i1 : help --loading the Macaulay2 documentation from /builddir/build/BUILD/Macaulay2-1.5-r15955/M2/Macaulay2/packages/Macaulay2Doc/ --warning: symbol "hilbertBasis" in FourTiTwo.Dictionary is shadowed by a symbol in Polyhedra.Dictionary -- use the synonym FourTiTwo$hilbertBasis --warning: symbol "rays" in FourTiTwo.Dictionary is shadowed by a symbol in Polyhedra.Dictionary -- use the synonym FourTiTwo$rays --warning: symbol "generalEquations" in PHCpack#"private dictionary" is shadowed by a symbol in NAGtypes.Dictionary -- no synonym is available --warning: symbol "addSlackVariables" in PHCpack#"private dictionary" is shadowed by a symbol in NAGtypes.Dictionary -- no synonym is available --warning: symbol "tDegree" in NumericalAlgebraicGeometry#"private dictionary" is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$tDegree --warning: symbol "gamma" in NumericalAlgebraicGeometry#"private dictionary" is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$gamma --warning: symbol "tDegree" in NumericalAlgebraicGeometry.Dictionary is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$tDegree --warning: symbol "gamma" in NumericalAlgebraicGeometry.Dictionary is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$gamma --warning: symbol "tDegree" in NumericalAlgebraicGeometry#"private dictionary" is shadowed by a symbol in PHCpack.Dictionary -- use one of the synonyms NAG$tDegree, NumericalAlgebraicGeometry$tDegree --warning: symbol "gamma" in NumericalAlgebraicGeometry#"private dictionary" is shadowed by a symbol in PHCpack.Dictionary -- use one of the synonyms NAG$gamma, NumericalAlgebraicGeometry$gamma --warning: symbol "tDegree" in NumericalAlgebraicGeometry.Dictionary is shadowed by a symbol in PHCpack.Dictionary -- use one of the synonyms NAG$tDegree, NumericalAlgebraicGeometry$tDegree --warning: symbol "gamma" in NumericalAlgebraicGeometry.Dictionary is shadowed by a symbol in PHCpack.Dictionary -- use one of the synonyms NAG$gamma, NumericalAlgebraicGeometry$gamma --warning: symbol "vertices" in SimplicialComplexes.Dictionary is shadowed by a symbol in Graphs.Dictionary -- use the synonym SimplicialComplexes$vertices --warning: symbol "Certification" in Core.Dictionary is shadowed by a symbol in RandomObjects#"private dictionary" -- use the synonym Core$Certification --warning: symbol "Certification" in Core.Dictionary is shadowed by a symbol in RandomObjects.Dictionary -- use the synonym Core$Certification --warning: symbol "nextPrime" in RandomSpaceCurves.Dictionary is shadowed by a symbol in RandomPlaneCurves.Dictionary -- use the synonym RandomSpaceCurves$nextPrime --warning: symbol "PushForward" in PackageDictionary is shadowed by a symbol in Schubert2#"private dictionary" -- use the synonym Package$PushForward --warning: symbol "PushForward" in PackageDictionary is shadowed by a symbol in Schubert2.Dictionary -- use the synonym Package$PushForward o1 = initial help ************ Welcome to Macaulay2 Try entering '2+2' at your next input prompt, which begins with i. The two output prompts begin with o. The first one, with the equal sign, '=', gives the value computed from your input, and the second one, with the colon, ':', tells what type of thing the value is. Type one of these commands to get started reading the documentation: * copyright -- the copyright * help "Macaulay2" -- top node of the documentation. * help "reading the documentation" -- * help "getting started" -- * help "a first Macaulay2 session" -- * help x -- display the documentation for x * ? f -- display brief documentation for a function f * printWidth = 80 -- set print width to 80 characters * viewHelp -- view documentation in a browser * viewHelp x -- view documentation on x in browser To read the documentation in info form, in case you happen to be running Macaulay2 in a terminal window, replace "help" by "infoHelp" in any of the commands above. o1 : DIV |
i2 : help ideal o2 = ideal -- make an ideal ********************** Ways to use ideal : =================== * "ideal(List)" -- make an ideal * ideal(Sequence), see "ideal(List)" -- make an ideal * "ideal(Matrix)" -- make an ideal * "ideal(Module)" -- converts a module to an ideal * "ideal(MonomialIdeal)" -- converts a monomial ideal to an ideal * ideal(QuotientRing), see "ideal(Ring)" -- returns the defining ideal * "ideal(Ring)" -- returns the defining ideal * ideal(Number), see "ideal(RingElement)" -- make an ideal * "ideal(RingElement)" -- make an ideal * "ideal(String)" -- make an ideal using classic Macaulay syntax * "ideal(Variety)" -- returns the defining ideal o2 : DIV |
i3 : help (ideal,List) o3 = ideal(List) -- make an ideal **************************** Synopsis ======== * Usage:ideal L * Function: "ideal" * Inputs: * L, a list, or a sequence of ring elements * Outputs: * an ideal, which is generated by the list or sequence of ring elements Description =========== +--------------------------------------------+ |i1 : R = ZZ/101[w,x,y,z]; | +--------------------------------------------+ |i2 : ideal{x^2-w*y, x*y-w*z, x*z-y^2} | | | | 2 2 | |o2 = ideal (x - w*y, x*y - w*z, - y + x*z)| | | |o2 : Ideal of R | +--------------------------------------------+ |i3 : ideal(y^2-x*z,x^2*y-z^2,x^3-y*z) | | | | 2 2 2 3 | |o3 = ideal (y - x*z, x y - z , x - y*z) | | | |o3 : Ideal of R | +--------------------------------------------+ |i4 : E = ZZ/2[x,y, SkewCommutative => true];| +--------------------------------------------+ |i5 : ideal(x^2,x*y) | | | |o5 = ideal (0, x*y) | | | |o5 : Ideal of E | +--------------------------------------------+ |i6 : W = QQ[x,dx, WeylAlgebra => {x => dx}];| +--------------------------------------------+ |i7 : ideal(dx*x+x*dx) | | | |o7 = ideal(2x*dx + 1) | | | |o7 : Ideal of W | +--------------------------------------------+ |i8 : I = ideal(12,18) | | | |o8 = ideal (12, 18) | | | |o8 : Ideal of ZZ | +--------------------------------------------+ |i9 : mingens I | | | |o9 = | 6 | | | | | 1 1 | |o9 : Matrix ZZ <--- ZZ | +--------------------------------------------+ An empty list or sequence of generators will yield an ideal of "ZZ", which can be promoted to another ring, if desired. +-------------------+ |i10 : ideal () | | | |o10 = ideal () | | | |o10 : Ideal of ZZ | +-------------------+ |i11 : promote(oo,R)| | | |o11 = ideal () | | | |o11 : Ideal of R | +-------------------+ See also ======== * "Ideal" -- the class of all ideals * "PolynomialRing" -- the class of all ordered monoid rings o3 : DIV |