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RingElement
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RingElement -- the class of all ring elements handled by the engine
See also
engine
Functions and methods returning a ring element :
Number % GroebnerBasis
-- see
%
-- a binary operator, usually used for remainder and reduction
RingElement * RingElement
-- see
*
-- a binary operator, usually used for multiplication
RingElement + RingElement
-- see
+
-- a unary or binary operator, usually used for addition
- RingElement
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
RingElement - RingElement
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
coefficient
-- coefficient of a monomial
contract(Number,RingElement)
-- see
contract(Matrix,Matrix)
-- contract a matrix by a matrix
contract(RingElement,Number)
-- see
contract(Matrix,Matrix)
-- contract a matrix by a matrix
contract(RingElement,RingElement)
-- see
contract(Matrix,Matrix)
-- contract a matrix by a matrix
determinant(Matrix)
-- see
determinant
-- determinant of a matrix
diff(RingElement,RingElement)
-- differentiation
discriminant(RingElement,RingElement)
gcd(RingElement,RingElement)
-- see
gcd
-- greatest common divisor
generator(Ideal)
-- see
generator
-- provide a single generator
generator(Module)
-- see
generator
-- provide a single generator
Ideal _ ZZ
-- see
generators of ideals and modules
homogenize(RingElement,RingElement,List)
-- see
homogenize
-- homogenize with respect to a variable
IndexedVariable _ Ring
-- get a ring variable by name
leadCoefficient(RingElement)
-- see
leadCoefficient
-- the coefficient of the leading term
leadMonomial(RingElement)
-- see
leadMonomial
-- the leading monomial of a ring element
leadTerm(RingElement)
-- get the greatest term
leadTerm(ZZ,RingElement)
-- get the lead polynomials using part of the monomial order
RingElement % GroebnerBasis
-- see
Matrix % GroebnerBasis
-- calculate the normal form of ring elements and matrices using a (partially computed) Gröbner basis
RingElement // RingElement
-- see
Matrix // Matrix
-- factor a map through another
Matrix _ Sequence
-- get entry of matrix
RingElement % RingElement
-- see
methods for normal forms and remainder
-- normal form of ring elements and matrices
MonoidElement _ Ring
(missing documentation)
part(InfiniteNumber,InfiniteNumber,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(InfiniteNumber,InfiniteNumber,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(InfiniteNumber,ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(InfiniteNumber,ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(List,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(Nothing,Nothing,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(Nothing,Nothing,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(Nothing,ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(Nothing,ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,InfiniteNumber,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,InfiniteNumber,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,Nothing,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,Nothing,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,ZZ,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
part(ZZ,ZZ,VisibleList,RingElement)
-- see
part
-- select terms of a polynomial by degree(s) or weight(s)
poincare
-- assemble degrees of a ring, module, or ideal into a polynomial
poincareN
-- assemble degrees into polynomial
poly(String)
-- make a polynomial using classic Macaulay syntax
RingElement _ Ring
-- see
promote
-- promote to another ring
pseudoRemainder(RingElement,RingElement)
-- see
pseudoRemainder
-- compute the pseudo-remainder
random(ZZ,Ideal)
-- get a random homogeneous element from a graded ideal
random(List,Ring)
-- see
random(ZZ,Ring)
-- get a random homogeneous element from a graded ring
random(ZZ,Ring)
-- get a random homogeneous element from a graded ring
resultant
-- see
resultant(RingElement,RingElement,RingElement)
Ring _ List
-- make a monomial from a list of exponents
Ring _ ZZ
-- get a ring variable by index
RingElement / RingElement
-- fraction
RingElement ^ ZZ
-- power
RingMap RingElement
-- apply a ring map
someTerms(RingElement,ZZ,ZZ)
-- see
someTerms
-- select some terms of a polynomial
String _ Ring
-- get a ring variable by name
substitute(Number,Ring)
-- see
substitute
-- substituting values for variables
substitute(Number,RingFamily)
-- see
substitute
-- substituting values for variables
substitute(RingElement,List)
-- see
substitute
-- substituting values for variables
substitute(RingElement,Matrix)
-- see
substitute
-- substituting values for variables
substitute(RingElement,Ring)
-- see
substitute
-- substituting values for variables
substitute(RingElement,RingFamily)
-- see
substitute
-- substituting values for variables
Symbol _ Ring
-- get a ring variable by name
trace(Matrix)
-- trace of a matrix
Methods that use a ring element :
Number % RingElement
-- see
%
-- a binary operator, usually used for remainder and reduction
RingElement % Number
-- see
%
-- a binary operator, usually used for remainder and reduction
Matrix * RingElement
-- see
*
-- a binary operator, usually used for multiplication
Ring * RingElement
-- see
*
-- a binary operator, usually used for multiplication
RingElement * ChainComplexMap
-- see
*
-- a binary operator, usually used for multiplication
RingElement * GradedModuleMap
-- see
*
-- a binary operator, usually used for multiplication
RingElement * Ideal
-- see
*
-- a binary operator, usually used for multiplication
RingElement * Matrix
-- see
*
-- a binary operator, usually used for multiplication
RingElement * Module
-- see
*
-- a binary operator, usually used for multiplication
RingElement * MonomialIdeal
-- see
*
-- a binary operator, usually used for multiplication
RingElement * MutableMatrix
-- see
*
-- a binary operator, usually used for multiplication
RingElement * Vector
-- see
*
-- a binary operator, usually used for multiplication
Vector * RingElement
-- see
*
-- a binary operator, usually used for multiplication
ChainComplexMap + RingElement
-- see
+
-- a unary or binary operator, usually used for addition
GradedModuleMap + RingElement
-- see
+
-- a unary or binary operator, usually used for addition
Ideal + RingElement
-- see
+
-- a unary or binary operator, usually used for addition
Matrix + RingElement
-- see
+
-- a unary or binary operator, usually used for addition
RingElement + ChainComplexMap
-- see
+
-- a unary or binary operator, usually used for addition
RingElement + GradedModuleMap
-- see
+
-- a unary or binary operator, usually used for addition
RingElement + Matrix
-- see
+
-- a unary or binary operator, usually used for addition
+ RingElement
(missing documentation)
ChainComplexMap - RingElement
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
GradedModuleMap - RingElement
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
Matrix - RingElement
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
RingElement - ChainComplexMap
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
RingElement - GradedModuleMap
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
RingElement - Matrix
-- see
-
-- a unary or binary operator, usually used for negation or subtraction
Number // RingElement
-- see
//
-- a binary operator, usually used for quotient
RingElement // Number
-- see
//
-- a binary operator, usually used for quotient
ChainComplexMap == RingElement
-- see
==
-- equality
GradedModuleMap == RingElement
-- see
==
-- equality
Matrix == RingElement
-- see
==
-- equality
Number == RingElement
-- see
==
-- equality
RingElement == ChainComplexMap
-- see
==
-- equality
RingElement == GradedModuleMap
-- see
==
-- equality
RingElement == Matrix
-- see
==
-- equality
RingElement == Number
-- see
==
-- equality
RingElement == RingElement
-- see
==
-- equality
RingElement == ZZ
-- see
==
-- equality
ZZ == RingElement
-- see
==
-- equality
analyticSpread(Ideal,RingElement)
-- see
analyticSpread
-- Compute the analytic spread of a module or ideal
analyticSpread(Module,RingElement)
-- see
analyticSpread
-- Compute the analytic spread of a module or ideal
annihilator(RingElement)
-- see
annihilator
-- the annihilator ideal
antipode(RingElement)
-- see
antipode
-- antipode for skew commuting polynomial rings
asin(RingElement)
(missing documentation)
atan(RingElement)
(missing documentation)
baseName(RingElement)
-- see
baseName
-- the base name of a generator
binomial(RingElement,ZZ)
-- see
binomial
-- binomial coefficient
clean(RR,RingElement)
-- see
clean
-- Set to zero elements that are approximately zero
coefficients(RingElement)
-- see
coefficients
-- monomials and their coefficients
cokernel(RingElement)
-- see
cokernel
-- cokernel of a map of modules, graded modules, or chaincomplexes
columnAdd(MutableMatrix,ZZ,RingElement,ZZ)
-- see
columnAdd
-- add a multiple of one column to another
columnMult(MutableMatrix,ZZ,RingElement)
-- see
columnMult
-- multiply a column by a ring element
Constant * RingElement
-- see
Constant
Constant + RingElement
-- see
Constant
Constant - RingElement
-- see
Constant
Constant / RingElement
-- see
Constant
RingElement * Constant
-- see
Constant
RingElement + Constant
-- see
Constant
RingElement - Constant
-- see
Constant
RingElement / Constant
-- see
Constant
content(RingElement)
-- see
content
-- the content of a polynomial
content(RingElement,RingElement)
-- see
content
-- the content of a polynomial
contract(Matrix,RingElement)
-- see
contract(Matrix,Matrix)
-- contract a matrix by a matrix
contract(RingElement,Matrix)
-- see
contract(Matrix,Matrix)
-- contract a matrix by a matrix
contract(RingElement,Vector)
-- see
contract(Matrix,Matrix)
-- contract a matrix by a matrix
contract(Vector,RingElement)
-- see
contract(Matrix,Matrix)
-- contract a matrix by a matrix
cos(RingElement)
(missing documentation)
cosh(RingElement)
(missing documentation)
degree(RingElement)
degree(RingElement,RingElement)
-- degree with respect to a variable
diff(RingElement,Vector)
-- see
diff(Matrix,Matrix)
-- differentiate a matrix by a matrix
diff(Vector,RingElement)
-- see
diff(Matrix,Matrix)
-- differentiate a matrix by a matrix
diff(Matrix,RingElement)
-- differentiation
diff(RingElement,Matrix)
-- differentiate each entry of a matrix
divideByVariable(Matrix,RingElement)
-- see
divideByVariable
-- divide all columns by a (power of a) variable
divideByVariable(Matrix,RingElement,ZZ)
-- see
divideByVariable
-- divide all columns by a (power of a) variable
dual(MonomialIdeal,RingElement)
-- the Alexander dual
eliminate(RingElement,Ideal)
-- see
eliminate
exp(RingElement)
expm1(RingElement)
(missing documentation)
exponents(RingElement)
-- see
exponents
-- the exponents of a polynomial
factor(RingElement)
-- factor a ring element
fraction(RingElement,RingElement)
-- see
fraction
fromDividedPowers(RingElement)
-- see
fromDividedPowers
-- Translates from divided power monomial basis to ordinary monomial basis
fromDual(RingElement)
-- see
fromDual
-- Ideal from inverse system
gcd(RingElement,ZZ)
-- see
gcd
-- greatest common divisor
gcd(ZZ,RingElement)
-- see
gcd
-- greatest common divisor
gcdCoefficients(RingElement,RingElement)
-- see
gcdCoefficients
-- gcd with coefficients
genericMatrix(Ring,RingElement,ZZ,ZZ)
-- see
genericMatrix
-- make a generic matrix of variables
genericSkewMatrix(Ring,RingElement,ZZ)
-- see
genericSkewMatrix
-- make a generic skew symmetric matrix of variables
genericSymmetricMatrix(Ring,RingElement,ZZ)
-- see
genericSymmetricMatrix
-- make a generic symmetric matrix
homogenize(Ideal,RingElement)
-- see
homogenize
-- homogenize with respect to a variable
homogenize(Matrix,RingElement)
-- see
homogenize
-- homogenize with respect to a variable
homogenize(Matrix,RingElement,List)
-- see
homogenize
-- homogenize with respect to a variable
homogenize(Module,RingElement)
-- see
homogenize
-- homogenize with respect to a variable
homogenize(Module,RingElement,List)
-- see
homogenize
-- homogenize with respect to a variable
homogenize(RingElement,RingElement)
-- see
homogenize
-- homogenize with respect to a variable
homogenize(Vector,RingElement)
-- see
homogenize
-- homogenize with respect to a variable
homogenize(Vector,RingElement,List)
-- see
homogenize
-- homogenize with respect to a variable
icPIdeal(RingElement,RingElement,ZZ)
-- see
icPIdeal
-- compute the integral closure in prime characteristic of a principal ideal
Ideal * RingElement
(missing documentation)
ideal(RingElement)
-- make an ideal
idealizer(Ideal,RingElement)
-- see
idealizer
-- compute Hom(I,I) as a quotient ring
image(RingElement)
-- see
image
-- image of a map
index(RingElement)
-- see
index
-- numeric index of a ring variable
indices(RingElement)
-- indices of variables occurring in a polynomial
InexactNumber % RingElement
(missing documentation)
InexactNumber * RingElement
(missing documentation)
InexactNumber + RingElement
(missing documentation)
InexactNumber - RingElement
(missing documentation)
InexactNumber / RingElement
(missing documentation)
InexactNumber // RingElement
(missing documentation)
InexactNumber == RingElement
(missing documentation)
installHilbertFunction(Ideal,RingElement)
(missing documentation)
installHilbertFunction(Matrix,RingElement)
(missing documentation)
installHilbertFunction(Module,RingElement)
(missing documentation)
integralClosure(Ideal,RingElement)
-- see
integralClosure(Ideal,RingElement,ZZ)
-- integral closure of an ideal in an affine domain
integralClosure(Ideal,RingElement,ZZ)
-- integral closure of an ideal in an affine domain
inverseSystem(RingElement)
-- see
inverseSystem
-- Inverse systems with equivariance
isConstant(RingElement)
-- see
isConstant
-- whether a ring element is constant
isHomogeneous(RingElement)
-- see
isHomogeneous
-- whether something is homogeneous (graded)
isLinearType(Ideal,RingElement)
-- see
isLinearType
-- Determine whether module has linear type
isLinearType(Module,RingElement)
-- see
isLinearType
-- Determine whether module has linear type
isMember(RingElement,Ideal)
-- test membership in an ideal
isNormal(RingElement)
(missing documentation)
isPrime(RingElement)
(missing documentation)
isReduction(Ideal,Ideal,RingElement)
-- see
isReduction
-- Determine whether an ideal is a reduction
isReduction(Module,Module,RingElement)
-- see
isReduction
-- Determine whether an ideal is a reduction
isUnit(RingElement)
-- see
isUnit
-- whether a ring element is a unit
jacobian(RingElement)
(missing documentation)
kernel(RingElement)
-- see
kernel(Matrix)
-- kernel of a matrix
lcm(RingElement,RingElement)
-- see
lcm
-- least common multiple
lcm(RingElement,ZZ)
-- see
lcm
-- least common multiple
lcm(ZZ,RingElement)
-- see
lcm
-- least common multiple
lift(Ideal,type of RingElement)
-- see
lift
-- lift to another ring
lift(Matrix,type of RingElement)
-- see
lift
-- lift to another ring
lift(Module,type of RingElement)
(missing documentation)
lift(MutableMatrix,type of RingElement)
(missing documentation)
lift(RingElement,type of MonoidElement)
(missing documentation)
lift(Vector,type of RingElement)
(missing documentation)
liftable(Constant,type of RingElement)
(missing documentation)
List % RingElement
(missing documentation)
List // RingElement
(missing documentation)
listForm(RingElement)
-- see
listForm
-- convert to list form
log1p(RingElement)
(missing documentation)
map(Module,Module,RingElement)
-- construct the map induced by multiplication by a ring element on the generators
Matrix ** RingElement
-- a binary operator, usually used for tensor product or Cartesian product
Matrix ++ RingElement
-- see
Matrix ++ Matrix
-- direct sum of maps
RingElement ++ Matrix
-- see
Matrix ++ Matrix
-- direct sum of maps
RingElement ++ RingElement
-- see
Matrix ++ Matrix
-- direct sum of maps
Matrix // RingElement
-- see
Matrix // Matrix
-- factor a map through another
Matrix \\ RingElement
-- see
Matrix // Matrix
-- factor a map through another
RingElement // GroebnerBasis
-- see
Matrix // Matrix
-- factor a map through another
RingElement // Matrix
-- see
Matrix // Matrix
-- factor a map through another
RingElement // MonomialIdeal
-- see
Matrix // Matrix
-- factor a map through another
RingElement \\ Matrix
-- see
Matrix // Matrix
-- factor a map through another
Matrix | RingElement
-- see
Matrix | Matrix
-- join matrices horizontally
RingElement | Matrix
-- see
Matrix | Matrix
-- join matrices horizontally
RingElement | RingElement
-- see
Matrix | Matrix
-- join matrices horizontally
Matrix || RingElement
-- see
Matrix || Matrix
-- join matrices vertically
RingElement || Matrix
-- see
Matrix || Matrix
-- join matrices vertically
RingElement || RingElement
-- see
Matrix || Matrix
-- join matrices vertically
matrix(RingElement)
-- make a matrix from a ring element
Matrix % RingElement
-- see
methods for normal forms and remainder
-- normal form of ring elements and matrices
RingElement % Ideal
-- see
methods for normal forms and remainder
-- normal form of ring elements and matrices
RingElement % Matrix
-- see
methods for normal forms and remainder
-- normal form of ring elements and matrices
RingElement % MonomialIdeal
-- see
methods for normal forms and remainder
-- normal form of ring elements and matrices
Module * RingElement
(missing documentation)
Module / RingElement
-- see
Module / Module
-- quotient module
MonomialIdeal : RingElement
(missing documentation)
monomialIdeal(RingElement)
-- see
monomialIdeal(Matrix)
-- monomial ideal of lead monomials
monomials(RingElement)
-- see
monomials
-- matrix of monomials in a ring element or matrix
multiplicity(Ideal,RingElement)
-- see
multiplicity
-- Compute the Hilbert-Samuel multiplicity of an ideal
MutableMatrix * RingElement
(missing documentation)
norm(InfiniteNumber,RingElement)
-- see
norm
norm(RingElement)
-- see
norm
norm(RR,RingElement)
-- see
norm
normalCone(Ideal,RingElement)
-- see
normalCone
-- The normal cone of a subscheme
parts(RingElement)
-- see
parts
-- display terms of a polynomial degree by degree
precision(RingElement)
-- see
precision
Ideal : RingElement
-- see
quotient(Module,Module)
-- ideal or submodule quotient
Module : RingElement
-- see
quotient(Module,Module)
-- ideal or submodule quotient
quotient(Ideal,RingElement)
-- see
quotient(Module,Module)
-- ideal or submodule quotient
quotient(Module,RingElement)
-- see
quotient(Module,Module)
-- ideal or submodule quotient
quotient(MonomialIdeal,RingElement)
-- see
quotient(Module,Module)
-- ideal or submodule quotient
quotientRemainder(InexactNumber,RingElement)
-- see
quotientRemainder(RingElement,RingElement)
-- quotient and remainder
quotientRemainder(Number,RingElement)
-- see
quotientRemainder(RingElement,RingElement)
-- quotient and remainder
quotientRemainder(RingElement,InexactNumber)
-- see
quotientRemainder(RingElement,RingElement)
-- quotient and remainder
quotientRemainder(RingElement,Number)
-- see
quotientRemainder(RingElement,RingElement)
-- quotient and remainder
quotientRemainder(RingElement,RingElement)
-- quotient and remainder
radicalContainment(RingElement,Ideal)
-- see
radicalContainment
-- whether an element is contained in the radical of an ideal
reesAlgebra(Ideal,RingElement)
-- see
reesAlgebra
-- Compute the defining ideal of the Rees Algebra
reesAlgebra(Module,RingElement)
-- see
reesAlgebra
-- Compute the defining ideal of the Rees Algebra
reesIdeal(Ideal,RingElement)
-- see
reesIdeal
-- Compute the defining ideal of the Rees Algebra
reesIdeal(Module,RingElement)
-- see
reesIdeal
-- Compute the defining ideal of the Rees Algebra
resultant(RingElement,RingElement,RingElement)
ring(RingElement)
-- see
ring
-- get the associated ring of an object
Ring / RingElement
-- see
Ring / Ideal
-- make a quotient ring
RingElement % InexactNumber
(missing documentation)
RingElement * InexactNumber
(missing documentation)
RingElement * Tally
(missing documentation)
RingElement * VirtualTally
(missing documentation)
RingElement + Ideal
(missing documentation)
RingElement + InexactNumber
(missing documentation)
RingElement - InexactNumber
(missing documentation)
RingElement .. RingElement
-- a sequence of consecutive generators of a polynomial ring
RingElement .. Thing
(missing documentation)
RingElement ..< RingElement
-- a sequence of consecutive generators of a polynomial ring
RingElement ..< Thing
(missing documentation)
RingElement / InexactNumber
(missing documentation)
RingElement // InexactNumber
(missing documentation)
RingElement == InexactNumber
(missing documentation)
RingElement _ Monoid
(missing documentation)
RingElement _ Thing
(missing documentation)
RingElement Number
-- see
RingElement Sequence
-- evaluation of polynomials
RingElement RingElement
-- see
RingElement Sequence
-- evaluation of polynomials
RingElement Sequence
-- evaluation of polynomials
ringFromFractions(Matrix,RingElement)
-- see
ringFromFractions
-- find presentation for f.g. ring
roots(RingElement)
-- compute the roots of a polynomial
rowAdd(MutableMatrix,ZZ,RingElement,ZZ)
-- see
rowAdd
-- add a multiple of one row to another
rowMult(MutableMatrix,ZZ,RingElement)
-- see
rowMult
-- multiply a row by a ring element
saturate(Ideal,RingElement)
-- see
saturate
-- saturation of ideal or submodule
saturate(Module,RingElement)
-- see
saturate
-- saturation of ideal or submodule
saturate(MonomialIdeal,RingElement)
-- see
saturate
-- saturation of ideal or submodule
saturate(Vector,RingElement)
-- see
saturate
-- saturation of ideal or submodule
sec(RingElement)
(missing documentation)
sech(RingElement)
(missing documentation)
sin(RingElement)
(missing documentation)
sinh(RingElement)
(missing documentation)
size(RingElement)
-- see
size
-- the size of an object
specialFiber(Ideal,RingElement)
-- see
specialFiber
-- Special fiber of a blowup
specialFiber(Module,RingElement)
-- see
specialFiber
-- Special fiber of a blowup
specialFiberIdeal(Ideal,RingElement)
-- see
specialFiberIdeal
-- Special fiber of a blowup
specialFiberIdeal(Module,RingElement)
-- see
specialFiberIdeal
-- Special fiber of a blowup
standardForm(RingElement)
-- see
standardForm
-- convert to standard form
substitute(RingElement,Option)
-- see
substitute
-- substituting values for variables
support(RingElement)
-- see
support
-- list of variables occurring in a polynomial or matrix
sylvesterMatrix(RingElement,RingElement,RingElement)
tan(RingElement)
(missing documentation)
tanh(RingElement)
(missing documentation)
terms(Ring,RingElement)
-- see
terms
-- provide a list of terms of a polynomial
terms(RingElement)
-- see
terms
-- provide a list of terms of a polynomial
testHunekeQuestion(RingElement)
-- see
testHunekeQuestion
-- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
Thing .. RingElement
(missing documentation)
Thing ..< RingElement
(missing documentation)
toDividedPowers(RingElement)
-- see
toDividedPowers
-- Translates to divided power monomial basis from ordinary monomial basis
topCoefficients(RingElement)
-- see
topCoefficients
-- first variable and its coefficient of a polynomial or matrix
vector(Module,RingElement)
-- see
vector
-- make a vector
vector(RingElement)
-- see
vector
-- make a vector
weightRange(List,RingElement)
-- see
weightRange
-- the pair of lowest and highest weights of the monomials
weightRange(RingElement)
-- see
weightRange
-- the pair of lowest and highest weights of the monomials
For the programmer
The object
RingElement
is
a
type
, with ancestor classes
BasicList
<
Thing
.