diff options
Diffstat (limited to 'Master/texmf-dist')
-rw-r--r-- | Master/texmf-dist/doc/plain/xintsession/README.md | 68 | ||||
-rw-r--r-- | Master/texmf-dist/tex/plain/xintsession/xintsession.tex | 132 |
2 files changed, 164 insertions, 36 deletions
diff --git a/Master/texmf-dist/doc/plain/xintsession/README.md b/Master/texmf-dist/doc/plain/xintsession/README.md index 422e5f88b67..2152a1be165 100644 --- a/Master/texmf-dist/doc/plain/xintsession/README.md +++ b/Master/texmf-dist/doc/plain/xintsession/README.md @@ -1,6 +1,6 @@ # xintsession README # -Release: 0.3b (2021-07-01) +Release: 0.4alpha (2021-11-01) ## Usage ## @@ -12,22 +12,22 @@ It will load [xintexpr](http://www.ctan.org/pkg/xint) and To start a session: -1. Execute `etex xintsession`, or if available, `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. +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. @@ -45,25 +45,38 @@ Here is a sample session (spaces do not matter): @_4 4.499205338329425 >>> add(1/i, i=1..1000); @_5 7.485470860550346 - >>> 1 - ... + - ... \message{xintsession is great!} - (executing \message {xintsession is great!} in background) - xintsession is great! - ... 2 - ... ; - @_6 3.0 + >>> &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-210531_09h08.tex + 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. Say `&fp=number` at the -`>>>` prompt to activate floating point mode with `number` digits -of precision. +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. @@ -72,6 +85,13 @@ 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](http://www.ctan.org/pkg/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 diff --git a/Master/texmf-dist/tex/plain/xintsession/xintsession.tex b/Master/texmf-dist/tex/plain/xintsession/xintsession.tex index d98af4f499e..f7aec508939 100644 --- a/Master/texmf-dist/tex/plain/xintsession/xintsession.tex +++ b/Master/texmf-dist/tex/plain/xintsession/xintsession.tex @@ -1,4 +1,4 @@ -% Release 0.3b (2021-07-01) of xintsession.tex +% Release 0.4alpha (2021-11-01) of xintsession.tex % author: Jean-Francois Burnol % License: LPPL 1.3c (author-maintained) % Usage: execute "etex (or pdftex) xintsession" @@ -55,7 +55,7 @@ _ / _ / / / /_ / __/ / / /_/ // /__ / /_ _ / __ |/ // __/__ /_/ /_/ /_/\__/ \___//_/ \__,_/ \___/ \__/ /_/ _____/ \___//_/% }% ?xdef?xs_copyright{% - xintsession 0.3a (2021-06-08) + xintsession 0.4alpha (2021-11-01) Copyright (c) Jean-Francois Burnol, 2021.% }}% \def\xs_no{0}% @@ -170,6 +170,7 @@ _ / _ / / / /_ / __/ / / /_/ // /__ / /_ _ / __ |/ // __/__ \edef\xs_funcname{\expandafter\xint_zapspaces\detokenize{#1} \xint_gobble_i}% \xint_gob_til_sc#2\xs_defvar;\xs_deffunc }% +\edef\xs_fourspaces{\space\space\space\space}% \def\xs_deffunc #1;% {% % attention: \xs_xintdeffunc needs to see parentheses immediately @@ -179,8 +180,16 @@ _ / _ / / / /_ / __/ / / /_/ // /__ / /_ _ / __ |/ // __/__ \detokenize\expandafter{\xs_right};}% \expandafter\ifx\xs_xintdeffunc\poldef \xs_message{\xs_funcname\space = \PolToExpr{\xs_funcname}}% - \xs_message{Issue \string\PolGenFloatVariant{\xs_funcname} if fp evaluations - with \xs_funcname\space are intended}% + \xs_message{\xs_fourspaces --> + &GenFloat(\xs_funcname) lets + \xs_funcname\space become usable as function in fp mode}% + \xs_message{\xs_fourspaces + --> &ROOTS(\xs_funcname) (resp. &ROOTS(\xs_funcname,N)) + finds all rational roots exactly and}% + \xs_message{\xs_fourspaces\xs_fourspaces + all irrational roots with at least + \xintsessiondefaultrootsprecision\space(resp. N) + fractional digits}% \else\xs_message{Function \xs_funcname\space defined}% \fi\xs_fetch }% @@ -247,6 +256,106 @@ _ / _ / / / /_ / __/ / / /_/ // /__ / /_ _ / __ |/ // __/__ \def\xs_xinteval{\xinteval}% }% \def\xs_magic@&mod{\xs_message{current mode: \xs_mode}}% +\def\xs_getpolname#1(#2#3)#4\xint_bye{\edef\xs_polname{\xint_zapspaces #2#3 \xint_gobble_i}}% +\def\xs_magic@&Gen +{% + \expandafter\xs_getpolname\xs_magic_inb\xint_bye + \PolGenFloatVariant{\xs_polname}% + \immediate\write\xs_out{\string\PolGenFloatVariant{\xs_polname}}% + \xs_message{Polynomial function \xs_polname\space for &fp mode usage now defined}% +}% +\def\xintsessiondefaultrootsprecision{10}% +\def\xs_getpolandE#1(#2#3)#4\xint_bye +{% + \xs_getpolandE_i#2#3,,\xint_bye +}% +\def\xs_getpolandE_i#1,#2,#3\xint_bye +{% + \edef\xs_polname{\xint_zapspaces #1 \xint_gobble_i}% + \edef\xs_rootsprecision{\if\relax#3\relax + \xintsessiondefaultrootsprecision\else + \xint_zapspaces #2 \xint_gobble_i\fi}% +}% +\expandafter\def\csname xs_magic@&ROO\endcsname +{% + \expandafter\xs_getpolandE\xs_magic_inb\xint_bye + \xs_message{Solving for real roots of \xs_polname\space and assigning them (please wait...)}% + \PolToSturm{\xs_polname}{@\xs_polname}% + \PolSturmIsolateZerosGetMultiplicitiesAndRationalRoots{@\xs_polname}% + \PolEnsureIntervalLengths{@\xs_polname}{-\xs_rootsprecision}% + \immediate\write\xs_out{\string\PolToSturm{\xs_polname}{@\xs_polname}}% + \immediate\write\xs_out{\string\PolSturmIsolateZerosGetMultiplicitiesAndRationalRoots{@\xs_polname}}% + \immediate\write\xs_out{\string\PolEnsureIntervalLengths{@\xs_polname}{-\xs_rootsprecision}}% + \immediate\write\xs_out{\string\PolPrintIntervals{@\xs_polname}}% + \xs_polprintintervals + \xs_message{Square-free irrational part: \PolToExpr{@\xs_polname _sqf_norr}}% + \ifnum\PolSturmNbOfIsolatedZeros{@\xs_polname}>\PolSturmNbOfRationalRoots{@\xs_polname} + \xs_message{\xs_fourspaces --> + &REFINEROOTS(\xs_polname,N) to extend real irr. roots to N fractional digits}% + \else + \xs_message{No irrational real roots.}% + \fi +}% +\expandafter\def\csname xs_magic@&REF\endcsname +{% + \expandafter\xs_getpolandE\xs_magic_inb\xint_bye + \xs_message{Refining real roots of \xs_polname\space to \xs_rootsprecision\space + digits (please wait...)}% + \PolEnsureIntervalLengths{@\xs_polname}{-\xs_rootsprecision}% + \immediate\write\xs_out{\string\PolEnsureIntervalLengths{@\xs_polname}{-\xs_rootsprecision}}% + \immediate\write\xs_out{\string\PolPrintIntervals{@\xs_polname}}% + \xs_polprintintervals +}% +\def\xs_polprintintervals +{% + \begingroup\xintglobaldefstrue + \def\PolPrintIntervalsNoRealRoots{\xs_message{No real roots.}}% + \let\PolPrintIntervalsBeginEnv\empty + \let\PolPrintIntervalsEndEnv\empty + \def\PolPrintIntervalsKnownRoot{\PolPrintIntervalsPrintExactZero}% + \def\PolPrintIntervalsUnknownRoot{\xintifSgn{\PolPrintIntervalsTheLeftEndPoint}% + {\PolPrintIntervalsPrintRightEndPoint}% + {\PolPrintIntervalsPrintLeftEndPoint}% + {\PolPrintIntervalsPrintLeftEndPoint}% + }% + \def\PolPrintIntervalsPrintExactZero + {\xs_message{(mult. \PolPrintIntervalsTheMultiplicity) + Root\xs_polname _\PolPrintIntervalsTheIndex\space = \PolPrintIntervalsTheLeftEndPoint}% + \immediate\write\xs_out{\string\xintdefvar\space + Root\xs_polname _\PolPrintIntervalsTheIndex:=\PolPrintIntervalsTheLeftEndPoint;}% + \XINT_expr_defvar_one{Root\xs_polname _\PolPrintIntervalsTheIndex}% + {{\xintRaw{\PolPrintIntervalsTheLeftEndPoint}}}% + }% + \def\PolPrintIntervalsPrintLeftEndPoint + {\xs_message{(mult. \PolPrintIntervalsTheMultiplicity) + Root\xs_polname _\PolPrintIntervalsTheIndex\space = \PolPrintIntervalsTheLeftEndPoint...}% + \immediate\write\xs_out{\string\xintdefvar\space + Root\xs_polname _\PolPrintIntervalsTheIndex:=\PolPrintIntervalsTheLeftEndPoint;}% + \XINT_expr_defvar_one{Root\xs_polname _\PolPrintIntervalsTheIndex}% + {{\xintRaw{\PolPrintIntervalsTheLeftEndPoint}}}% + }% + \def\PolPrintIntervalsPrintRightEndPoint + {\xs_message{(mult. \PolPrintIntervalsTheMultiplicity) + Root\xs_polname _\PolPrintIntervalsTheIndex\space = \PolPrintIntervalsTheRightEndPoint...}% + \immediate\write\xs_out{\string\xintdefvar\space + Root\xs_polname _\PolPrintIntervalsTheIndex:=\PolPrintIntervalsTheRightEndPoint;}% + \XINT_expr_defvar_one{Root\xs_polname _\PolPrintIntervalsTheIndex}% + {{\xintRaw{\PolPrintIntervalsTheRightEndPoint}}}% + }% + \def\POL@PrintIntervals@Loop{% + \POL@SturmIfZeroExactlyKnown\PolPrintIntervalsTheSturmName\PolPrintIntervalsTheIndex + \PolPrintIntervalsKnownRoot + \PolPrintIntervalsUnknownRoot + \xdef\PolPrintIntervalsTheIndex{\the\numexpr\PolPrintIntervalsTheIndex+\@ne}% + \unless\ifnum\PolPrintIntervalsTheIndex> + \@nameuse{POL_ZL\PolPrintIntervalsTheSturmName*0} + \POL@PrintIntervals@DoDefs + \expandafter\POL@PrintIntervals@Loop + \fi + }% + \PolPrintIntervals{@\xs_polname}% + \endgroup +}% \def\xs_setenv {% \newlinechar10\endlinechar-1\errorcontextlines0\relax @@ -276,16 +385,15 @@ _ / _ / / / /_ / __/ / / /_/ // /__ / /_ _ / __ |/ // __/__ \xs_logo - input is `;'-terminated and can extend over multiple lines - ("\xs_prime_invite" is main input invite, "\xs_second_invite" is continuation prompt) - - definitions are done with `:=' not with `='. -% - any line starting with a control sequence is executed in the -% background, the interrupted numerical input resumes at prompt. - - Magic words: `&pause' (or `;'), `&help', `&bye', - `&exact', `&fp', `&int', `&pol'. + - definitions of variables and functions are done with `:='. \string\jobname is \jobname Transcript will go to log and to \xs_name + Typing at the prompt + - `&pause' or `;' exits to normal TeX (typesetting) interaction, + - `&bye' terminates the session, + - `&help' triggers help panels, + - `&exact', `&fp', `&int', or `&pol' switches among modes. }}% \xdef\xs_welcome_back{\noexpand\message{% You are back to the xintexpr interactive session! @@ -353,7 +461,7 @@ _ / _ / / / /_ / __/ / / /_/ // /__ / /_ _ / __ |/ // __/__ - Polynomials in pol mode are defined using polname(x):=expression; (or with another letter). They can serve as functions in the exact mode. To use a polynomial also as an fp mode function, issue - \PolGenFloatVariant{<polname>} at the prompt. + &GenFloat(<polname>) at the prompt. - Whenever a variable is defined, or a computation is performed, the result is assigned a label @_<integer>. These labels are |