2.11.4 Commands and Functions returning RINGELEM |
abs | absolute value of a number |
apply | apply homomorphism |
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 |
CoeffListWRT | list of coefficients of a polynomial wrt and indet |
CoeffOfTerm | coefficient of a term of a polynomial |
ComputeElimFirst | ComputeElimFirst |
content | content of a polynomial |
ContentWRT | content of a polynomial wrt and indet or a list of indets |
cyclotomic | n-th cyclotomic polynomial |
den | denominator |
DensePoly | the sum of all power-products of a given degree |
deriv | the derivative of a polynomial or rational function |
det | the determinant of a matrix |
DF | the degree form of a polynomial |
discriminant | the discriminant of a polynomial |
eigenfactors | eigenfactors of a matrix |
EvalQuasiPoly | Evaluate a quasi-polynomial at an integer |
FirstNonZero | the first non-zero entry in a MODULEELEM |
FirstNonZeroPosn | the first non-zero entry in a MODULEELEM |
gcd | greatest common divisor |
GraverBasis | Graver basis |
HilbertPoly | the Hilbert polynomial |
homog | homogenize with respect to an indeterminate |
ImplicitHypersurface | implicitization of hypersurface |
indet | individual indeterminates |
Interpolate | interpolating polynomial |
interreduce, interreduced | interreduce a list of polynomials |
InverseSystem | Inverse system of an ideal of derivations |
JanetBasis | the Janet basis of an ideal |
LC | the leading coefficient of a polynomial or ModuleElem |
lcm | least common multiple |
LF | the leading form of a polynomial or an ideal |
LinKerBasis | find the kernel of a matrix |
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 |
MakeTerm | returns a monomial (power-product) with given exponents |
MinPoly | minimal polynomial of a matrix |
MinPolyModular | minimal polynomial with modular method |
MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat | compute a minimal polynomial |
monic | divide polynomials by their leading coefficients |
NF | normal form |
NmzDiagInvariants | ring of invariants of a diagonalizable group action |
NmzEhrhartRing | Computes the Ehrhart ring |
NmzFiniteDiagInvariants | ring of invariants of a finite group action |
NmzIntClosureMonIdeal | integral closure of a monomial ideal |
NmzIntClosureToricRing | integral closure of a toric ring |
NmzIntersectionValRings | intersection of ring of valuations |
NmzNormalToricRing | normalization of a toric ring |
NmzTorusInvariants | ring of invariants of torus action |
NR | normal reduction |
num | numerator |
one | one of a ring |
pfaffian | the Pfaffian of a skew-symmetric matrix |
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 |
ReadExpr | Read RINGELEM expression from string |
ReducedGBasis | compute reduced Groebner basis |
resultant | the resultant of two polynomials |
RingElem | convert an expression into a RINGELEM |
SymbolRange | range of symbols for the indeterminates of a PolyRing |
SymmetricPolys | list of symmetric polynomials |
UniversalGBasis | universal Groebner basis of the input ideal |
zero | zero of a ring |
ZPQ | change field for polynomials and ideals |