texlive[60926] Master/texmf-dist: xintsession (1nov21)
commits+karl at tug.org
commits+karl at tug.org
Mon Nov 1 21:35:16 CET 2021
Revision: 60926
http://tug.org/svn/texlive?view=revision&revision=60926
Author: karl
Date: 2021-11-01 21:35:16 +0100 (Mon, 01 Nov 2021)
Log Message:
-----------
xintsession (1nov21)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/plain/xintsession/README.md
trunk/Master/texmf-dist/tex/plain/xintsession/xintsession.tex
Modified: trunk/Master/texmf-dist/doc/plain/xintsession/README.md
===================================================================
--- trunk/Master/texmf-dist/doc/plain/xintsession/README.md 2021-11-01 20:35:03 UTC (rev 60925)
+++ trunk/Master/texmf-dist/doc/plain/xintsession/README.md 2021-11-01 20:35:16 UTC (rev 60926)
@@ -1,6 +1,6 @@
# xintsession README #
-Release: 0.3b (2021-07-01)
+Release: 0.4alpha (2021-11-01)
## Usage ##
@@ -12,22 +12,22 @@
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 @@
@_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 @@
## 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
Modified: trunk/Master/texmf-dist/tex/plain/xintsession/xintsession.tex
===================================================================
--- trunk/Master/texmf-dist/tex/plain/xintsession/xintsession.tex 2021-11-01 20:35:03 UTC (rev 60925)
+++ trunk/Master/texmf-dist/tex/plain/xintsession/xintsession.tex 2021-11-01 20:35:16 UTC (rev 60926)
@@ -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 at PrintIntervals@Loop{%
+ \POL at SturmIfZeroExactlyKnown\PolPrintIntervalsTheSturmName\PolPrintIntervalsTheIndex
+ \PolPrintIntervalsKnownRoot
+ \PolPrintIntervalsUnknownRoot
+ \xdef\PolPrintIntervalsTheIndex{\the\numexpr\PolPrintIntervalsTheIndex+\@ne}%
+ \unless\ifnum\PolPrintIntervalsTheIndex>
+ \@nameuse{POL_ZL\PolPrintIntervalsTheSturmName*0}
+ \POL at PrintIntervals@DoDefs
+ \expandafter\POL at 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.
+ - definitions of variables and functions are done with `:='.
- Magic words: `&pause' (or `;'), `&help', `&bye',
- `&exact', `&fp', `&int', `&pol'.
-
\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
More information about the tex-live-commits
mailing list.