Support
The SINGULAR Team provides free support.
Release
February 2010: Release of SINGULAR version 3-1-1. More
Jenks Prize
July 2004: The Richard D. Jenks Prize for Excellence in Software Engineering for Computer Algebra was awarded to the Singular team. More
Book: "A Singular Introduction to Commutative Algebra"
SINGULAR Examples
algebraic dependence, 87 |
annihilator, 186 |
Betti numbers, 135 |
- graded, 137 |
classification of singularities, 493 |
computation |
- in fields, 5 |
- in polynomial rings, 7 |
- in quotient rings, 25 |
- of d(I,K[x]), 222 |
- of Hom, 106 |
- of the dimension, 211 |
- of Tor, 340 |
computing with radicals, 27 |
counting nodes, 489 |
creating ring maps, 8 |
cyclic decomposition, 159 |
deformation of singularities, 495 |
degree, 289 |
- of projection, 469 |
- of projective variety, 478 |
diagonal form, 154 |
dimension, 289 |
- embedding, 304 |
- of a module, 302 |
elimination |
- and resultant, 431 |
- of module components, 180 |
- of variables, 71 |
- projective, 466 |
equidimensional |
- decomposition, 263 |
- part, 261 |
estimating the determinacy, 491 |
finite maps, 196 |
finiteness test, 324 |
Fitting ideal, 186, 345 |
flat locus, 356 |
flatness test, 369 |
flattening stratification, 352 |
global versus local rings, 35 |
graded |
- Betti numbers, 137 |
- rings and modules, 116 |
highest corner, 60 |
Hilbert |
- function, 289 |
- polynomial, 299 |
Hilbert-Poincare series, 282 |
homogeneous resolution, 137 |
ideal membership, 68 |
image of module homomorphism, 99 |
independent set, 220 |
initial ideal, 299 |
injective, 420 |
integral |
- closure of an ideal, 202 |
- elements, 195 |
intersection |
- of ideals, 79 |
- of submodules, 102, 181 |
inverse of a power series, 316 |
Jacobian criterion, 304 |
Jordan normal form, 163 |
kernel |
- of a ring map, 85 |
- of module homomorphism, 99, 187 |
Koszul complex, 378 |
leading data, 11 |
linear combination of ideal members, 68 |
local and global dimension, 472 |
lying over theorem, 225 |
maps induced by Hom, 96 |
matrix operations, 94 |
Milnor and Tjurina number, 488 |
minimal |
- associated primes, 209 |
- presentations, 109 |
module |
- annihilator, 186 |
- membership, 178 |
- presentation of, 104 |
- quotient, 102 |
- radical and zerodivisors, 184 |
monomial orderings, 16 |
morphisms of projective varieties, 455 |
multiplicity, 480 |
Noether normalization, 216 |
non-normal locus, 232 |
normal form, 51, 123 |
normalization, 230 |
Poincare series, 299 |
presentation of a module, 104 |
primary |
- decomposition, 258 |
- test, 252 |
projective |
- closure, 443 |
- elimination, 466 |
- Nullstellensatz, 437 |
- subschemes, 446 |
properties of ring maps, 20 |
quotient |
- of ideals, 81 |
- of submodules, 102, 183 |
radical, 184, 265 |
- membership, 78 |
realization of rings, 42 |
reduction to zero-dimensional case, 257 |
regular |
- sequences, 372 |
- system of parameters, 304 |
regularity test, 400 |
resolution, 135 |
- homogeneous, 137 |
saturation, 83, 446 |
Schreyer resolution, 150 |
singular locus, 309 |
solving equations, 76 |
- linear, 189 |
standard bases, 59, 124 |
subalgebra membership, 87 |
submodules, 104 |
- intersection of, 102, 181 |
- of A^{n}, 98 |
sum of submodules, 102 |
surface plot, 407, 413 |
surjective, 420 |
syzygies, 141 |
tangent cone, 480 |
tensor product |
- of maps, 170 |
- of modules, 172 |
- of rings, 175 |
test |
- for Cohen-Macaulayness, 386, 392, 394 |
- for flatness, 354 |
- for local freeness, 347 |
Weierstrass polynomial, 321 |
Zariski closure of the image, 74 |
zero-dimensional primary decomposition, 253 |
zerodivisors, 184 |
z-general power series, 320 |