curate changelog
OBS-URL: https://build.opensuse.org/package/show/science/pari?expand=0&rev=62
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pari.changes
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pari.changes
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Thu Oct 27 13:41:40 UTC 2022 - Andrea Manzini <andrea.manzini@suse.com>
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- Update to release 2.15.0
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[The GP language]
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- Notion of DebugLevel "domains" that allow to finely control diagnostics.
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See setdebug()[,1] to obtain a list of domains. You can still print out
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everything using \g 10, but you can also be more specific and use
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\g qflll 10
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which sets the debug level to 10 only for the "qflll" domain,
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i.e. everything related to the LLL algorithm (there are 60 domains so far).
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The alternate syntax setdebug("qflll", 10) is available.
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- The syntax setdebug(dom, val) and default(def, val) are now recognized in
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the GPRC file
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- Recall that random(10) returns an integer in [0,9]; now random(-10) draws
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a random integer in the symetrized interval [-9,9]. More generally,
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recall that random(10 * x^3) returns a polynomial of degree <= 3 and
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coefficients in [0, 9]; now random(-10 * x3) draws coefficients in [-9,9].
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- Recall that valuation(x, t) computes the t-valuation of x; the t argument
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is now optional for types affording a natural valuation: t_PADIC, t_POL
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and t_SER:
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? valuation(sin(x))
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%1 = 1
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? valuation(175 + O(5^5))
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%2 = 2
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[Linear Algebra]
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- qflll() now implements most LLL modes in fplll (fast, dpe and heuristic),
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allowing large speedups. Directly and in the many functions that use the
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LLL algorithm.
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- new GP function snfrank(), a utility function returning q-ranks from
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Smith Normal Forms
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[Elementary Number Theory]
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- New GP function: harmonic(), to compute generalized harmonic numbers
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- Rework Euler numbers, analogously to Benoulli's: eulervec() is now
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faster and caches computed values, and a new GP function eulerreal()
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computes floating point approximations.
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- dirpowerssum() now allows to twist by a completely multiplicative function
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? dirpowerssum(N, s, n->kronecker(-23,n)) \\ sum_{n <= N} chi(n)n^{-s}
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- New GP function factormodcyclo(n, p) to quickly factor the n-th
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cyclotomic polynomial over Fp
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[Elliptic Curves]
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- New module to compute the Mordell-Weil group of rational elliptic curves:
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ell2cover ellrank ellrankinit ellsaturation
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See the tutorial (slides and video) at
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http://pari.math.u-bordeaux.fr/Events/PARI2022/index.html#ELL
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* ellrank() implements 2-descent together with Cassels's pairing
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restrictions yielding rational points and an interval for the rank. If the
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Tate-Shafarevic group has no 4 torsion and we spend enough time looking for
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rational points (on the curve and auxiliary quartics), we obtain the
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Mordell-Weil rank and generators V for a subgroup of finite index in E(Q).
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* ellrankinit() precomputes ellrank() data for all quadratic twists of E.
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* function ellsaturation(E,V,B) updates the generators V and guarantees
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than any prime dividing the index must be > B.
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* ell2cover() returns everywhere locally soluble 2-covers of E
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(rational quartics on which we try to find a rational point).
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- New GP function elltrace() summing the Galois conjugates of a point on E
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- New input format for elliptic curves: ellinit([j]) as a shortcut for
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ellfromj(j).
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[Curves of Higher Genus]
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- genus2red(): the given integral model is now a pair [P,Q] such that
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y^2+Q*y = P is minimal everywhere (was minimal over Z[1/2]).
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- new GP functions to handle models of hyperelliptic curves
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hyperelldisc hyperellisoncurve hyperellminimalmodel
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hyperellminimaldisc hyperellred
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[L-functions]
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- New module for hypergeometric motives, see ??hgm. GP functions
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hgmalpha hgmbydegree hgmcyclo hgminit
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hgmtwist hgmcoef hgmeulerfactor hgmissymmetrical
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lfunhgm hgmcoefs hgmgamma hgmparams
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See the tutorial (slides and video) at
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http://pari.math.u-bordeaux.fr/Events/PARI2022/index.html#HGM
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- New GP function lfunparams() to return the [N, k, Gamma factors] attached
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to a motivic L-function.
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- New GP function lfuneuler() to return the local Euler factor at a prime p
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[Modular Forms]
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- Faster implementation of mfinit() and mfbasis() in weight 1
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- Add optional argument to ramanujantau() to compute the newform of level 1
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and given small weight; parallelize implementation.
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[Quadratic Fields]
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- qfbcomp() now implements general composition of integral binary quadratic
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forms (of different discriminants); f * g and f^n are shorthand for
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composition and powerings of forms, including (real) extended forms with a
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Shanks distance component.
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- New GP function qfbcornacchia, solving x^2 + Dy^2 = n in integers
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in essentially linear time.
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- New GP functions quadunitindex() (index of the unit group of a quadratic
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order in the units for the maximal order), quadunitnorm() (norm of the
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fundamental unit). Used to improve qfbclassno for non fundamental
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positive discriminants.
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[General Number Fields]
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- nfinit(), nfdisc(), nfbasis() now use lazy factorization: partially
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factor the polynomial discriminant, hoping the unfactored part will be a
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square coprime to the field discriminant, and that we will be able to
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prove it via a variant of Buchmann-Lenstra's algorithm.
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- New bit in nfinit flag to prevent LLL on nf.zk, which is a major speedup
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when the field degree is large and only basic field or ideal arithmetic
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is needed.
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- New GP functions nfeltissquare() and nfeltispower() to quickly check whether
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an algebraic number is a k-th power (and obtain a k-th root when it is).
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- New GP function galoissplittinginit(T) to compute the Galois group of the
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splitting field of T. This can be used in all Galois theory functions,
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e.g., galoissubgroups(), galoisidentify(), etc.
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- New GP function nflist to list number fields with given small Galois
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group by increasing discriminant. Some groups (such as A5 and A5(6))
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require the new 'nflistdata' package. The same function gives a regular
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extension of Q(t) with the requested Galois group for all transitive
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subgroups of S_n, n <= 15.
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- New GP function nfresolvent() computes classical Galois resolvents
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attached to fields of small degree
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- Recal that ideallist(nf, B) returns integral ideals of norm bounded
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by B > 0. The new ideallist(nf, negative B) returns integral ideals
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of norm |B| (in factored form).
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[Class Field Theory]
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- New GP function bnrcompositum() to construct the compositum of two
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abelian extensions given by a class field theoretic description.
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- New module to deal with class groups of abelian fields and their Iwasawa
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invariants:
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subcyclohminus subcycloiwasawa subcyclopclgp
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See the tutorial (slides and video) at
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http://pari.math.u-bordeaux.fr/Events/PARI2022/index.html#CYCLO
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- New module to generate and compute with Hecke characters:
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gchareval gcharalgebraic gcharconductor
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gcharduallog gcharidentify gcharinit gcharisalgebraic
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gcharlocal gcharlog gcharnewprec
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See ??"Hecke Grossencharacters" as well as the tutorial at
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http://pari.math.u-bordeaux.fr/Events/PARI2022/index.html#HECKE
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[Transcendental functions]
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- New GP function lerchphi(), lerchzeta() for the Lerch Phi and zeta function.
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- New GP functions bessljzero(), besselyzero(), for J and Y Bessel functions
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- Lambert W functions are now all supported, one can specify a branch as an
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optional argument: lambertw(y, -1) corresponds to W_{-1}, defined for
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-exp(-1) <= y < 0. Complex arguments are allowed (as well as power series
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and p-adics)
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- Speedup for a number of transcendental functions at rational
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arguments, in particular atanh(), gamma() and lngamma().
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- Allow sqrtint(), sqrtnint() and logint() for positive real number arguments
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- We now allow hypergeom(N, D, t_SER)
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[Numerical summation and integration]
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- New GP function sumnumsidi() for Sidi summation.
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- New GP function intnumosc() to integrate quasi-periodic functions of
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half-period H on a real half-line:
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? \p200
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? H = Pi; intnumosc(x = 0, sinc(x), H) - Pi/2
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time = 1,241 ms.
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%2 = 0.E-211
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A number of summation algorithms are used (Lagrange, Sidi, Sumalt, Sumpos).
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See ??9 for a comparison of available integration or summation algorithms
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- Allow endpoints in solve() to by +oo or -oo
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[Miscellaneous]
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- poliscyclo(): replace Bradford-Davenport's Graeffe method by their
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invphi algorithm (much faster)
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- New GP function polsubcyclofast: fast variant of polsubcyclo() in small
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degree, returning ad hoc generators (instead of Gaussian periods)
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- New GP function poltomonic(T): fast monic integral generating polynomial
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for Q[x] / (T)
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- New GP function qfminimize to minimize a rational quadratic form.
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- New GP function setdelta() for symmetric difference.
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- New GP function serdiffdep() to find linear relations with polynomial
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coefficients of bounded degree between derivatives of a power series:
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? y = sum(i=0, 50, binomial(3*i,i)*t^i) + O(t^51);
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? serdiffdep(y, 4, 3) \\ order <= 4 and degrees <= 3
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%2 = [(27*t^2 - 4*t)*x^2 + (54*t - 2)*x + 6, 0]
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? (27*t^2 - 4*t)*y'' + (54*t - 2)*y' + 6*y
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%3 = O(T^50)
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COMPATIBILITY ISSUES BETWEEN 2.13.* and 2.15.*
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============================================
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0) Obsoleted functions and interfaces:
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- default(debugfiles,) is now obsolete, use setdebug("io",)
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- Unify real and imaginary binary quadratic forms: there are no longer
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t_QFI and t_QFR for real an imaginary forms, only generic t_QFB.
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One can still create a form using q = Qfb(a,b,c) [ or Qfb(v) if v=[a,b,c] ],
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and a pair [q, d] denotes an extended (real) form including a Shanks
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distance component 'd' (which used to be part of 'q', but no longer).
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1) Output changes:
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- system(cmd) now returns the shell return value
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- elltwist now returns an ellinit, and accepts the same input formats
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as ellinit ([a1,a2,a3,a4,a6], [a4,a6], Cremona label)
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- genus2red 3rd component is now a pair [P,Q] such that y^2+Q*y=P is
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minimal everywhere.
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2) Input changes:
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- qfbredsl2(q, S): change format of S: was [D,isD], is now isD
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* The GP language:
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* Notion of DebugLevel "domains" that allow to finely control
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diagnostics.
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* The syntax setdebug(dom, val) and default(def, val) are now
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recognized in the GPRC file.
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* Linear Algebra:
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* qflll() now implements most LLL modes in fplll (fast, dpe and
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heuristic), allowing large speedups. Directly and in the many
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functions that use the LLL algorithm.
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* New GP function snfrank(), a utility function returning
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q-ranks from Smith Normal Forms
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* Elementary Number Theory:
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* New GP function: harmonic(), to compute generalized harmonic
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numbers
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* Reworked Euler numbers, analogously to Benoulli's: eulervec()
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is now faster and caches computed values, and a new GP
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function eulerreal() computes floating point approximations.
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* Elliptic Curves: New module to compute the Mordell-Weil group
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of rational elliptic curves
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* See https://pari.math.u-bordeaux.fr/pub/pari/unix/pari-2.15.0.changelog
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for details.
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-------------------------------------------------------------------
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Wed Apr 13 18:58:43 UTC 2022 - Anton Shvetz <shvetz.anton@gmail.com>
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