Changeset 475f8b in git for doc/usercard.tex
 Timestamp:
 Jun 18, 1998, 10:27:38 PM (25 years ago)
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 (u'spielwiese', 'ec94ef7a30b928574c0c3daf41f6804dff5f6b69')
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 bbbb4eaba2da8de30042f4773a96a350b8660f53
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 f7bdb8d25ea232b54a420f71935785dd3cace954
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doc/usercard.tex
rf7bdb8 r475f8b 1 % $Id: usercard.tex,v 1. 5 19980618 15:46:17schmidt Exp $1 % $Id: usercard.tex,v 1.6 19980618 20:27:38 schmidt Exp $ 2 2 3 3 % … … 60 60 61 61 \sec Names and objects() 62 \sectext 63 Names (= identifiers) have to be declared before they are used:\cr 64 \entryskip 62 65 \longentry {\it type\/} {\it name\/} \opt{= {\it expression\/}};& 63 declare variable {\it name}. All names (= 64 identifiers) have to be declared before 65 they are used.\cr 66 declare variable {\it name}\cr 66 67 kill({\it name\/})& delete variable {\it name}\cr 67 68 \entryskip … … 369 370 \entryskip 370 371 \longentry fetch({\it ringname}, {\it name\/})& 371 map object {\it name\/} from ring {\it372 ringname\/} to current base\ring. The rings373 have to be ``almost'' identical.\cr372 map from ring {\it ringname\/} to current 373 base\ring. The rings have to be identical up 374 to names of ring variables\cr 374 375 \longentry imap({\it ringname}, {\it name\/})& 375 map object {\it name\/} from subring {\it376 ringname\/} to currentbasering\cr376 map from subring {\it ringname\/} to current 377 basering\cr 377 378 \longentry subst({\it expression}, {\it ringvar}, {\it monomial\/})& 378 379 substitute {\it ringvar\/} by {\it monomial\/} … … 381 382 382 383 \sec Miscellany(1.5cm) 383 \longentry setring({\it name\/})&384 make {\it name\/} the current basering\cr384 \longentry setring({\it ringname\/})& 385 make {\it ringname\/} the current basering\cr 385 386 \subsec{Data on polynomials} 386 387 \longentry ord({\it poly\/\alt vector\/})& … … 395 396 (2) number of monomials; (3) length\cr 396 397 \longentry lead({\it expression\/})& 397 return initial term(s) of {\it expression}\cr398 return initial term(s)\cr 398 399 \subsec{Operations on polynomials} 399 400 \longentry gcd({\it $\hbox{poly}_1$}, {\it $\hbox{poly}_2$\/})& 400 return greatest common divisor of {\it 401 $\hbox{poly}_1$\/} and {\it $\hbox{poly}_2$}\cr 401 return greatest common divisor\cr 402 402 \longentry factorize({\it poly\/}\opt{, {\it int\/}})& 403 return irreducible factors of {\it poly}. A404 constant factor and multiplicities are returned405 in dependency on {\it int}.\cr403 return irreducible factors. Return constant 404 factor and multiplicities in dependency on {\it 405 int}.\cr 406 406 \endsec 407 407 … … 410 410 diff({\it expression}, {\it ringvar\/})\par 411 411 diff({\it $\hbox{ideal}_1$}, {\it $\hbox{ideal}_2$\/})& 412 (1) return partial deriv .\ of {\it expression\/}413 by {\it ringvar\/}; (2) differentiate each elt.\414 of {\it$\hbox{ideal}_2$\/} by the differential415 operators corres ponding to the elements of {\it412 (1) return partial derivation by {\it 413 ringvar\/}; (2) differentiate each elt.\ of {\it 414 $\hbox{ideal}_2$\/} by the differential 415 operators corres\pon\ding to the elements of {\it 416 416 $\hbox{ideal}_1$}\cr 417 417 \longentry jacob({\it poly\/\alt ideal\/})& 418 return thejacobi ideal or matrix, resp.\cr418 return jacobi ideal or matrix, resp.\cr 419 419 \longentry jet({\it expression}, {\it int\/}\opt{, {\it intvec\/}})& 420 return the{\it int\/}jet of {\it expression}.420 return {\it int\/}jet of {\it expression}. 421 421 Return weighted {\it int\/}jet if {\it 422 422 intvec\/} is specifified.\cr 423 423 \endsec 424 425 \eject 424 426 425 427 \sec Standard bases(1.5cm) … … 435 437 \longentry stdfglm({\it ideal\/}\opt{, {\it string\/}})& 436 438 use FGLM algorithm to compute a SB from a SB 437 w.r.t.\ a ``simple'' ordering {\it string\/}439 w.r.t.\ the ``simpler'' ordering {\it string\/} 438 440 (de\faults to {\tt dp})\cr 439 441 \longentry stdhilb({\it ideal\/}\opt{, {\it intvec\/}})& … … 451 453 \endsec 452 454 453 \sec Invariants of ideals and modules(1.5cm) 455 \sec Computation of invariants(1.5cm) 456 \sectext 457 Most of the results are meaningful only if the input ideal or module is 458 represented by a standard basis.\cr 459 \longentry degree({\it ideal\/\alt module\/})& 460 display (Krull) dimension, codimension and 461 multiplicity\cr 462 \longentry dim({\it ideal\/\alt module\/})& 463 return (Krull) dimension\cr 454 464 \longentry hilb({\it ideal\/\alt module\/}\opt{, {\it int\/}})& 455 465 display first and second Hilbert series with one 456 argument.\cr 466 argument. Return {\it int}th Hilber series 467 otherwise (${\it \hbox{int}} = 1,2$).\cr 468 \longentry mult({\it ideal\/\alt module\/})& 469 return multiplicity\cr 470 \longentry vdim({\it ideal\/\alt module\/})& 471 return vector space dimension of current 472 basering modulo {\it ideal\/} or {\it module}, 473 resp.\cr 474 \endsec 475 476 \sec Resolutions(1.5cm) 477 \sectext 478 An integer argument {\it length\/} in the following descriptions specifies the 479 length of the resolution to compute. If {\it length\/} equals zero, the whole 480 resolution is computed.\cr 481 \longentry res({\it ideal\/\alt module}, {\it length\/}\opt{, {\it int\/}})& 482 compute a free resolution (FR) of {\it ideal\/} 483 resp.\ {\it module\/} using a heuristically 484 chosen method. Compute a minimal resolution if 485 a third argument is given.\cr 486 \longentry mres({\it ideal\/\alt module}, {\it length\/})& 487 compute a minimal FR using the standard basis 488 method\cr 489 \longentry lres({\it ideal\/\alt module}, {\it length\/})& 490 compute a FR using LaSacala's method\cr 491 \longentry sres({\it ideal\/\alt module}, {\it length\/})& 492 compute a FR using Schreyer's method\cr 493 \longentry syz({\it ideal\/\alt module\/})& 494 compute the first syzygy\cr 495 \longentry minres({\it resolution\/\alt list\/})& 496 minimize a free resolution\cr 497 \longentry betty({\it resolution\/\alt list\/})& 498 compute the graded Betti numbers of a module 499 represented by a resolution\cr 457 500 \endsec 458 501
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