  
  [1X9 [33X[0;0YSparse Chain complexes[133X[101X
  
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseMat(A)[110X[133X
  
  [33X[0;0YInputs a matrix [22XA[122X and returns the matrix in sparse format.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XTransposeOfSparseMat(A)[110X[133X
  
  [33X[0;0YInputs a sparse matrix [22XA[122X and returns its transpose sparse format.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XReverseSparseMat(A)[110X[133X
  
  [33X[0;0YInputs  a  sparse  matrix  [22XA[122X  and  modifies it by reversing the order of the
  columns. This function modifies [22XA[122X and returns no value.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseRowMult(A,i,k)[110X[133X
  
  [33X[0;0YMultiplies  the  i-th  row of a sparse matrix [22XA[122X by [22Xk[122X. The sparse matrix [22XA[122X is
  modified but nothing is returned.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseRowInterchange(A,i,k)[110X[133X
  
  [33X[0;0YInterchanges  the  i-th  and j-th rows of a sparse matrix [22XA[122X by [22Xk[122X. The sparse
  matrix [22XA[122X is modified but nothing is returned.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseRowAdd(A,i,j,k)[110X[133X
  
  [33X[0;0YAdds  [22Xk[122X  times the j-th row to the i-th row of a sparse matrix [22XA[122X. The sparse
  matrix [22XA[122X is modified but nothing is returned.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseSemiEchelon(A)[110X[133X
  
  [33X[0;0YConverts a sparse matrix [22XA[122X to semi-echelon form (which means echelon form up
  to  a  permutation  of rows). The sparse matrix [22XA[122X is modified but nothing is
  returned.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XRankMatDestructive(A)[110X[133X
  
  [33X[0;0YReturns  the  rank  of  a  sparse  matrix [22XA[122X. The sparse matrix [22XA[122X is modified
  during the calculation.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XRankMat(A)[110X[133X
  
  [33X[0;0YReturns the rank of a sparse matrix [22XA[122X.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseChainComplex(Y)[110X[133X
  
  [33X[0;0YInputs  a  regular  CW-complex [22XY[122X and returns a sparse chain complex which is
  chain  homotopy  equivalent to the cellular chain complex of [22XY[122X. The function
  uses discrete vector fields to calculate a smallish chain complex.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseChainComplexOfRegularCWComplex(Y)[110X[133X
  
  [33X[0;0YInputs  a  regular  CW-complex [22XY[122X and returns its cellular chain complex as a
  sparse chain complex. The function SparseChainComplex(Y) will usually return
  a smaller chain complex.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XSparseBoundaryMatrix(C,n)[110X[133X
  
  [33X[0;0YInputs  a  sparse  chain  complex [22XC[122X and integer [22Xn[122X. Returns the n-th boundary
  matrix of the chain complex in sparse format.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XBettinumbers(C,n)[110X[133X
  
  [33X[0;0YInputs a sparse chain complex [22XC[122X and integer [22Xn[122X. Returns the n-th Netti number
  of the chain complex.[133X
  
