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 An, 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 |