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Macaulay2Doc
::
RingElement
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
"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
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
"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
discriminant(RingElement,RingElement)
"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)
-- exponential function
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
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 + 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 Array
-- substitution of variables
"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
"variety(RingElement)"
-- see
variety(Ring)
-- the variety previously associated to a given ring
"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
.