Series Rings over \(p\)-Adic Rings
- Introduction
- Background
- Basic Operations
- Creation Intrinsics
SnuRing(F, nu): FldPad, FldRatElt → SnuRngSpRing(F, nu): FldPad, FldRatElt → SpRngSuRing(F, nu): FldPad, FldRatElt → SuRngSnuRing(F): FldPad → SnuRngSpRing(F): FldPad → SpRngSuRing(F): FldPad → SuRngSnuRing(p, e): RngIntElt, RngIntElt → SnuRngSnuRing(p): RngIntElt → SnuRngSpRing(p, e): RngIntElt, RngIntElt → SpRngSpRing(p): RngIntElt → SpRngSuRing(p, e): RngIntElt, RngIntElt → SuRngSuRing(p): RngIntElt → SuRngSnuRing(S, nu): RngSerPow, FldRatElt → SnuRngSpRing(S, nu): RngSerPow, FldRatElt → SpRngSuRing(S, nu): RngSerLaur, FldRatElt → SuRngSnuRing(S): SpRng → SnuRngSpRing(S): SnuRng → SpRngSnuRing(S): SuRng → SnuRngSuRing(S): SnuRng → SuRng
- Access Functions
- Element Operations
- Euclidean Algorithm
- Intrinsics
WeierstrassPreparation(f): SnuElement → SnuElement, SnuElementQuotrem(A, B): SnuElement, SnuElement → SnuElement, SnuElementQuotrem(A, B): SpElement, SpElement → SpElement, SpElementQuotrem(A, B): SuElement, SuElement → SuElement, SuElementExtendedGcd(A, B): SnuElement, SnuElement → SnuElement, SnuElement, SnuElement, SnuElement, SnuElement, SnuElementExtendedGcd(A, B): SpElement, SpElement → SpElement, SpElement, SpElement, SpElement, SpElement, SpElementExtendedGcd(A, B): SuElement, SuElement → SuElement, SuElement, SuElement, SuElement, SuElement, SuElementCanonicalElement(S, v): SuRng, FldRatElt → SuElementExample: Euclidean Basics
- Matrices and Modules
- Matrices
SpMatrixSpace(S, r, c): SpRng, RngIntElt, RngIntElt → SpMatRngSuMatrixSpace(S, r, c): SuRng, RngIntElt, RngIntElt → SuMatRngIdentityMatrix(S, n): SpRng, RngIntElt → SpMatIdentityMatrix(S): SpMatRng → SpMatZeroMatrix(S): SpMatRng → SpMatZeroMatrix(S, n): SpRng, RngIntElt → SpMatZeroMatrix(S, r, c): SpRng, RngIntElt, RngIntElt → SpMatIdentityMatrix(S, n): SuRng, RngIntElt → SuMatIdentityMatrix(S): SuMatRng → SuMatZeroMatrix(S): SuMatRng → SuMatZeroMatrix(S, n): SuRng, RngIntElt → SuMatZeroMatrix(S, r, c): SuRng, RngIntElt, RngIntElt → SuMatSpMatrix(A): SeqEnum → SpMatSpMatrix(r, c, A): RngIntElt, RngIntElt, SeqEnum → SpMatSpMatrix(v): SeqEnum → SpMatSpMatrix(A): SeqEnum → SpMatSuMatrix(r, c, A): RngIntElt, RngIntElt, SeqEnum → SuMatSuMatrix(v): SeqEnum → SuMatGaussValuations(M): SpMat → SeqEnumGaussValuations(M): SuMat → SeqEnumWeierstrassDegrees(M): SpMat → SeqEnumWeierstrassDegrees(M): SuMat → SeqEnumLeadingTerms(M): SpMat → MtrxLeadingTerms(M): SuMat → MtrxWeierstrassTerms(M): SpMat → MtrxWeierstrassTerms(M): SuMat → MtrxIsWeaklyZero(M): SpMat → BoolEltIsWeaklyZero(M): SuMat → BoolEltEchelonForm(M): SpMat → SpMat, SpMatEchelonForm(M): SuMat → SuMat, SuMatHermiteForm(M): SpMat → SpMat, SpMatHermiteForm(M): SuMat → SuMat, SuMatSmithForm(M): SpMat → SpMat, SpMat, SpMatSmithForm(M): SuMat → SuMat, SuMat, SuMatKernel(M): SpMat → SpSpcKernel(M): SuMat → SuSpcImage(M): SpMat → SpSpcImage(M): SuMat → SuSpcExample: Sp MatricesExample: Su Matrices
- Modules
SpSpace(R, n): SpRng, RngIntElt → SpSpcSuSpace(R, n): SuRng, RngIntElt → SuSpcSpSpace(M): SpMat → SpSpcSuSpace(M): SuMat → SuSpcSpSpace(v): SeqEnum → SpSpcSuSpace(v): SeqEnum → SuSpcAmbient(S): SpSpc → SpSpcAmbient(S): SuSpc → SuSpcParent(v): SpVec → SpSpcParent(v): SuVec → SuSpcZeroVector(S): SpSpc → SpVecZeroVector(S): SuSpc → SuVecSpVector(e): SeqEnum → SpVecSuVector(e): SeqEnum → SuVecBasis(S): SpSpc → SeqEnumBasis(S): SuSpc → SeqEnumBasisMatrix(S): SpSpc → SpMatBasisMatrix(S): SuSpc → SuMatDimension(S): SpSpc → RngIntEltDimension(S): SuSpc → RngIntEltDegree(S): SpSpc → RngIntEltDegree(S): SuSpc → RngIntEltLeadingTerms(v): SpVec → ModTupRngEltLeadingTerms(v): SuVec → ModTupRngEltWeierstrassTerms(v): SpVec → ModTupRngEltWeierstrassTerms(v): SuVec → ModTupRngEltGaussValuations(v): SpVec → SeqEnumGaussValuations(v): SuVec → SeqEnumWeierstrassDegrees(v): SpVec → SeqEnumWeierstrassDegrees(v): SuVec → SeqEnumIsWeaklyZero(v): SpVec → BoolEltIsWeaklyZero(v): SuVec → BoolEltM1 + M2: SpSpc, SpSpc → SpSpcM1 + M2: SuSpc, SuSpc → SuSpcDirectSum(M1, M2): SpSpc, SpSpc → SpSpcDirectSum(M1, M2): SuSpc, SuSpc → SuSpcM1 meet M2: SpSpc, SpSpc → SpSpcM1 meet M2: SuSpc, SuSpc → SuSpcS * M: SpSpc, SpMat → SpSpcS * M: SuSpc, SuMat → SuSpcIsConsistent(M, v): SpMat, SpVec → BoolElt, SpVecIsConsistent(M, v): SuMat, SuVec → BoolElt, SuVecIsConsistent(M, e): SpMat, SeqEnum → BoolElt, SeqEnumIsConsistent(M, e): SuMat, SeqEnum → BoolElt, SeqEnumIsConsistent(M, W): SpMat, SpMat → BoolElt, SpMat, SpMatIsConsistent(M, W): SuMat, SpMat → BoolElt, SuMat, SuMatv in M: SpVec, SpMat → BoolElt, SpVecv in M: SuVec, SpMat → BoolElt, SuVecIsSubspace(A, B): SpSpc, SpSpc → BoolElt, SpMatIsSubspace(A, B): SuSpc, SuSpc → BoolElt, SuMatExample: Sp Mod BasicsExample: Sp KernelExample: Su Module
