xintsession README

Release: 0.4alpha (2021-11-01)

Usage

xintsession.tex is to be used with etex (or pdftex or the other engines with Plain as preloaded format) interactively on the command line.

It will load xintexpr and polexpr.

To start a session:

1. Execute etex xintsession,
2. An >>> invite appears, and computations can begin!
   
   Start entering input, terminate it via a semi-colon ;. Say &help for help and &bye to quit.

In more details: if available at your locale use rlwrap etex xintsession to benefit from arrow keys navigation and other improvements such as parentheses highlighting. Alternatively, execute rlwrap etex and enter xintsession at the ** prompt.

One can also use the -jobname option of etex at this step.

At my locale I added alias xs="rlwrap etex xintsession" to my .bashrc so I only have to type xs at the command line.

The above explanations have been tested on a Unixen (Mac OS), and probably rlwrap is not available on all platforms, but it is not a requirement.

Here is a sample session (spaces do not matter):

>>> 1+1/2+1/3+1/4+1/5;
@_1     137/60
>>> @_^3;
@_2     2571353/216000
>>> add(1/i, i=1..50);
@_3     13943237577224054960759/3099044504245996706400
>>> &fp
fp mode (16 digits)
>>> @_;
@_4     4.499205338329425
>>> add(1/i, i=1..1000);
@_5     7.485470860550346
>>> &pol
pol mode (i.e. function definitions use \poldef)
>>> P(x):=(x-0.1)^3 (x+1.8)^2 (x^10 - (100x-1)^2);

P = x^15+33*x^14/10+219*x^13/100-865*x^12/1000+936*x^11/10000-324*x^10/100000-1
0000*x^7-328000*x^6/10-2124100*x^5/100+9084700*x^4/1000-11111900*x^3/10000+5198
500*x^2/100000-74160*x/100000+324/100000
    --> &GenFloat(P) lets P become usable as function in fp mode
    --> &ROOTS(P) (resp. &ROOTS(P,N)) finds all rational roots exactly and
        all irrational roots with at least 10 (resp. N) fractional digits
>>> &ROOTS(P,30)
Solving for real roots of P and assigning them (please wait...)
(mult. 1) RootP_1 = -3.164772734675337090200909653480...
(mult. 2) RootP_2 = -1.8
(mult. 1) RootP_3 = 0.009999999999000000000499999999...
(mult. 1) RootP_4 = 0.010000000001000000000500000000...
(mult. 3) RootP_5 = 0.1
(mult. 1) RootP_6 = 3.159772703424837079727026834533...
Square-free irrational part: x^10-10000*x^2+200*x-1
    --> &REFINEROOTS(P,N) to extend real irr. roots to N fractional digits
>>> &bye
Did I say something wrong?
Session transcript written on xintsession-211101_18h17.tex
 )
No pages of output.
Transcript written on xintsession.log.

As this example illustrates, the computational engine can work in various modes: exact, fp, int, and pol (the &ROOTS() will work in any mode the same once the polynomial as been defined in pol mode). Say &fp=number at the >>> prompt to activate floating point mode with number digits of precision.

If ill-formed input drops you deep into TeX error interaction mode, try hitting S as it may work to bring you back to normal session.

For additional explanations, enter &help at the >>> prompt.

Change log

• 0.4alpha (2021-11-01)
  • add &GenFloat interface to \PolGenFloatVariant
  • add &ROOTS and &REFINEROOTS interface to under-the-hood usage of the polexpr facilities allowing to get all real roots of the given polynomial to arbitrary precision (and all rational roots exactly)
• 0.3b (2021-07-01)
  • fix output still uses (@_<n>) when a variable is defined but the parentheses were dropped a while ago in general
• 0.3a (2021-06-08)
  • fix extremely weird 0.3 breakage of user function definition interface, caused by last line being \endinput\xintsession, and the latter using \scantokens in certain circumstances
  • fix extra ( in a help panel
• 0.3 (2021-05-31)
  • implement >>> primary and ... secondary invite prompts
  • breaking: rename \xintresume into \xintsession
• 0.2b (2021-05-23)
  • use \errorcontextlines=0 regime (if not paused)
  • load xintexpr with \newlinechar set to 10 to activate nicer error messages coming with xintexpr 1.4g
  • add help panel navigation via n, p, q and 1, ..., 5
  • fix catcode of @ was set to letter
  • fix version was not updated to 0.2a in banner
  • fix some spaces in help and welcome panels
• 0.2a (2021-05-06)
  • fix help panels mentioning topics obsoleted by xintexpr 1.4f
• 0.2 (2021-05-05)
  • fix typos in help panels, improve welcome panel
  • fix "can't send \par to background typesetting"
  • track xintexpr 1.4f
  • add &fp=N parameterized floating point mode interface
• 0.1 (2021-04-13) Initial release

License

Copyright (c) 2021 Jean-François Burnol

See documentation of package xintexpr for contact information.

This Work may be distributed and/or modified under the conditions of the LaTeX Project Public License version 1.3c. This version of this license is in

http://www.latex-project.org/lppl/lppl-1-3c.txt

and version 1.3 or later is part of all distributions of LaTeX version 2005/12/01 or later.

This Work has the LPPL maintenance status author-maintained.

The Author of this Work is Jean-François Burnol.

This Work consists of the package files xintsession.tex and README.md