Computermathematik2_1

def gauss(A,a=0,b=0): p=min([p for p in [a,..,A.nrows()-1] if A[p][b]!=0]) #pivot !=0 A.swap_rows(a,p); A.rescale_row(a,1/A[a][b]) #<-transpose and rescale, add other row: [A.add_multiple_of_row(c,a,-A[c][b]/A[a][b]) for c in [0,..,A.nrows()-1] if c!=a] return gauss(A,a+1,b+1) if a+1<A.nrows() else A @interact def main(A=matrix(QQ,[[1,3,-2,1],[2,6,1,4],[-1,2,3,-4]])): pretty_print(gauss(A)) main() 

def invert(A): if A.is_invertible(): #add identity and use gauss E=matrix([list(A[x])+[N(x==y) for y in [0,..,A.nrows()-1]] for x in [0,..,A.nrows()-1]]) return matrix([list(x[E.nrows():E.ncols()]) for x in gauss(E)]) @interact def main(A=matrix(QQ,[[1,3,-2,1],[2,6,1,4],[-1,2,3,-4]])): pretty_print(invert(A)) main() 

var('j') def laplace(A,i=0,j=0): if A.ncols()==1: return A[0][0] return sum([(-1)^(i+j)*A[i][j]*laplace( matrix([[A[x if x<i else x+1][y if y<j else y+1] for x in [0,..,A.nrows()-2]] for y in [0,..,A.ncols()-2]]) ) for i in [0,..,A.ncols()-1]]) @interact def main(A=matrix([[1,2,3],[2,3,1],[1,3,2]])): print "determinant: ",laplace(A) main() 

var('a') @interact def main(A=matrix([[2,1,2,1],[3,a,1,3],[4,1,1-a,a+4]])): result=gauss(A) pretty_print(A); print("\nnot solveable for:\n") pretty_print(list(set([str(solve(1/result[i][A.ncols()-1]==0,a)).replace("\n","") for i in [0,..,A.nrows()-1]]))) main()