diff options
Diffstat (limited to 'src/algebra/intclos.spad.pamphlet')
| -rw-r--r-- | src/algebra/intclos.spad.pamphlet | 32 |
1 files changed, 16 insertions, 16 deletions
diff --git a/src/algebra/intclos.spad.pamphlet b/src/algebra/intclos.spad.pamphlet index 7507efae..b8190fc9 100644 --- a/src/algebra/intclos.spad.pamphlet +++ b/src/algebra/intclos.spad.pamphlet @@ -53,10 +53,10 @@ TriangularMatrixOperations(R,Row,Col,M): Exports == Implementation where offset := minColIndex AI - minRowIndex AI for i in minRowIndex AI .. maxRowIndex AI for j in minColIndex AI .. maxColIndex AI repeat - qsetelt_!(AI,i,j,(denom exquo qelt(A,i,j))::R) + qsetelt!(AI,i,j,(denom exquo qelt(A,i,j))::R) for i in minRowIndex AI .. maxRowIndex AI repeat for j in offset + i + 1 .. maxColIndex AI repeat - qsetelt_!(AI,i,j, - (((+/[qelt(AI,i,k) * qelt(A,k-offset,j) + qsetelt!(AI,i,j, - (((+/[qelt(AI,i,k) * qelt(A,k-offset,j) for k in i+offset..(j-1)]) exquo qelt(A, j-offset, j))::R)) AI @@ -66,10 +66,10 @@ TriangularMatrixOperations(R,Row,Col,M): Exports == Implementation where offset := minColIndex AI - minRowIndex AI for i in minRowIndex AI .. maxRowIndex AI for j in minColIndex AI .. maxColIndex AI repeat - qsetelt_!(AI,i,j,(denom exquo qelt(A,i,j))::R) + qsetelt!(AI,i,j,(denom exquo qelt(A,i,j))::R) for i in minColIndex AI .. maxColIndex AI repeat for j in i - offset + 1 .. maxRowIndex AI repeat - qsetelt_!(AI,j,i, - (((+/[qelt(A,j,k+offset) * qelt(AI,k,i) + qsetelt!(AI,j,i, - (((+/[qelt(A,j,k+offset) * qelt(AI,k,i) for k in i-offset..(j-1)]) exquo qelt(A, j, j+offset))::R)) AI @@ -108,7 +108,7 @@ IntegralBasisTools(R,UP,F): Exports == Implementation where ++ matrixGcd(mat,sing,n) is \spad{gcd(sing,g)} where \spad{g} is the ++ gcd of the entries of the \spad{n}-by-\spad{n} upper-triangular ++ matrix \spad{mat}. - divideIfCan_!: (Matrix R,Matrix R,R,Integer) -> R + divideIfCan!: (Matrix R,Matrix R,R,Integer) -> R ++ divideIfCan!(matrix,matrixOut,prime,n) attempts to divide the ++ entries of \spad{matrix} by \spad{prime} and store the result in ++ \spad{matrixOut}. If it is successful, 1 is returned and if not, @@ -161,13 +161,13 @@ IntegralBasisTools(R,UP,F): Exports == Implementation where one? d => return d d - divideIfCan_!(matrix,matrixOut,prime,n) == + divideIfCan!(matrix,matrixOut,prime,n) == -- note: both 'matrix' and 'matrixOut' will be upper triangular; -- no need to do anything below the diagonal for i in 1..n repeat for j in i..n repeat (a := (qelt(matrix,i,j) exquo prime)) case "failed" => return prime - qsetelt_!(matrixOut,i,j,a :: R) + qsetelt!(matrixOut,i,j,a :: R) 1 leastPower(p,n) == @@ -444,8 +444,8 @@ WildFunctionFieldIntegralBasis(K,R,UP,F): Exports == Implementation where bi : F := 0 for j in 1..n repeat bi := bi + qelt(rb,i,j) * qelt(standardBasis,j) - qsetelt_!(bas,i,bi) - qsetelt_!(pows,i,bi ** p) + qsetelt!(bas,i,bi) + qsetelt!(pows,i,bi ** p) coor0 := transpose coordinates(pows,bas) denPow := rbden ** ((p - 1) :: NNI) (coMat0 := coor0 exquo denPow) case "failed" => @@ -463,15 +463,15 @@ WildFunctionFieldIntegralBasis(K,R,UP,F): Exports == Implementation where frob := copy pPows; tmpMat : Matrix sae := new(n,n,0) for r in 2..leastPower(p,q) repeat for i in 1..n repeat for j in 1..n repeat - qsetelt_!(tmpMat,i,j,qelt(frob,i,j) ** p) - times_!(frob,pPows,tmpMat)$MATSTOR(sae) + qsetelt!(tmpMat,i,j,qelt(frob,i,j) ** p) + times!(frob,pPows,tmpMat)$MATSTOR(sae) frobPow := frob ** lp -- compute the p-radical ns := nullSpace frobPow - for i in 1..n repeat for j in 1..n repeat qsetelt_!(tfm,i,j,0) + for i in 1..n repeat for j in 1..n repeat qsetelt!(tfm,i,j,0) for vec in ns for i in 1.. repeat for j in 1..n repeat - qsetelt_!(tfm,i,j,lift qelt(vec,j)) + qsetelt!(tfm,i,j,lift qelt(vec,j)) id := squareTop rowEchelon(tfm,prime) -- id = basis matrix of the p-radical idinv := UpTriBddDenomInv(id, prime) @@ -480,7 +480,7 @@ WildFunctionFieldIntegralBasis(K,R,UP,F): Exports == Implementation where rbinv := idealiser(id * rb, rbinv * idinv, prime * rbden) index := diagonalProduct rbinv rb := rowEchelon LowTriBddDenomInv(rbinv,rbden * prime) - if divideIfCan_!(rb,matrixOut,prime,n) = 1 + if divideIfCan!(rb,matrixOut,prime,n) = 1 then rb := matrixOut else rbden := rbden * prime rbinv := UpTriBddDenomInv(rb,rbden) @@ -620,7 +620,7 @@ NumberFieldIntegralBasis(UP,F): Exports == Implementation where for j in minIndex(b)..maxIndex(b) for jj in minColIndex(rb)..maxColIndex(rb) repeat a := a + qelt(rb,ii,jj) * qelt(b,j) - qsetelt_!(v,i,a**p) + qsetelt!(v,i,a**p) mat := transpose coordinates v ((transpose(rbinv) * mat) exquo (rbden ** p)) :: Mat @@ -746,7 +746,7 @@ NumberFieldIntegralBasis(UP,F): Exports == Implementation where rbinv := idealiser(id * rb, rbinv * idinv, p * rbden) index := diagonalProduct rbinv rb := rowEchelon LowTriBddDenomInv(rbinv, p * rbden) - if divideIfCan_!(rb,matrixOut,p,n) = 1 + if divideIfCan!(rb,matrixOut,p,n) = 1 then rb := matrixOut else rbden := p * rbden rbinv := UpTriBddDenomInv(rb, rbden) |