- Introduction
- Differential Rings and Fields
- Structure Operations on Differential Rings
- Element Operations on Differential Ring Elements
- Changing Related Structures
- ChangeDerivation(R, f) : RngDiff, RngElt -> RngDiff, Map
- Example RngDiff_diff-ring-change-derivation (H118E18)
- ChangeDifferential(F, df) : RngDiff, DiffFunElt -> RngDiff, Map
- Example RngDiff_diff-ring-change-differential (H118E19)
- ConstantFieldExtension(F, C) : RngDiff, Fld -> RngDiff, Map
- Example RngDiff_diff-ring-constant-field-extension (H118E20)
- Example RngDiff_diff-ring-constant-field-extension-series (H118E21)
- Completion(F, p) : RngDiff, PlcFunElt -> RngDiff, Map
- Example RngDiff_diff-ring-completion-create (H118E22)
- Example RngDiff_diff-ring-completion-elliptic (H118E23)
- Ring and Field Extensions
- Ideals and Quotient Rings
- Wronskian Matrix
- Differential Operator Rings
- Structure Operations on Differential Operator Rings
- Element Operations on Differential Operators
- Related Maps
- Changing Related Structures
- ChangeDerivation(R, f) : RngDiffOp, RngElt -> RngDiffOp, Map
- ChangeDifferential(R, df) : RngDiffOp, DiffFunElt -> RngDiffOp, Map
- Example RngDiff_example-diff-op-ring-changing-differential (H118E46)
- ConstantFieldExtension(R, C) : RngDiffOp,Fld -> RngDiffOp, Map
- PurelyRamifiedExtension(R,f) : RngDiffOp,RngUPolElt -> RngDiffOp, Map
- Example RngDiff_diff-op-ring-purely-ramified-extension-DLSR (H118E47)
- Completion(R, p) : RngDiffOp, PlcFunElt -> RngDiffOp, Map
- Localization(R, p) : RngDiffOp, PlcFunElt -> RngDiffOp, Map, PlcFunElt
- Localization(L, p) : RngDiffOpElt, PlcFunElt -> RngDiffOpElt, Map, PlcFunElt
- Localization(R) : RngDiffOp -> RngDiffOp, Map
- Localization(L) : RngDiffOpElt -> RngDiffOpElt, Map
- Example RngDiff_example-diff-op-ring-changing-attributes-DLSR (H118E48)
- Example RngDiff_example-diff-op-ring-completion (H118E49)
- Example RngDiff_example-diff-op-ring-localization (H118E50)
- Euclidean Algorithms, GCDs and LCMs
- Euclidean Right and Left Division
- Greatest Common Right and Left Divisors
- GreatestCommonRightDivisor(A, B) : RngDiffOpElt, RngDiffOpElt -> RngDiffOpElt
- ExtendedGreatestCommonRightDivisor(A, B) : RngDiffOpElt, RngDiffOpElt -> RngDiffOpElt, RngDiffOpElt, RngDiffOpElt
- GreatestCommonLeftDivisor(A, B) : RngDiffOpElt, RngDiffOpElt -> RngDiffOpElt
- ExtendedGreatestCommonLeftDivisor(A, B) : RngDiffOpElt, RngDiffOpElt -> RngDiffOpElt, RngDiffOpElt, RngDiffOpElt
- Example RngDiff_example-GCRD-GCLD (H118E52)
- Least Common Left Multiples
- Related Matrices
- Singular Places and Indicial Polynomials
- Rational Solutions
- Newton Polygons
- Symmetric Powers
- Differential Operators of Algebraic Functions
- Factorisation of Operators over Differential Laurent Series Rings
- Bibliography
V2.28, 13 July 2023