PARI 2.18.1 alpha released (prerelease for PARI 2.19.0)

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

Dear PARI lovers,

I have released PARI 2.18.1-alpha as a preview of PARI 2.19.0 that we will release
in September. Please test, this is a major update.

This release include a work-around to make parallelism reliable on macos.

See <https://pari.math.u-bordeaux.fr/download.html> for download options.

On behalf of the PARI team,
Bill

P.S.: the changelog:

Bug numbers refer to the BTS at http://pari.math.u-bordeaux.fr/Bugs/
Done for version 2.18.1 (released 24/07/2026):
  Fixed
     1- reduce memory use in Z_ppo
BA   2- ellrootno over number fields could be slow [#2595]
BA   3- matsolvemod could fail [#2604]
BA   4- nfcompositum(nfinit(y-2),x^2-y,x^3-x-1) -> error [#2605]
     5- vecsearch(t_MAT, t_COL or t_VEC) -> error
     6- Mod(a,A) == Mod(b,B) was checking a == b && A == B instead
        of the documented Mod(a,A) - Mod(b,B) == 0
     7- charpoly: memory leak
     8- normlp(, oo): support components equal to oo or -oo
BA   9- lfungenus2 could give wrong result at odd primes (#2487)
    10- sqrtn(27+O(3^4),3) -> 1 + O(3) (wrong valuation in Qp_sqrtn_ram)
    11- vectorsmall(5, i, 2^63-1).normfu -> SEGV
AP  12- alginit would sometimes not sort primes -> wrong alghasse
AP  13- alginit(nf,[a,b]) would reject a in basis form
BA  14- for(i=1,10^6,bernpol(5,1)) -> "no more variables" [#2611]
BA  15- Flx_mod_Xn1(T,n), deg T >= 2*n -> wrong result
    16- forprime(p=1099505335069-100000,1099505335069+10000,) -> crash [#2612]
    17- sumnumrat & friends: use full precision estimates to avoid failing with
        domain error when "close" to boundary, e.g., sumeulerrat(1/p, 1+1e-17)
    18- zeta([3,2,1]) -> oo-loop
BA  19- parforeach([1..1000],j,vector(10^5,i,i)) -> stack overflow
    20- mfpetersson() incorrect when one form not cuspidal
    21- gc_all: support any number of arguments
    22- lift_to_frac: use of cgiv could corrupt PARI stack
    23- sumeulerrat / prodeulerrat fail in cases where they shouldn't [#2620]
        e.g., sumeulerrat(1/(p^2-5),1.1), prodeulerrat(1+1/(p^2-p-23),0.6)
    24- lfun(bnr, vector of chars) -> impossible division [#2623]
    25- incgam(0,10^-50) -> GEN corruption
BA  26- 12*harmonic(1) -> 12/1
    27- hyperellratpoints(P, d) could miss points when P(-d) = 0
    28- obscure bnrclassfield bug [internally creating an incorrect ideal
        factorization whose prime ideals were not sorted]
BA  29- qfeval(Qfb(2,3,4),[1,2;3,4]).disc was wrong [#2630]
    30- bnfisunit: could fail to detect non-S-units
    31- elliptic functions ignored ellperiods(,1) quasi-period component
BA  32- lfunan: overflow error with large bad primes.
    33- Z[CM]_hnfremdiv(A,B,&Q) was setting Q to the negative of the
        documented value
    34- mftonew: fix problem with mfbd forms [#2619]
    35- lfunthetainit: lost accuracy for large shifts.
HC  36- hypergeom([8,8.5],7,-0.4) was wrong [#2628]
HC  37- lfunmfspec(L) divided by zero if period vanishes
BA  38- fforder(,factor(1)) -> crash [#2618]
    39- mateigen must not call qfjacobi on non-real matrices [#2636]
BA  40- ^C\n^C in parfor could crash GP
    41- solve() iteration could incorrectly abort and return 0.0 [#2638]
    42- zeta(1/2+10^22*I) -> precision too low
BA  43- lfuninit(lfunshift(1,3,1)) was incorrect [#2631]
BA  44- call(printsep, [" "]) -> SEGV
    45- absZ_factor_limit_strict could include a composite in prime list [#2648]
    46- we could have factorlimit < primelimit [=> composite not detected
        in absZ_factor_limit_strict]
    47- forsubset: handle trivial case of negative cardinalities [#2652]
BA  48- ellchangecurve(E).roots could be wrong [#2660]
BA  49- default(new_galois_format,1) broke nflist([6,6]) [#2667]
    50- charpoly(Mod(x+y,y^2+x+1),y) -> invalid t_POL [#2668]
HC  51- elleta was wrong when imag(w1/w2) < 0
BA  52- parvector(-10,i,i) -> SEGV
    53- writebin(file) only saved polynomials variables in file
BA  54- lfun(1/3+I*10^19) -> overflow in expo()
BA  55- fflog(a, b, o) was very slow for small o but large fields [#2676]
LGr 56- psi(1+O(x^5)) -> wrong result [#2677]
    57- zetahurwitz(large s, |x| > 1) is inaccurate (correct absolute accuracy
        but zeta(s,x) is small and relative error is large) [#2673]
BA  58- ellcard(ellinit([ffgen([53,36]),1])) -> wrong result
    59- polcyclofactors(((x^6+x^3+1)*(3*x^3+1))^2) -> oo loop [#2680]
BA  60- [pthread] ^C could cause a SEGV [#2665]
BA  61- qfbred(large real QFB) could SEGV
    62- ZX_factor: rare "no factor" bug [#2670]
    63- === for t_REAL 0: was not ignoring mantissa
    64- bnfisprincipal: uninitialized parameter in a deprecated branch
        (using either bnfinit(,1) or bnfisprincipal(,4) avoided the problem)

  Added
     1- [libpari] prodprimes, prodprimeslim
BA   2- new GP functions ellcharpoly, genus2charpoly
BA   3- [libpari] Flm_hess_pre
BA   4- new default doctest and meta-command \z
BA   5- ellfromeqn: option to return the map to the curve
BA   6- new meta command \qf
BA   7- [libpari] Flx_unscale, Flx_Fl_translate, FpXQX_FpXQ_translate
BA   8- [libpari] FlxqC_red_pre, FlxqM_red_pre, FlxM_mul
BA   9- [libpari] FlxC_Fl_translate, FlxM_Fl_translate
    10- [libpari] RgX_type_code
    11- [libpari] mkpadic, retmkpadic, retmkpadic_i, padic_p, padic_u, padic_pd
AP  12- new GP functions algskolemnoether, algisisom
    13- allow t_PADICs in chinese
MTB 14- FpXQ_sqrtn: implement fast algorithm
HC  15- New semantics for theta, now computes all four 1-variable theta
        functions simultaneously, new GP functions thetanull, elljacobi.
    16- new GP function matmodhnf
    17- [libpari] ZC_modhnf, ZM_modhnf, zv_canon_inplace
BA  18- polclass, polmodular: add support for Atkin modular invariants of
        level 3 to 31
BA  19- [libpari] FpXQX_is_squarefree
BA  20- [libpari] FqV_to_FFV
BA  21- [libpari] Rg_is_QXk, ZXk_gcd, QXk_gcd, ZXk_divexact, ZXk_divides
BA  22- [libpari] FpXk_gcd, FpXk_red, Rg_is_FpXk, Rg_to_FpXk
BA  23- [libpari] get_FlxqX_algebra
    24- [libpari] gc_INT_affii
    25- [libpari] affgc
BA  26- [libpari] zero_FlxM_copy
    27- [libpari] abmap_char_image, abmap_nchar_image
BA  28- [libpari] ZMV_producttree, ZM_trace, FpM_trace, Flm_trace
    29- [libpari] bnrconductor_factored_arch, bnrtoprimitive
    30- [libpari] char_renormalize
AP  31- [libpari] alg_get_invol
    32- [libpari] dblllog2, dbllambertW0, dbllambertW_1, dblcnorm, dblcabs,
        dblcarg, dblclog
    33- [libpari] hnf_Znproj
    34- [libpari] qfi_red, qfr_red
BA  35- [libpari] FqC_to_FlxqC FqM_to_FlxqM
BA  36- [libpari] hash_create_INT, hash_create_GEN, hash_values_GEN
BA  37- [libpari] thuemorseu
BA  38- new accessor macros uel, ucoeff, umael, umael2, umael3, umael4, umael5
    39- [libpari] nf_to_scalar_or_polmod
BA  40- [libpari] FlxX_resultant_pre, ZXX_resultant
BA  41- [libpari] RgX_is_ZXX
BA  42- [libpari] FqM_add, FqM_sub
BA  43- new GP functions bitset, bitclear, bitflip
BA  44- [libpari] FlxY_Flx_mul_pre, FlxY_Flx_div_pre
BA  45- ellmaninconstant: add flag=1: use Cremona table.
    46- [libpari] mulimag
    47- allow elleisnum(w, [k1, ..., kn])
BA  48- [libpari] Zn_sqrtall
BA  49- bnfinit: add optional parallel search for relation
BA  50- bnfinit: add extra technical parameters max_fact, idex, usethr
BA  51- [libpari] gen_parapply, gen_parapply_percent, gen_parapply_slice,
                  gen_parapply_slice_zv
BA  52- [libpari] zMs_compress
BA  53- [libpari] FlxV_factorback
BA  54- [libpari] ZpM_ZpC_gauss
BA  55- [libpari] retmkvec6, mkvec6, mkvec5s, mkvec6s
    56- [libpari] bnr_sanitize
BA  57- nextprime(a, q): nextprime in arithmetic progression q
BA  58- new GP functions primeisregular
BA  59- [libpari] polgalois0 (compat version for polgalois)
BA  60- [libpari] ZXQXQ_minpoly
    61- new GP function fingerprint
BA  62- new GP function hyperellextremalmodels
    63- [libpari] RgXX_to_Kronecker_var
PMo 64- new GP function hyperellperiods
BA  65- new GP function parmatrix
BA  66- [libpari] ZM_hnfintersectmod
    67- [libpari] mpacos, mpacosh, mpasin, mpasinh, mpatan, mpatanh, mpcosh,
        mpcotan, mpcotanh, mplog1p, mpsinc, mpsinh, mptan, mptanh
BA  68- [libpari] RgE_is_FpXQE, RgE_to_FpE
BA  69- new GP functions hyperellchangepoint, hyperellchangepointinv
BA  70- [libpari] RgX_homogenous_eval
BA  71- new GP functions hyperellchangeinvert, hyperellchangecompose
BA  72- [libpari] RgX_derivn, RgX_homogenous_derivn
BA  73- new GP functions hyperellisisom, hyperellauto
BA  74- [libpari] nfV_idealhnf
BA  75- [libpari] RgM_flatten_RgC, RgM_flatten_RgV
BA  76- new GP function idealfromgens
BA  77- [libpari] FpXX_Fp_sub
BA  78- [libpari] ZpXQXQ_div ZpXQXQ_inv ZpXQXQ_invlift gen_ZpXX_Newton
BA  79- [libpari] F3m_rank, F3v_dotproduct, F3v_dotsquare
BA  80- [libpari] newblock_t, clone_lock, clone_unlock, clone_unlock_deep
    81- [libpari] divmpr, divrmp
BA  82- [libpari] RgX_Graeffe
BA  83- [libpari] FlxqXn_div, FlxqXn_div_pre
BA  84- [libpari] gen_parpairwiseop, gen_parpairwiseop_percent
BA  85- [libpari] ZMV_prod
BA  86- [libpari] get_Flx_algebra, get_Flxq_algebra
BA  87- [libpari] ZXX_shifti, ZXX_pval, ZXV_pval
BA  88- [libpari] FpXQV_ellcharpoly
BA  89- [libpari] ellheegner_z
BA  90- [libpari] uisnilpotent
BA  91- contfrac for real t_QFB and t_QUAD
BA  92- galoisinit: support for non-WSS Galois groups
BA  93- new GP function ellheegnertwist
    94- [libpari] Z_has_prime_3mod4
    95- support vecsort(vector of t_VECSMALL, k)

  Changed
     1- subst: use fast RgX_affine function to compute P(a*x+b) + RgX_deflate
     2- removed elleisnum optional flag. If you really want elliptic
        invariants, use E4/12 and -E6/216.
AP   3- strtime: use days in addition to hours, minutes, ms.
BA   4- rename gerepilecopy -> gc_GEN, gerepileuptoint -> gc_INT
     5- rename gerepileupto -> gc_upto, gerepileuptoleaf -> gc_leaf,
        gerepilecoeffs -> gc_slice, gerepilecoeffssp -> gc_slice_unsafe
        The old gerepile is now obsolete: don't use it.
     6- rename chk_gerepileupto -> chk_gc_upto, dbg_gerepile -> dbg_stack,
        dbg_gerepileupto -> dbg_gc_upto
     7- implement 3M multiplication for t_QUADs
     8- affgr(x,y): no longer support t_QUAD x; use gtofp
     9- rnfconductor: return a bnr not including generators (which is the
        default for bnrinit); this saves time and no PARI function needs them
BA  10- hammingl renamed to hammingu
BA  11- Rename RgX_translate -> RgX_Rg_translate
               RgXQX_translate -> RgXQX_RgXQ_translate
               ZX_translate -> ZX_Z_translate
               FpX_translate -> FpX_Fp_translate
               FqX_translate -> FqX_Fq_translate
    12- faster strjoin when delimiter is empty
BA  13- Rename FlxX_Flx_mul->FlxY_Flx_mul
               FlxX_Flx_add->FlxY_Flx_add
               FlxX_Flx_sub->FlxY_Flx_sub
    14- elleisnum(elliptic curve, k): return exact result
    15- [libpari] lfunthetacost now has an optional argument
    16- [libpari] new factorlimit argument to pari_init_primes and
        initprimetable
BA  17- lfuncreate now allows non-integral conductors and weights
BA  18- default 'new_galois_format' now default to 1.
BA  19- default 'simplify' now default to 0.
BA  20- vecsum, vecprod now accept t_LIST
BA  21- [libpari] RgX_homogenous_evalpow now requires the homogenous degree
BA  22- polteichmuller now requires T to be irreducible
    23- mpdiv is now obsolete, use divmpr or divrmp instead.
    24- ZX_gcd_all(A, B, &Anew) returns d = gcd(A,B) and used to set Anew to an
    integer multiple of A / d. We now set Anew to the primitive part of A / d.
    25- ZX_radical is now guaranteed to be primitive
    26- gphelp: remove GPHELP_TMPDIR and GPHELP_DOCDIR aliases for GPTMPDIR
        and GPDOCDIR environment variables (obsoleted and left undocumented
        since pari-2.0.12 (1998)).
    27- gphelp -k and ??? : case sensitive search if keyword is all uppercase.
        For instance ??? LLL no longer outputs elllog and ellL1, whereas
        ??? lll still does.

  Removed
     1- obsolete functions gerepileall, gerepilemany: use gc_all
     2- renamed gerepileallsp -> gc_all_unsafe
     3- obsolete function gerepilemanysp : use gc_all_unsafe
     4- obscure function cgetp: use mkpadic
     5- obsolete functions mpcosz, mpsinz, mplogz, mpexpz: use affrr or
        proper GC
     6- obsolete functions gabsz, gaddz, gdiventz, gdivz, gmodz, gmul2nz,
        gmulz, gnegz, gshiftz, gsubz: use gaffect or (better) proper GC
     7- obsolete functions addiiz, addirz, addriz, addrrz, addsiz, addsrz,
     addssz, diviiz, divirz, divisz, divriz, divrrz, divrsz, divsiz, divsrz,
     divssz, dvdiiz, dvdisz, dvdiuz, dvmdiiz, dvmdisz, dvmdsiz, dvmdssz,
     modiiz, modisz, modsiz, modssz, mpaddz, mpmulz, mpsubz, muliiz, mulirz,
     mulriz, mulrrz, mulsiz, mulsrz, mulssz, remiiz, remisz, remsiz, remssz,
     subiiz, subirz, subisz, subriz, subrrz, subrsz, subsiz, subsrz, subssz.
     Use affii, affrr or proper GC
     8- obsolete functions gaffsg and gaffect
     9- obsolete functions mpaff, affiz, affsz
    10- obsolete functions bnrchar_primitive, bnrchar_primitive_raw. Use
        bnrmap.
    11- obsolete function bnrconductor_i. Use bnrconductor instead (which is
        also obsolete but still present) or (better) bnrtoprimitive and bnrmap
    12- ZXC_to_FlxqC, ZXM_to_FlxqM: use FqC_to_FlxqC, FqM_to_FlxqM

Done for version 2.18.0 (released 04/01/2025):
  Fixed
BA   1- incorrect GP proto for ellpadicfrobenius, mftocoset, qfcvp [#2575]
AP   2- fix idealismaximal for ideal p*ZK [Sage issue 38766]
AP   3- segfault in algsubalg when input is linearly dependent
AP   4- fix alglatinter trivial intersection (misuse of matkermod(,1))
BA   5- ellrank could try many more curves than requested by effort [#2577]
     6- wrong result in issquare(Mod(a, composite)) [#2578]
     7- gener_FpXQ_local(t_POL of degre 1) -> oo loop [#2581]
     8- GC error when squaring integer 2x2 matrices [#2582]
AP   9- algebras: fix splitting field for CSA, algtomatrix / algnorm / algtrace
        / algcharpoly were sometimes wrong by an automorphism of the center.
BA  10- paridecl.h could conflict with complex.h [#2583]
    11- forprime(p=524288,1048576,1) -> crash [#2584]
        forprime(p=1048607,1048617,1) -> oo loop
    12- printf("%10.6f", tiny rational) -> undefined result [#2576]
AP  13- alginit(nf,[a,b]) was only allowing a,b integral over the power basis
        instead of arbitrary algebraic integers.
HC  14- zeta not continous around 1/2+3000*I [#2585]
    15- missing type checks for change of variables in ellchangecurve,
        ellchangepoint, ellchangepointinv
BA  16- control-C could lead to segfault later [#2496]
    17- nfmodpr at deg 1 prime: "wrong" invisible variable in t_FFELT [#2580]
    18- [libpari] missing normalization in FpX_mulu (when p is not prime)
HC  19- mfsymboleval could return wrong sign [#2586]
    20- missing type checks in factorback [#2590]
BA  21- charpoly(Mod(x,x^20+1/2)) -> crash [#2591]
    22- psi(x close to a nonpositive integer) -> error
    23- rnf functions which assume polynomial with integral coeffs (rnfinit,
        rnfpseudobasis, rnfdisc, rnfdedekind) were missing relevant sanity
        checks
BA  24- polresultant(t_POL with RFRAC coeffs) could be incorrect [#2588]
BA  25- qflll(non-maximal rank) -> potential oo-loop [#2587]

  Added
AP   1- new GP function algnewprec
BA   2- [loongarch64] add loongarch64 assembly kernel
BA   3- [libpari] closuretoinl
BA   4- [libpari] using closuretoinl, closures can be made usable with E/I
        GP prototype codes
BA   5- quadclassunit now uses MPQS for negative discriminants.
AP   6- [libpari] FqC_red, FqM_red, FqC_to_FFC, FqM_to_FFM
     7- [libpari] pr_anti_uniformizer
AP   8- new GP functions algeltfromnf, algmodprinit, algmodpr, algmodprlift,
        algeichlerbasis
     9- [libpari] checkellpt_i
AP  10- new GP functions algquattobasis, algbasistoquat, algisquatalg
BA  11- new GP functions ellchangecompose, ellchangeinvert
HC  12- zetahurwitz(t_PADIC,,d): use dth-power of the Teichmuller character
BA  13- [libpari] ZVV_nv_mod_tree, ZVV_to_FlvV
MTB 14- gen_order: implement faster recursive algorithm
MTB 15- FpXQ_sqrt: implement fast algorithm
BA  16- [libpari] F2xqX_Frobenius, F2xqX_nbroots, FF_nbroots
    17- core, ispowerfu, moebius: implement fast trial division
AP  18- new GP function alginvol

  Changed
BA   1- idealfactorback, rnfisnorminit: flag is now a long to match GP proto.
     2- polsturm obsolete undocumented form polsturm(pol, a, b) where a or b
        could be omitted is now disabled. Use polsturm(pol, [a,b]), where
        a = -oo and b = +oo can be used instead of an omitted argument.
     3- undocumented deprecated 3-arguments form of deprecated function
        polred is now disabled. Use polredbest !
     4- [libpari] deprecated function polred0 implementing deprecated polred
        function now accepts only two arguments: the 3 argument form
        polred0(x, flag, fa = NULL) is no longer possible. Use
          polred0(mkvec2(x, gel(fa,1)), flag)
        instead. And preferably polredbest!
AP   5- allow algpoleval(al, basis form, relative polynomial).
AP   6- alginit: construction from Hasse invariants now allows a shortcut in the
        quaternion case, giving only the ramification set.
AP   7- alginit(nf,[a,b]) now allows a to be a square in nf.
     8- nfmodpr now returns a t_INTMOD when the residue field is Z/pZ
     9- [libpari] oncurve renamed ellisoncurve_i
    10- ellchangepoint / ellchangepointinv: now require the elliptic curve as
        first argument (to indicate the domain over which the transformation
        is performed); backward compatibility is maintained for now:
        ellchangepoint(P, urst) still works when it used to do; but
        ellchangepoint(E, P, urst) now works also when E, P, urst are defined
        over a number field with components in basis form
    11- renamed ZC_hnfremdiv -> ZC_hnfdivrem
    12- factorint: after trial division, never use rho first. Start by squfof
        then rho.

  Removed
BA   1- GP function trap, use iferr instead.
BA   2- GP functions listcreate, listkill, use L = List() instead.