# Directory `macros/plain/contrib/xintsession`

# 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:

- Execute
`etex xintsession`

, - 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)

- add
- 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

- fix output still uses
- 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

- fix extremely weird
- 0.3 (2021-05-31)
- implement
`>>>`

primary and`...`

secondary invite prompts - breaking: rename
`\xintresume`

into`\xintsession`

- implement
- 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

- use
- 0.2a (2021-05-06)
- fix help panels mentioning topics obsoleted by
`xintexpr 1.4f`

- fix help panels mentioning topics obsoleted by
- 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

Download the contents of this package in one zip archive (9.5k).

## xintsession – Interactive computing sessions (fractions, floating points, polynomials)

This package provides support for interactive computing sessions with etex (or pdftex) executed on the command line, on the basis of the xintexpr and polexpr packages.

Once xintsession is loaded, ε-TeX becomes an interactive computing software capable of executing arbitrary precision calculations, or exact calculations with arbitrarily big fractions. It can also manipulate polynomials as algebraic entities.

Numerical variables and functions can be defined during the session, and each evaluation result is stored in automatically labeled variables. A file is automatically created storing inputs and outputs.

Package | xintsession |

Version | 0.4alpha 2021-11-01 |

Licenses | The LaTeX Project Public License 1.3c |

Copyright | 2021 Jean-François Burnol |

Maintainer | Jean-François Burnol |

Contained in | TeX Live as xintsession MiKTeX as xintsession |

Topics | Calculation Maths |