2.11.3 Commands and Functions for RINGELEM |
abs | absolute value of a number |
apply | apply homomorphism |
ApproxSolve | Approximate real solutions for polynomial system |
AsINT | convert into an INT |
AsRAT | convert into a RAT |
binomial | binomial coefficient |
CanonicalRepr | representative of a class in a quotient ring |
CharPoly | characteristic polynomial of a matrix |
ClearDenom | clear common denominator of a polynomial with rational coeffs |
coefficients | list of coefficients of a polynomial |
CoefficientsWRT | list of coeffs and PPs of a poly wrt indet or list of indets |
CoeffListWRT | list of coefficients of a polynomial wrt and indet |
CoeffOfTerm | coefficient of a term of a polynomial |
content | content of a polynomial |
ContentFreeFactor | factorization of multivariate polynomial into content-free factors |
ContentWRT | content of a polynomial wrt and indet or a list of indets |
CRTPoly | Chinese Remainder Theorem on polynomial coefficients |
cyclotomic | n-th cyclotomic polynomial |
DecimalStr | convert rational number to decimal string |
deg | the standard degree of a polynomial or moduleelem |
den | denominator |
deriv | the derivative of a polynomial or rational function |
DerivationAction | Action of a derivation |
DF | the degree form of a polynomial |
discriminant | the discriminant of a polynomial |
DivAlg | division algorithm |
eigenfactors | eigenfactors of a matrix |
eigenvectors | eigenvalues and eigenvectors of a matrix |
elim | eliminate variables |
eval | substitute numbers or polynomials for indeterminates |
EvalQuasiPoly | Evaluate a quasi-polynomial at an integer |
exponents | the list of exponents of the leading term of a polynomial |
factor | factor a polynomial |
FloatApprox | approx. of rational number of the form M*2^E |
FloatStr | convert rational number to a decimal string |
FrbAlexanderDual | Alexander Dual of monomial ideals |
gcd | greatest common divisor |
GenRepr | representation in terms of generators |
homog | homogenize with respect to an indeterminate |
ideal | ideal generated by list |
IndetIndex | index of an indeterminate |
IndetName | the name of an indeterminate |
IndetSubscripts | the index of an indeterminate |
interreduce, interreduced | interreduce a list of polynomials |
IsConstant | checks if a ringelem is in the coefficient ring |
IsDivisible | checks if A is divisible by B |
IsElem | checks if A is an element of B |
IsHomog | test whether given polynomials are homogeneous |
IsIn | check if one object is contained in another |
IsIndet | checks argument is an indetermiante |
IsInRadical | check if a polynomial (or ideal) is in a radical |
IsInteger | check if a RINGELEM is integer |
IsInvertible | check if a RINGELEM is invertible |
IsIrred | check if a RINGELEM is irreducible |
IsOne | test whether an object is one |
IsPthPower | p-th power test |
IsRational | check if a RINGELEM is rational |
IsSqFree | check if an INT or RINGELEM is square-free |
IsTerm | checks if the argument is a term |
IsZero | test whether an object is zero |
IsZeroDivisor | test whether a RINGELEM is a zero-divisor |
jacobian | the Jacobian of a list of polynomials |
LC | the leading coefficient of a polynomial or ModuleElem |
lcm | least common multiple |
LF | the leading form of a polynomial or an ideal |
LinearSimplify | simplifying linear substitution for a univariate poly over QQ |
LM | the leading monomial of a polynomial or ModuleElem |
LPP | the leading power-product of a polynomial or ModuleElem |
LT | the leading term of an object |
MantissaAndExponent2 | convert rational number to a binary float |
max | a maximum element of a sequence or list |
min | a minimum element of a sequence or list |
MinPoly | minimal polynomial of a matrix |
MinPolyModular | minimal polynomial with modular method |
MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat | compute a minimal polynomial |
MinPowerInIdeal | the mininum power of a polynomial is an ideal |
monic | divide polynomials by their leading coefficients |
monomials | the list of monomials of a polynomial |
MultiplicationMat | the multiplication matrix of a ringelem |
NewMatFilled | matrix filled with value |
NF | normal form |
NmzEhrhartRing | Computes the Ehrhart ring |
NmzIntClosureMonIdeal | integral closure of a monomial ideal |
NmzIntClosureToricRing | integral closure of a toric ring |
NmzNormalToricRing | normalization of a toric ring |
NR | normal reduction |
num | numerator |
NumTerms | number of terms in a polynomial |
PerpIdealOfForm | Ideal of derivations annihilating a form |
PreImage | preimage of a RINGELEM |
product | the product of the elements of a list |
PthRoot | Compute p-th root |
QZP | change field for polynomials and ideals |
randomize | randomize the coefficients of a given polynomial |
randomized | randomize the coefficients of a given polynomial |
RationalAffinePoints | Affine rational solutions |
RationalProjectivePoints | Projective rational solutions |
RationalSolve | Rational solutions for polynomial system |
RatReconstructPoly | Rational reconstruction of polynomial coefficents |
RealRoots | computes the real roots of a univariate polynomial |
RealRootsApprox | approximations to the real roots of a univariate poly |
resultant | the resultant of two polynomials |
RingElem | convert an expression into a RINGELEM |
RingOf | the ring of the object |
RingsOf | list of the rings of an object |
RootBound | bound on roots of a polynomial over QQ |
ScientificStr | convert integer/rational to a floating-point string |
SqFreeFactor | compute a squarefree factorization |
StarPrint, StarSprint | print polynomial with *'s for multiplications |
SubalgebraRepr | representation of a polynomial as a subalgebra element |
subst | substitute values for indeterminates |
sum | the sum of the elements of a list |
support | the list of terms of a polynomial or moduleelem |
sylvester | the Sylvester matrix of two polynomials |
syz | syzygy modules |
UnivariateIndetIndex | the index of the indeterminate of a univariate polynomial |
wdeg | multi-degree of an polynomial |
ZPQ | change field for polynomials and ideals |