h$լ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     !Gaussian elimination subroutines.(c) Nils Alex, 2020MITnils.alex@fau.deNone?@* safe-tensor8Returns the pivot columns of an upper triangular matrix.  let mat = (3 >< 4) [1, 0, 2, -3, 0, 0, 1, 0, 0, 0, 0, 0]  mat (3><4) [ 1.0, 0.0, 2.0, -3.0 , 0.0, 0.0, 1.0, 0.0 , 0.0, 0.0, 0.0, 0.0 ]  pivotsU mat [0,2]  safe-tensorFind pivot element below position (i, j) with greatest absolute value in the ST monad. safe-tensor.Gaussian elimination perfomed in-place in the  monad. safe-tensorGaussian elimination as pure function. Involves a copy of the input matrix.  let mat = (3 >< 4) [1, 1, -2, 0, 0, 2, -6, -4, 3, 0, 3, 1]  mat (3><4) [ 1.0, 1.0, -2.0, 0.0 , 0.0, 2.0, -6.0, -4.0 , 3.0, 0.0, 3.0, 1.0 ]  gaussian mat (3><4) [ 3.0, 0.0, 3.0, 1.0 , 0.0, 2.0, -6.0, -4.0 , 0.0, 0.0, 0.0, 1.6666666666666667 ]  safe-tensorReturns the indices of a maximal linearly independent subset of the columns in the matrix.  let mat = (3 >< 4) [1, 1, -2, 0, 0, 2, -6, -4, 3, 0, 3, 1]  mat (3><4) [ 1.0, 1.0, -2.0, 0.0 , 0.0, 2.0, -6.0, -4.0 , 3.0, 0.0, 3.0, 1.0 ]  independentColumns mat [0,1,3]  safe-tensorReturns a sub matrix containing a maximal linearly independent subset of the columns in the matrix.  let mat = (3 >< 4) [1, 1, -2, 0, 0, 2, -6, -4, 3, 0, 3, 1]  mat (3><4) [ 1.0, 1.0, -2.0, 0.0 , 0.0, 2.0, -6.0, -4.0 , 3.0, 0.0, 3.0, 1.0 ]  independentColumnsMat mat (3><3) [ 1.0, 1.0, 0.0 , 0.0, 2.0, -4.0 , 3.0, 0.0, 1.0 ] (Scalar types for usage as Tensor values.(c) Nils Alex, 2020MITnils.alex@fau.deSafe8:D  safe-tensorPolynomial: Can be constant, affine, or something of higher rank which is not yet implemented. safe-tensorconstant value safe-tensorconstant value plus linear term safe-tensor higher rank safe-tensorLinear combination represented as mapping from variable number to prefactor. safe-tensorProduces an affine value c + a\cdot x_i safe-tensor Maps over  safe-tensor;Returns list of variable numbers present in the polynomial. safe-tensor>Shifts variable numbers in the polynomial by a constant value. safe-tensorNormalizes a polynomial:  \mathrm{normalize}(c) = 1 \\ \mathrm{normalize}(c + a_1\cdot x_1 + a_2\cdot x_2 + \dots + a_n\cdot x_n) = \frac{c}{a_1} + 1\cdot x_1 + \frac{a_2}{a_1}\cdot x_2 + \dots + \frac{a_n}{a_1}\cdot x_n  safe-tensorconstant safe-tensorvariable number safe-tensor prefactor  3Type families and singletons for generalized types.(c) Nils Alex, 2020MITnils.alex@fau.deNone '(./0289:>?E`   !"#$%&'()*+,;:-/.0213456879<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ ()*+,;:-/.0213456879 < =@ ?> CE HI K N P LR OQM TS UV W Y Z X gpsx{Aed}vuz|wynmrtoqlk~ij G F D B  J  h^`_ []\fcba  !$#%&   "' ,Type level equalities for generalized ranks.(c) Nils Alex, 2020MITnils.alex@fau.deNone'(./>?h safe-tensorThe  of a sane rank type is sane. safe-tensorIf a rank type has a  instance, the tail has a  instance. safe-tensor8Successfully merging two sane rank types (result is not Nothing) yields a sane rank type. safe-tensor.If two rank types can be merged and the first +0 of the first rank type is less than the first + of the second rank type, the  of the merged rank type is equal to the tail of the first rank type merged with the second rank type. safe-tensor.If two rank types can be merged and the first +2 of the first rank type coincides with the first + of the second rank type, the first index of the first rank type cannot equal the first index of the second rank type. safe-tensor.If two rank types can be merged and the first +2 of the first rank type coincides with the first + of the second rank type and the first index of the first rank type compares less than the first index of the second rank type, the  of the merged rank type is equal to the tail of the first rank type merged with the second rank type. safe-tensor.If two rank types can be merged and the first +3 of the first rank type is greater than the first + of the second rank type, the  of the merged rank type is equal to the first rank type merged with the tail of the second rank type. safe-tensor.If two rank types can be merged and the first +2 of the first rank type coincides with the first + of the second rank type and the first index of the first rank type compares greater than the first index of the second rank type, the  of the merged rank type is equal to the first rank type merged with the tail of the second rank type. safe-tensor5If a rank type is sane, its contraction is also sane. safe-tensor>The contraction of the empty rank type is the empty rank type. safe-tensorIf the first two labels of a rank type cannot be contracted because they belong to different +s, the  of the contracted rank type is equal to the contraction of the  of the rank type. safe-tensorIf the first two labels of a rank type cannot be contracted because the first label is covariant, the  of the contracted rank type is equal to the contraction of the  of the rank type. safe-tensorIf the first two labels of a rank type cannot be contracted because the second label is covariant, the  of the contracted rank type is equal to the contraction of the  of the rank type. safe-tensorIf the first two labels of a rank type cannot be contracted because they differ, the  of the contracted rank type is equal to the contraction of the  of the rank type. safe-tensorIf the first two labels of a rank type can be contracted, the contracted rank type is equal to the contraction of the tail.&Template Haskell for Math.Tensor.Basic(c) Nils Alex, 2020MITnils.alex@fau.deNone '(./029>?iPLength-typed vector.(c) Nils Alex, 2020MITnils.alex@fau.deNone'(/2o!Dependently typed tensor algebra.(c) Nils Alex, 2020MITnils.alex@fau.deNone'(./2>?x  safe-tensorThe , type parameterized by its generalized rank r and arbitrary value type v. safe-tensorGiven a  and  instance, remove all zero values from the tensor, eventually replacing a zero Scalar or an empty Tensor with  ZeroTensor. safe-tensorTensor addition. Generalized ranks of summands and sum coincide. Zero values are removed from the result. safe-tensorTensor subtraction. Generalized ranks of operands and difference coincide. Zero values are removed from the result. safe-tensor(Tensor multiplication. Generalized anks r, r' of factors must not overlap. The product rank is the merged rank  r r' of the factor ranks. safe-tensorTensor contraction. Contracting a tensor is the identity function on non-contractible tensors. Otherwise, the result is the contracted tensor with the contracted labels removed from the generalized rank. safe-tensorTensor transposition. Given a vector space and two index labels, the result is a tensor with the corresponding entries swapped. Only possible if the indices are part of the rank. The generalized rank remains untouched. safe-tensorTransposition of multiple labels. Given a vector space and a transposition rule, the result is a tensor with the corresponding entries swapped. Only possible if the indices are part of the generalized rank. The generalized rank remains untouched. safe-tensorTensor relabelling. Given a vector space and a relabelling rule, the result is a tensor with the resulting generalized rank after relabelling. Only possible if labels to be renamed are part of the generalized rank and if uniqueness of labels after relabelling is preserved. safe-tensorGet assocs list from +. Keys are length-typed vectors of indices. safe-tensor Construct  from assocs list. Keys are length-typed vectors of indices. Generalized rank is passed explicitly as singleton. safe-tensor Construct < from assocs list. Keys are length-typed vectors of indices.. (*)+,:;-./0312456789.+,:;031245 -./6789(*)6676Existentially quantified wrapper for Math.Tensor.Safe.(c) Nils Alex, 2020MITnils.alex@fau.deNone'(./2>? safe-tensor/The unrefined type of generalized tensor ranks.   5 ~ 4   ~ [(+  , 0 )] safe-tensor!The unrefined type of dimensions.  Demote Nat ~  safe-tensorThe unrefined type of labels.  Demote Symbol ~  safe-tensor wraps around ! and exposes only the value type v. safe-tensor of given value. Result is pure because there is only one possible rank: '[] safe-tensor of given rank r. Throws an error if  r ~ '. safe-tensor=Pure function removing all zeros from a tensor. Wraps around . safe-tensor8Tensor product. Throws an error if ranks overlap, i.e.  r1 r2 ~ '. Wraps around . safe-tensor"Scalar multiplication of a tensor. safe-tensorTensor addition. Throws an error if summand ranks do not coincide. Wraps around . safe-tensorTensor subtraction. Throws an error if summand ranks do not coincide. Wraps around . safe-tensorTensor contraction. Pure function, because a tensor of any rank can be contracted. Wraps around . safe-tensorTensor transposition. Throws an error if given indices cannot be transposed. Wraps around . safe-tensorTransposition of multiple indices. Throws an error if given indices cannot be transposed. Wraps around . safe-tensorRelabelling of tensor indices. Throws an error if given relabellings are not allowed. Wraps around . safe-tensorHidden rank over which % quantifies. Possible because of the  r constraint. safe-tensorAssocs list of the tensor. safe-tensorConstructs a tensor from a rank and an assocs list. Throws an error for illegal ranks or incompatible assocs lists. safe-tensorContravariant rank from vector space label, vector space dimension, and list of index labels. Throws an error for illegal ranks. safe-tensorCovariant rank from vector space label, vector space dimension, and list of index labels. Throws an error for illegal ranks. safe-tensorMixed rank from vector space label, vector space dimension, and lists of index labels. Throws an error for illegal ranks.776 Linear tensor equations.(c) Nils Alex, 2020MITnils.alex@fau.deNone@ safe-tensorThe solution to a linear system is represented as a list of substitution rules, stored as  ( ). safe-tensorA linear equation is a mapping from variable indices to coefficients safe-tensorExtract linear equations from tensor components. The equations are normalized, sorted, and made unique. safe-tensorExtract linear equation with integral coefficients from polynomial tensor component with rational coefficients. Made made integral by multiplying with the lcm of all denominators. safe-tensorConvert list of equations to sparse matrix representation of the linear system. safe-tensorConvert list of equations to dense matrix representation of the linear system. safe-tensorExtract sparse matrix representation for the linear system given by a list of existentially quantified tensors with polynomial values. safe-tensorExtract dense matrix representation for the linear system given by a list of existentially quantified tensors with polynomial values. safe-tensorRank of the linear system given by a list of existentially quantified tensors with polynomial values. safe-tensorRead substitution rules from reduced row echelon form of a linear system. safe-tensorRead single substitution rule from single row of reduced row echelon form. safe-tensor-Apply substitution rules to tensor component. safe-tensor7Apply substitution rules to all components of a tensor. safe-tensorSolve a linear system and apply solution to the tensorial indeterminants. safe-tensorRelabelling of the indeterminants present in a list of tensors. Redefines the labels of n indeterminants as [1..n]!, preserving the previous order. safe-tensorTensorial linear system safe-tensorList of indeterminant tensors safe-tensorSolved indeterminant tensors$Linear algebra for tensor equations.(c) Nils Alex, 2020MITnils.alex@fau.deNone (Definitions of epsilon tensor densities.(c) Nils Alex, 2020MITnils.alex@fau.deNone '(./>? safe-tensorSign of a permutation: / permSign [1,2,3] = 1 permSign [2,1,3] = -1  safe-tensorTotally antisymmetric covariant tensor density of weight -1 such that \epsilon_{12\dots n} = 1. Vector space label, vector space dimension and index labels are passed as singletons. safe-tensorTotally antisymmetric contravariant tensor density of weight +1 such that \epsilon^{12\dots n} = 1. Vector space label, vector space dimension and index labels are passed as singletons. safe-tensorTotally antisymmetric covariant tensor density of weight -1 such that \epsilon_{12\dots n} = 1. Vector space label, vector space dimension and index labels are passed as values. Result is existentially quantified. safe-tensorTotally antisymmetric contravariant tensor density of weight +1 such that \epsilon^{12\dots n} = 1. Vector space label, vector space dimension and index labels are passed as values. Result is existentially quantified.  Definitions of Kronecker deltas.(c) Nils Alex, 2020MITnils.alex@fau.deNone'(./>? safe-tensorThe Kronecker delta \delta^a_{\hphantom ab}  for a given + id n! with contravariant index label a and covariant index label b<. Labels and dimension are passed explicitly as singletons. safe-tensorThe Kronecker delta \delta^a_{\hphantom ab}  for a given + id n! with contravariant index label a and covariant index label b. safe-tensorThe Kronecker delta \delta^a_{\hphantom ab}  for a given + id n! with contravariant index label a and covariant index label b. Labels and dimension are passed as values. Result is existentially quantified. !Definitions of symmetric tensors.(c) Nils Alex, 2020MITnils.alex@fau.deNone '(./>? &Definitions of area-symmetric tensors.(c) Nils Alex, 2020MITnils.alex@fau.deNone '(./>?Definitions of basic tensors.(c) Nils Alex, 2020MITnils.alex@fau.deNone14 Safe-Inferred !"#$%&'()*+,-./0123456789:;<=>?@@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     *safe-tensor-0.2.1.1-HV6XtoU04VwKCpzbN3KLoQMath.Tensor.Safe.THMath.Tensor.Basic.TH Math.Tensor.LinearAlgebra.Matrix Math.Tensor.LinearAlgebra.ScalarMath.Tensor.Safe.ProofsMath.Tensor.Safe.VectorMath.Tensor.Safe Math.Tensor#Math.Tensor.LinearAlgebra.EquationsMath.Tensor.Basic.EpsilonMath.Tensor.Basic.DeltaMath.Tensor.Basic.Sym2Math.Tensor.Basic.Area GHC.NaturalNatural Data.TextTextMath.Tensor.LinearAlgebraMath.Tensor.BasicPaths_safe_tensorrelabelTranspositions' zipConCov relabelNEtranspositions'elemNEcanTransposeConcanTransposeCov canTransposesubsetNEprepICovprepICon contractI contractRmergemergeNEmergeILmergeRtailRheadR removeUntillengthNElengthILlengthR isLengthNE isAscending isAscendingNE isAscendingIsane relabelIL' relabelILrelabelRrelabelTranspositions saneTransRulesaneRelabelRule ixComparezipConzipCovtranspositionscanTransposeMultfromNatNZSVSpaceIxIConICovIListConCovCovConGRankRank TransRuleTransConTransCov RelabelRulevIdvDimLambda_6989586621679095928Case_6989586621679095955Case_6989586621679095957Case_6989586621679095962Case_6989586621679095967Case_6989586621679095982Lambda_6989586621679095996Case_6989586621679096001Lambda_6989586621679096007Case_6989586621679096012Lambda_6989586621679096019Lambda_6989586621679096022Case_6989586621679096029Case_6989586621679096043Case_6989586621679096064Lambda_6989586621679096066Case_6989586621679096093Case_6989586621679096095Lambda_6989586621679096097Case_6989586621679096104Lambda_6989586621679096106Case_6989586621679096112Case_6989586621679096118Lambda_6989586621679096130Case_6989586621679096133Case_6989586621679096173Case_6989586621679096175Lambda_6989586621679096191Lambda_6989586621679096195Lambda_6989586621679096198Lambda_6989586621679096202Case_6989586621679096218Case_6989586621679096220Case_6989586621679096225Case_6989586621679096242Case_6989586621679096244Case_6989586621679096249Case_6989586621679096269Case_6989586621679096273Case_6989586621679096275Case_6989586621679096278Case_6989586621679096284Case_6989586621679096291Case_6989586621679096313Case_6989586621679096320Case_6989586621679096340Case_6989586621679096344Case_6989586621679096363Case_6989586621679096372Case_6989586621679096392Case_6989586621679096394Case_6989586621679096399Case_6989586621679096403Case_6989586621679096408Case_6989586621679096415Case_6989586621679096419Case_6989586621679096424Case_6989586621679096447Case_6989586621679096449Case_6989586621679096454Case_6989586621679096458Case_6989586621679096463Case_6989586621679096470Case_6989586621679096474Case_6989586621679096479Case_6989586621679096498Case_6989586621679096521Case_6989586621679096523Case_6989586621679096525Case_6989586621679096532Case_6989586621679096538Case_6989586621679096544Case_6989586621679096549Case_6989586621679096555Case_6989586621679096599Case_6989586621679096614Case_6989586621679096630Lambda_6989586621679096642Lambda_6989586621679096645Lambda_6989586621679096653Lambda_6989586621679096660Lambda_6989586621679096667Lambda_6989586621679096678Case_6989586621679096701Lambda_6989586621679096703Lambda_6989586621679096706Case_6989586621679096720Case_6989586621679096726Case_6989586621679096735Case_6989586621679096744Case_6989586621679096755Case_6989586621679096763Case_6989586621679096772Case_6989586621679096778Case_6989586621679096848Case_6989586621679096855Case_6989586621679096866Case_6989586621679100026Case_6989586621679100029Equals_6989586621679100168Equals_6989586621679100174Equals_6989586621679100182Equals_6989586621679100190Equals_6989586621679100202surjAreaCovRanksurjAreaConRankinjAreaCovRankinjAreaConRanksym2DiminjSym2ConRanksurjSym2CovRankinjSym2CovRanksurjSym2ConRankepsilonInvRank epsilonRank deltaRankCase_6989586621679547762Case_6989586621679547788Case_6989586621679547814Case_6989586621679547840Case_6989586621679547915Case_6989586621679547938Case_6989586621679547955Case_6989586621679547970Case_6989586621679547974Case_6989586621679547990Case_6989586621679547994pivotsU pivotsUFFfindPivotMaxFF findPivotMax findRowPivot gaussianFFST gaussianSTrrefSTisrefisrref'isrrefrref gaussianFFgaussianindependentColumnsRREFindependentColumnsFFindependentColumnsVerifiedFFindependentColumnsverifyindependentColumnsMatRREFindependentColumnsMatFFindependentColumnsMatPolyConstAffine NotSupportedLin singletonPolypolyMapgetVars shiftVars normalize $fNumPoly $fShowPoly $fOrdPoly$fEqPoly $fGenericPoly $fNFDataPoly $fShowLin$fOrdLin$fEqLin $fGenericLin $fNFDataLin STransRule STransCon STransCovSIListSConCovSCovSConSIxSIConSICovSVSpaceSNSZSS!ShowsPrec_6989586621679100147Sym3!ShowsPrec_6989586621679100147Sym2.ShowsPrec_6989586621679100147Sym2KindInference!ShowsPrec_6989586621679100147Sym1.ShowsPrec_6989586621679100147Sym1KindInference!ShowsPrec_6989586621679100147Sym0.ShowsPrec_6989586621679100147Sym0KindInferenceShowsPrec_6989586621679100147Compare_6989586621679100129Sym2Compare_6989586621679100129Sym1,Compare_6989586621679100129Sym1KindInferenceCompare_6989586621679100129Sym0,Compare_6989586621679100129Sym0KindInferenceCompare_6989586621679100129!ShowsPrec_6989586621679100102Sym3!ShowsPrec_6989586621679100102Sym2.ShowsPrec_6989586621679100102Sym2KindInference!ShowsPrec_6989586621679100102Sym1.ShowsPrec_6989586621679100102Sym1KindInference!ShowsPrec_6989586621679100102Sym0.ShowsPrec_6989586621679100102Sym0KindInferenceShowsPrec_6989586621679100102Compare_6989586621679100088Sym2Compare_6989586621679100088Sym1,Compare_6989586621679100088Sym1KindInferenceCompare_6989586621679100088Sym0,Compare_6989586621679100088Sym0KindInferenceCompare_6989586621679100088!ShowsPrec_6989586621679100067Sym3!ShowsPrec_6989586621679100067Sym2.ShowsPrec_6989586621679100067Sym2KindInference!ShowsPrec_6989586621679100067Sym1.ShowsPrec_6989586621679100067Sym1KindInference!ShowsPrec_6989586621679100067Sym0.ShowsPrec_6989586621679100067Sym0KindInferenceShowsPrec_6989586621679100067Compare_6989586621679100053Sym2Compare_6989586621679100053Sym1,Compare_6989586621679100053Sym1KindInferenceCompare_6989586621679100053Sym0,Compare_6989586621679100053Sym0KindInferenceCompare_6989586621679100053!ShowsPrec_6989586621679100036Sym3!ShowsPrec_6989586621679100036Sym2.ShowsPrec_6989586621679100036Sym2KindInference!ShowsPrec_6989586621679100036Sym1.ShowsPrec_6989586621679100036Sym1KindInference!ShowsPrec_6989586621679100036Sym0.ShowsPrec_6989586621679100036Sym0KindInferenceShowsPrec_6989586621679100036#FromInteger_6989586621679100020Sym1#FromInteger_6989586621679100020Sym00FromInteger_6989586621679100020Sym0KindInferenceFromInteger_6989586621679100020Signum_6989586621679100013Sym1Signum_6989586621679100013Sym0+Signum_6989586621679100013Sym0KindInferenceSignum_6989586621679100013Abs_6989586621679100006Sym1Abs_6989586621679100006Sym0(Abs_6989586621679100006Sym0KindInferenceAbs_6989586621679100006 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TFHelper_6989586621679099555Sym0-TFHelper_6989586621679099555Sym0KindInferenceTFHelper_6989586621679099555!ShowsPrec_6989586621679098253Sym3!ShowsPrec_6989586621679098253Sym2.ShowsPrec_6989586621679098253Sym2KindInference!ShowsPrec_6989586621679098253Sym1.ShowsPrec_6989586621679098253Sym1KindInference!ShowsPrec_6989586621679098253Sym0.ShowsPrec_6989586621679098253Sym0KindInferenceShowsPrec_6989586621679098253VIdVDimFromNat IxCompare IsAscending IsAscendingNE IsAscendingI IsLengthNELengthNELengthILLengthRSaneHeadRTailRMergeRMergeILMergeMergeNE ContractRPrepIConPrepICov ContractISubsetNEElemNECanTransposeConCanTransposeCov CanTranspose RemoveUntil SaneTransRuleCanTransposeMultTranspositionsZipConZipCovTranspositions'SaneRelabelRule RelabelNERelabelR RelabelIL RelabelIL'RelabelTranspositions ZipConCovRelabelTranspositions'VIdSym1VIdSym0VIdSym0KindInferenceVDimSym1VDimSym0VDimSym0KindInference FromNatSym1 FromNatSym0FromNatSym0KindInference IxCompareSym2 IxCompareSym1IxCompareSym1KindInference IxCompareSym0IxCompareSym0KindInferenceIsAscendingSym1IsAscendingSym0IsAscendingSym0KindInferenceIsAscendingNESym1IsAscendingNESym0IsAscendingNESym0KindInferenceIsAscendingISym1IsAscendingISym0IsAscendingISym0KindInferenceIsLengthNESym2IsLengthNESym1IsLengthNESym1KindInferenceIsLengthNESym0IsLengthNESym0KindInference LengthNESym1 LengthNESym0LengthNESym0KindInference LengthILSym1 LengthILSym0LengthILSym0KindInference LengthRSym1 LengthRSym0LengthRSym0KindInferenceSaneSym1SaneSym0SaneSym0KindInference HeadRSym1 HeadRSym0HeadRSym0KindInference TailRSym1 TailRSym0TailRSym0KindInference MergeRSym2 MergeRSym1MergeRSym1KindInference MergeRSym0MergeRSym0KindInference MergeILSym2 MergeILSym1MergeILSym1KindInference MergeILSym0MergeILSym0KindInference MergeSym2 MergeSym1MergeSym1KindInference MergeSym0MergeSym0KindInference MergeNESym2 MergeNESym1MergeNESym1KindInference MergeNESym0MergeNESym0KindInference ContractRSym1 ContractRSym0ContractRSym0KindInference PrepIConSym2 PrepIConSym1PrepIConSym1KindInference PrepIConSym0PrepIConSym0KindInference PrepICovSym2 PrepICovSym1PrepICovSym1KindInference PrepICovSym0PrepICovSym0KindInference ContractISym1 ContractISym0ContractISym0KindInference SubsetNESym2 SubsetNESym1SubsetNESym1KindInference SubsetNESym0SubsetNESym0KindInference ElemNESym2 ElemNESym1ElemNESym1KindInference ElemNESym0ElemNESym0KindInferenceCanTransposeConSym4CanTransposeConSym3 CanTransposeConSym3KindInferenceCanTransposeConSym2 CanTransposeConSym2KindInferenceCanTransposeConSym1 CanTransposeConSym1KindInferenceCanTransposeConSym0 CanTransposeConSym0KindInferenceCanTransposeCovSym4CanTransposeCovSym3 CanTransposeCovSym3KindInferenceCanTransposeCovSym2 CanTransposeCovSym2KindInferenceCanTransposeCovSym1 CanTransposeCovSym1KindInferenceCanTransposeCovSym0 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sContractRsMergeNEsMergesMergeILsMergeRsTailRsHeadRsSanesLengthR sLengthIL sLengthNE sIsLengthNE sIsAscendingIsIsAscendingNE sIsAscending 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$fPShowVSpace;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100036Sym09$fSuppressUnusedWarnings->Compare_6989586621679100053Sym1 $fPOrdVSpace9$fSuppressUnusedWarnings->Compare_6989586621679100053Sym0;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100067Sym2;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100067Sym1 $fPShowIx;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100067Sym09$fSuppressUnusedWarnings->Compare_6989586621679100088Sym1$fPOrdIx9$fSuppressUnusedWarnings->Compare_6989586621679100088Sym0;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100102Sym2;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100102Sym1 $fPShowIList;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100102Sym09$fSuppressUnusedWarnings->Compare_6989586621679100129Sym1 $fPOrdIList9$fSuppressUnusedWarnings->Compare_6989586621679100129Sym0;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100147Sym2;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100147Sym1$fPShowTransRule;$fSuppressUnusedWarnings->ShowsPrec_6989586621679100147Sym0$fPEqN $fPEqVSpace$fPEqIx $fPEqIList$fPEqTransRule$fSingI->SSym0 $fSingINS $fSingINZ$fShowSN$fTestCoercionNSN$fTestEqualityNSN $fSDecideN$fSEqN$fSNumN$fSOrdN$fSShowN $fSingKindN$fSingI->VSpaceSym1$fSingI->VSpaceSym0$fSingIVSpaceVSpace $fShowSVSpace$fTestCoercionVSpaceSVSpace$fTestEqualityVSpaceSVSpace$fSDecideVSpace $fSEqVSpace $fSOrdVSpace $fSShowVSpace$fSingKindVSpace$fSingI->ICovSym0 $fSingIIxICov$fSingI->IConSym0 $fSingIIxICon $fShowSIx$fTestCoercionIxSIx$fTestEqualityIxSIx $fSDecideIx$fSEqIx$fSOrdIx $fSShowIx $fSingKindIx$fSingI->ConSym0$fSingIIListCon$fSingI->CovSym0$fSingIIListCov$fSingI->ConCovSym1$fSingI->ConCovSym0$fSingIIListConCov $fShowSIList$fTestCoercionIListSIList$fTestEqualityIListSIList$fSDecideIList 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proofMergeGTproofMergeIxGTsaneContractProofsingletonContractProofcontractTailDiffVProofcontractTailSameVNoConProofcontractTailSameVNoCovProofcontractTailSameVDiffIProofcontractTailSameVSameIProof DeltaRank EpsilonRankEpsilonInvRankSym2DimInjSym2ConRankInjSym2CovRankSurjSym2ConRankSurjSym2CovRankInjAreaConRankInjAreaCovRankSurjAreaConRankSurjAreaCovRank DeltaRankSym4 DeltaRankSym3DeltaRankSym3KindInference DeltaRankSym2DeltaRankSym2KindInference DeltaRankSym1DeltaRankSym1KindInference DeltaRankSym0DeltaRankSym0KindInferenceEpsilonRankSym3EpsilonRankSym2EpsilonRankSym2KindInferenceEpsilonRankSym1EpsilonRankSym1KindInferenceEpsilonRankSym0EpsilonRankSym0KindInferenceEpsilonInvRankSym3EpsilonInvRankSym2EpsilonInvRankSym2KindInferenceEpsilonInvRankSym1EpsilonInvRankSym1KindInferenceEpsilonInvRankSym0EpsilonInvRankSym0KindInference Sym2DimSym1 Sym2DimSym0Sym2DimSym0KindInferenceInjSym2ConRankSym5InjSym2ConRankSym4InjSym2ConRankSym4KindInferenceInjSym2ConRankSym3InjSym2ConRankSym3KindInferenceInjSym2ConRankSym2InjSym2ConRankSym2KindInferenceInjSym2ConRankSym1InjSym2ConRankSym1KindInferenceInjSym2ConRankSym0InjSym2ConRankSym0KindInferenceInjSym2CovRankSym5InjSym2CovRankSym4InjSym2CovRankSym4KindInferenceInjSym2CovRankSym3InjSym2CovRankSym3KindInferenceInjSym2CovRankSym2InjSym2CovRankSym2KindInferenceInjSym2CovRankSym1InjSym2CovRankSym1KindInferenceInjSym2CovRankSym0InjSym2CovRankSym0KindInferenceSurjSym2ConRankSym5SurjSym2ConRankSym4 SurjSym2ConRankSym4KindInferenceSurjSym2ConRankSym3 SurjSym2ConRankSym3KindInferenceSurjSym2ConRankSym2 SurjSym2ConRankSym2KindInferenceSurjSym2ConRankSym1 SurjSym2ConRankSym1KindInferenceSurjSym2ConRankSym0 SurjSym2ConRankSym0KindInferenceSurjSym2CovRankSym5SurjSym2CovRankSym4 SurjSym2CovRankSym4KindInferenceSurjSym2CovRankSym3 SurjSym2CovRankSym3KindInferenceSurjSym2CovRankSym2 SurjSym2CovRankSym2KindInferenceSurjSym2CovRankSym1 SurjSym2CovRankSym1KindInferenceSurjSym2CovRankSym0 SurjSym2CovRankSym0KindInferenceInjAreaConRankSym6InjAreaConRankSym5InjAreaConRankSym5KindInferenceInjAreaConRankSym4InjAreaConRankSym4KindInferenceInjAreaConRankSym3InjAreaConRankSym3KindInferenceInjAreaConRankSym2InjAreaConRankSym2KindInferenceInjAreaConRankSym1InjAreaConRankSym1KindInferenceInjAreaConRankSym0InjAreaConRankSym0KindInferenceInjAreaCovRankSym6InjAreaCovRankSym5InjAreaCovRankSym5KindInferenceInjAreaCovRankSym4InjAreaCovRankSym4KindInferenceInjAreaCovRankSym3InjAreaCovRankSym3KindInferenceInjAreaCovRankSym2InjAreaCovRankSym2KindInferenceInjAreaCovRankSym1InjAreaCovRankSym1KindInferenceInjAreaCovRankSym0InjAreaCovRankSym0KindInferenceSurjAreaConRankSym6SurjAreaConRankSym5 SurjAreaConRankSym5KindInferenceSurjAreaConRankSym4 SurjAreaConRankSym4KindInferenceSurjAreaConRankSym3 SurjAreaConRankSym3KindInferenceSurjAreaConRankSym2 SurjAreaConRankSym2KindInferenceSurjAreaConRankSym1 SurjAreaConRankSym1KindInferenceSurjAreaConRankSym0 SurjAreaConRankSym0KindInferenceSurjAreaCovRankSym6SurjAreaCovRankSym5 SurjAreaCovRankSym5KindInferenceSurjAreaCovRankSym4 SurjAreaCovRankSym4KindInferenceSurjAreaCovRankSym3 SurjAreaCovRankSym3KindInferenceSurjAreaCovRankSym2 SurjAreaCovRankSym2KindInferenceSurjAreaCovRankSym1 SurjAreaCovRankSym1KindInferenceSurjAreaCovRankSym0 SurjAreaCovRankSym0KindInference3Let6989586621679547992Scrutinee_69895866216795454527Let6989586621679547992Scrutinee_6989586621679545452Sym37Let6989586621679547992Scrutinee_6989586621679545452Sym2Let6989586621679547992Scrutinee_6989586621679545452Sym2KindInference7Let6989586621679547992Scrutinee_6989586621679545452Sym1Let6989586621679547992Scrutinee_6989586621679545452Sym1KindInference7Let6989586621679547992Scrutinee_6989586621679545452Sym0Let6989586621679547992Scrutinee_6989586621679545452Sym0KindInference3Let6989586621679547988Scrutinee_69895866216795454507Let6989586621679547988Scrutinee_6989586621679545450Sym37Let6989586621679547988Scrutinee_6989586621679545450Sym2Let6989586621679547988Scrutinee_6989586621679545450Sym2KindInference7Let6989586621679547988Scrutinee_6989586621679545450Sym1Let6989586621679547988Scrutinee_6989586621679545450Sym1KindInference7Let6989586621679547988Scrutinee_6989586621679545450Sym0Let6989586621679547988Scrutinee_6989586621679545450Sym0KindInference3Let6989586621679547972Scrutinee_69895866216795454567Let6989586621679547972Scrutinee_6989586621679545456Sym37Let6989586621679547972Scrutinee_6989586621679545456Sym2Let6989586621679547972Scrutinee_6989586621679545456Sym2KindInference7Let6989586621679547972Scrutinee_6989586621679545456Sym1Let6989586621679547972Scrutinee_6989586621679545456Sym1KindInference7Let6989586621679547972Scrutinee_6989586621679545456Sym0Let6989586621679547972Scrutinee_6989586621679545456Sym0KindInference3Let6989586621679547968Scrutinee_69895866216795454547Let6989586621679547968Scrutinee_6989586621679545454Sym37Let6989586621679547968Scrutinee_6989586621679545454Sym2Let6989586621679547968Scrutinee_6989586621679545454Sym2KindInference7Let6989586621679547968Scrutinee_6989586621679545454Sym1Let6989586621679547968Scrutinee_6989586621679545454Sym1KindInference7Let6989586621679547968Scrutinee_6989586621679545454Sym0Let6989586621679547968Scrutinee_6989586621679545454Sym0KindInferenceLet6989586621679547947GoLet6989586621679547947GoSym3Let6989586621679547947GoSym2)Let6989586621679547947GoSym2KindInferenceLet6989586621679547947GoSym1)Let6989586621679547947GoSym1KindInferenceLet6989586621679547947GoSym0)Let6989586621679547947GoSym0KindInference3Let6989586621679547953Scrutinee_69895866216795454587Let6989586621679547953Scrutinee_6989586621679545458Sym37Let6989586621679547953Scrutinee_6989586621679545458Sym2Let6989586621679547953Scrutinee_6989586621679545458Sym2KindInference7Let6989586621679547953Scrutinee_6989586621679545458Sym1Let6989586621679547953Scrutinee_6989586621679545458Sym1KindInference7Let6989586621679547953Scrutinee_6989586621679545458Sym0Let6989586621679547953Scrutinee_6989586621679545458Sym0KindInference3Let6989586621679547936Scrutinee_69895866216795454607Let6989586621679547936Scrutinee_6989586621679545460Sym57Let6989586621679547936Scrutinee_6989586621679545460Sym4Let6989586621679547936Scrutinee_6989586621679545460Sym4KindInference7Let6989586621679547936Scrutinee_6989586621679545460Sym3Let6989586621679547936Scrutinee_6989586621679545460Sym3KindInference7Let6989586621679547936Scrutinee_6989586621679545460Sym2Let6989586621679547936Scrutinee_6989586621679545460Sym2KindInference7Let6989586621679547936Scrutinee_6989586621679545460Sym1Let6989586621679547936Scrutinee_6989586621679545460Sym1KindInference7Let6989586621679547936Scrutinee_6989586621679545460Sym0Let6989586621679547936Scrutinee_6989586621679545460Sym0KindInferenceLet6989586621679547934RLet6989586621679547934RSym5Let6989586621679547934RSym4(Let6989586621679547934RSym4KindInferenceLet6989586621679547934RSym3(Let6989586621679547934RSym3KindInferenceLet6989586621679547934RSym2(Let6989586621679547934RSym2KindInferenceLet6989586621679547934RSym1(Let6989586621679547934RSym1KindInferenceLet6989586621679547934RSym0(Let6989586621679547934RSym0KindInference3Let6989586621679547913Scrutinee_69895866216795454627Let6989586621679547913Scrutinee_6989586621679545462Sym57Let6989586621679547913Scrutinee_6989586621679545462Sym4Let6989586621679547913Scrutinee_6989586621679545462Sym4KindInference7Let6989586621679547913Scrutinee_6989586621679545462Sym3Let6989586621679547913Scrutinee_6989586621679545462Sym3KindInference7Let6989586621679547913Scrutinee_6989586621679545462Sym2Let6989586621679547913Scrutinee_6989586621679545462Sym2KindInference7Let6989586621679547913Scrutinee_6989586621679545462Sym1Let6989586621679547913Scrutinee_6989586621679545462Sym1KindInference7Let6989586621679547913Scrutinee_6989586621679545462Sym0Let6989586621679547913Scrutinee_6989586621679545462Sym0KindInferenceLet6989586621679547911RLet6989586621679547911RSym5Let6989586621679547911RSym4(Let6989586621679547911RSym4KindInferenceLet6989586621679547911RSym3(Let6989586621679547911RSym3KindInferenceLet6989586621679547911RSym2(Let6989586621679547911RSym2KindInferenceLet6989586621679547911RSym1(Let6989586621679547911RSym1KindInferenceLet6989586621679547911RSym0(Let6989586621679547911RSym0KindInference3Let6989586621679547838Scrutinee_69895866216795454647Let69895866216795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9586621679547758RSym2KindInferenceLet6989586621679547758RSym1(Let6989586621679547758RSym1KindInferenceLet6989586621679547758RSym0(Let6989586621679547758RSym0KindInferencesSurjAreaCovRanksSurjAreaConRanksInjAreaCovRanksInjAreaConRanksSurjSym2CovRanksSurjSym2ConRanksInjSym2CovRanksInjSym2ConRanksSym2DimsEpsilonInvRank sEpsilonRank sDeltaRank5$fSuppressUnusedWarnings->Let6989586621679547758RSym55$fSuppressUnusedWarnings->Let6989586621679547758RSym45$fSuppressUnusedWarnings->Let6989586621679547758RSym35$fSuppressUnusedWarnings->Let6989586621679547758RSym25$fSuppressUnusedWarnings->Let6989586621679547758RSym15$fSuppressUnusedWarnings->Let6989586621679547758RSym0$fSuppressUnusedWarnings->Let6989586621679547760Scrutinee_6989586621679545470Sym5$fSuppressUnusedWarnings->Let6989586621679547760Scrutinee_6989586621679545470Sym4$fSuppressUnusedWarnings->Let6989586621679547760Scrutinee_6989586621679545470Sym3$fSuppressUnusedWarnings->Let6989586621679547760Scrutinee_6989586621679545470Sym2$fSuppressUnusedWarnings->Let6989586621679547760Scrutinee_6989586621679545470Sym1$fSuppressUnusedWarnings->Let6989586621679547760Scrutinee_6989586621679545470Sym05$fSuppressUnusedWarnings->Let6989586621679547784RSym55$fSuppressUnusedWarnings->Let6989586621679547784RSym45$fSuppressUnusedWarnings->Let6989586621679547784RSym35$fSuppressUnusedWarnings->Let6989586621679547784RSym25$fSuppressUnusedWarnings->Let6989586621679547784RSym15$fSuppressUnusedWarnings->Let6989586621679547784RSym0$fSuppressUnusedWarnings->Let6989586621679547786Scrutinee_6989586621679545468Sym5$fSuppressUnusedWarnings->Let6989586621679547786Scrutinee_6989586621679545468Sym4$fSuppressUnusedWarnings->Let6989586621679547786Scrutinee_6989586621679545468Sym3$fSuppressUnusedWarnings->Let6989586621679547786Scrutinee_6989586621679545468Sym2$fSuppressUnusedWarnings->Let6989586621679547786Scrutinee_6989586621679545468Sym1$fSuppressUnusedWarnings->Let6989586621679547786Scrutinee_6989586621679545468Sym05$fSuppressUnusedWarnings->Let6989586621679547810RSym55$fSuppressUnusedWarnings->Let6989586621679547810RSym45$fSuppressUnusedWarnings->Let6989586621679547810RSym35$fSuppressUnusedWarnings->Let6989586621679547810RSym25$fSuppressUnusedWarnings->Let6989586621679547810RSym15$fSuppressUnusedWarnings->Let6989586621679547810RSym0$fSuppressUnusedWarnings->Let6989586621679547812Scrutinee_6989586621679545466Sym5$fSuppressUnusedWarnings->Let6989586621679547812Scrutinee_6989586621679545466Sym4$fSuppressUnusedWarnings->Let6989586621679547812Scrutinee_6989586621679545466Sym3$fSuppressUnusedWarnings->Let6989586621679547812Scrutinee_6989586621679545466Sym2$fSuppressUnusedWarnings->Let6989586621679547812Scrutinee_6989586621679545466Sym1$fSuppressUnusedWarnings->Let6989586621679547812Scrutinee_6989586621679545466Sym05$fSuppressUnusedWarnings->Let6989586621679547836RSym55$fSuppressUnusedWarnings->Let6989586621679547836RSym45$fSuppressUnusedWarnings->Let6989586621679547836RSym35$fSuppressUnusedWarnings->Let6989586621679547836RSym25$fSuppressUnusedWarnings->Let6989586621679547836RSym15$fSuppressUnusedWarnings->Let6989586621679547836RSym0$fSuppressUnusedWarnings->Let6989586621679547838Scrutinee_6989586621679545464Sym5$fSuppressUnusedWarnings->Let6989586621679547838Scrutinee_6989586621679545464Sym4$fSuppressUnusedWarnings->Let6989586621679547838Scrutinee_6989586621679545464Sym3$fSuppressUnusedWarnings->Let6989586621679547838Scrutinee_6989586621679545464Sym2$fSuppressUnusedWarnings->Let6989586621679547838Scrutinee_6989586621679545464Sym1$fSuppressUnusedWarnings->Let6989586621679547838Scrutinee_6989586621679545464Sym0$fSuppressUnusedWarnings->Let6989586621679547953Scrutinee_6989586621679545458Sym2$fSuppressUnusedWarnings->Let6989586621679547953Scrutinee_6989586621679545458Sym1$fSuppressUnusedWarnings->Let6989586621679547953Scrutinee_6989586621679545458Sym06$fSuppressUnusedWarnings->Let6989586621679547947GoSym26$fSuppressUnusedWarnings->Let6989586621679547947GoSym16$fSuppressUnusedWarnings->Let6989586621679547947GoSym0$fSuppressUnusedWarnings->Let6989586621679547968Scrutinee_6989586621679545454Sym2$fSuppressUnusedWarnings->Let6989586621679547968Scrutinee_6989586621679545454Sym1$fSuppressUnusedWarnings->Let6989586621679547968Scrutinee_6989586621679545454Sym0$fSuppressUnusedWarnings->Let6989586621679547972Scrutinee_6989586621679545456Sym2$fSuppressUnusedWarnings->Let6989586621679547972Scrutinee_6989586621679545456Sym1$fSuppressUnusedWarnings->Let6989586621679547972Scrutinee_6989586621679545456Sym0$fSuppressUnusedWarnings->Let6989586621679547988Scrutinee_6989586621679545450Sym2$fSuppressUnusedWarnings->Let6989586621679547988Scrutinee_6989586621679545450Sym1$fSuppressUnusedWarnings->Let6989586621679547988Scrutinee_6989586621679545450Sym0$fSuppressUnusedWarnings->Let6989586621679547992Scrutinee_6989586621679545452Sym2$fSuppressUnusedWarnings->Let6989586621679547992Scrutinee_6989586621679545452Sym1$fSuppressUnusedWarnings->Let6989586621679547992Scrutinee_6989586621679545452Sym0$fSingI->SurjAreaCovRankSym5-$fSuppressUnusedWarnings->SurjAreaCovRankSym5$fSingI->SurjAreaCovRankSym4-$fSuppressUnusedWarnings->SurjAreaCovRankSym4$fSingI->SurjAreaCovRankSym3-$fSuppressUnusedWarnings->SurjAreaCovRankSym3$fSingI->SurjAreaCovRankSym2-$fSuppressUnusedWarnings->SurjAreaCovRankSym2$fSingI->SurjAreaCovRankSym1-$fSuppressUnusedWarnings->SurjAreaCovRankSym1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$fNFDataVec $fShowVecTensor ZeroTensorScalar removeZeros&+&-&*contract transpose transposeMultrelabeltoList fromList'fromList$fFunctorTensor$fNFDataTensor $fShowTensor $fEqTensorRankT DimensionLabelTscalarTzeroT removeZerosT.*.°.+.- contractT transposeTtransposeMultTrelabelTrankTtoListT fromListTconRankcovRank conCovRank $fFunctorT $fNFDataT$fShowTSolutionEquationtensorToEquationsequationFromRationalequationsToSparseMatequationsToMattensorsToSparseMat tensorsToMat systemRankfromRref fromRrefRevfromRow fromRowRev applySolution solveTensor solveSystemredefineIndetspermSignepsilon' epsilonInv' someEpsilonsomeEpsilonInvdelta'delta someDelta trianMapSym2 facMapSym2 sym2Assocs sym2AssocsFacgamma'gammaeta'eta gammaInv'gammaInvetaInv'etaInv injSym2Con' injSym2Cov' surjSym2Con' surjSym2Cov' someGamma someGammaInvsomeEta someEtaInvsomeInjSym2ConsomeInjSym2CovsomeSurjSym2ConsomeSurjSym2CovsomeInterSym2ConsomeInterSym2Cov someDeltaSym2 trianMapArea facMapAreaareaSignsortArea injAreaCon' 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