  
  [1X10 [33X[0;0YSparse Chain complexes[133X[101X
  
  
  [1X10.1 [33X[0;0Y [133X[101X
  
  [1X10.1-1 SparseMat[101X
  
  [33X[1;0Y[29X[2XSparseMat[102X( [3XA[103X ) [32X function[133X
  
  [33X[0;0YInputs a matrix [22XA[122X and returns the matrix in sparse format.[133X
  
  [33X[0;0Y[12XExamples:[112X 1 ([7X../tutorial/chap10.html[107X) [133X
  
  [1X10.1-2 TransposeOfSparseMat[101X
  
  [33X[1;0Y[29X[2XTransposeOfSparseMat[102X( [3XA[103X ) [32X function[133X
  
  [33X[0;0YInputs a sparse matrix [22XA[122X and returns its transpose sparse format.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X10.1-3 ReverseSparseMat[101X
  
  [33X[1;0Y[29X[2XReverseSparseMat[102X( [3XA[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-4 SparseRowMult[101X
  
  [33X[1;0Y[29X[2XSparseRowMult[102X( [3XA[103X, [3Xi[103X, [3Xk[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-5 SparseRowInterchange[101X
  
  [33X[1;0Y[29X[2XSparseRowInterchange[102X( [3XA[103X, [3Xi[103X, [3Xk[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-6 SparseRowAdd[101X
  
  [33X[1;0Y[29X[2XSparseRowAdd[102X( [3XA[103X, [3Xi[103X, [3Xj[103X, [3Xk[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-7 SparseSemiEchelon[101X
  
  [33X[1;0Y[29X[2XSparseSemiEchelon[102X( [3XA[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-8 RankMatDestructive[101X
  
  [33X[1;0Y[29X[2XRankMatDestructive[102X( [3XA[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-9 RankMat[101X
  
  [33X[1;0Y[29X[2XRankMat[102X( [3XA[103X ) [32X function[133X
  
  [33X[0;0YReturns the rank of a sparse matrix [22XA[122X.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X10.1-10 SparseChainComplex[101X
  
  [33X[1;0Y[29X[2XSparseChainComplex[102X( [3XY[103X ) [32X function[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[12XExamples:[112X             1             ([7X../tutorial/chap10.html[107X) ,            2
  ([7X../www/SideLinks/About/aboutPersistent.html[107X) [133X
  
  [1X10.1-11 SparseChainComplexOfRegularCWComplex[101X
  
  [33X[1;0Y[29X[2XSparseChainComplexOfRegularCWComplex[102X( [3XY[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-12 SparseBoundaryMatrix[101X
  
  [33X[1;0Y[29X[2XSparseBoundaryMatrix[102X( [3XC[103X, [3Xn[103X ) [32X function[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[12XExamples:[112X[133X
  
  [1X10.1-13 Bettinumbers[101X
  
  [33X[1;0Y[29X[2XBettinumbers[102X( [3XC[103X, [3Xn[103X ) [32X function[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
  
  [33X[0;0Y[12XExamples:[112X       1       ([7X../www/SideLinks/About/aboutMetrics.html[107X) ,       2
  ([7X../www/SideLinks/About/aboutTDA.html[107X) [133X
  
