 4,z 4]]. Functions Drop(i,j) and RP(i) are
auxiliary. Function Drop(i,j) as a function of j returns the sequence of integers in which
the number i is dropped. Function RP(i) returns the vector of the right parts of the
system of equations given by the matrix M in which i-th element is dropped.
#11: Drop(i,j):=if(j