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-rw-r--r--Master/texmf-dist/doc/latex/polexpr/polexpr.txt66
1 files changed, 60 insertions, 6 deletions
diff --git a/Master/texmf-dist/doc/latex/polexpr/polexpr.txt b/Master/texmf-dist/doc/latex/polexpr/polexpr.txt
index 51008763dcf..d77361edc4a 100644
--- a/Master/texmf-dist/doc/latex/polexpr/polexpr.txt
+++ b/Master/texmf-dist/doc/latex/polexpr/polexpr.txt
@@ -4,8 +4,8 @@
Package polexpr documentation
===============================
-0.7 (2018/12/08)
-================
+0.7.2 (2018/12/09)
+==================
.. contents::
@@ -334,7 +334,7 @@ A degree five polynomial with three rational roots
\PolSturmIsolateZeros**{Q}
\PolPrintIntervals{Q}
- $Q_norr(x) = \PolTypeset{Q_norr}$
+ $Q_{norr}(x) = \PolTypeset{Q_norr}$
Here, all real roots are rational::
@@ -367,7 +367,7 @@ A Mignotte type polynomial
\PolSturmIsolateZeros{P} % finds 4 real roots
This polynomial has \PolSturmNbOfIsolatedZeros{P} distinct real roots:
\PolPrintIntervals{P}%
- % reports -2 < Z_1 < -1, 0 < Z_2 < 0.1, 0.1 < Z_3 < 0.2, 1 < Z_4 < 2
+ % reports -2 < Z_1 < -1, 0.09 < Z_2 < 0.10, 0.1 < Z_3 < 0.2, 1 < Z_4 < 2
Let us refine the second and third intervals to separate the corresponding
roots:
\PolRefineInterval*{P}{2}% will refine to 0.0999990 < Z_2 < 0.0999991
@@ -470,6 +470,56 @@ decimal digits is relatively faster. Here is for the ten real roots of
Z_9 = 8.9172502485...
Z_10 = 20.8469081014...
+The second Wilkinson polynomial
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+::
+
+ \documentclass{article}
+ \usepackage{polexpr}
+ \begin{document}
+ \poldef f(x) := mul(x - 2^-i, i = 1..20);
+
+ %\PolTypeset{f}
+
+ \PolToSturm{f}{f}
+ \PolSturmIsolateZeros**{f}
+ \PolPrintIntervals{f}
+ \end{document}
+
+This takes more time than the polynomial with 1, 2, .., 20 as roots but
+less than the latter modified by the ``2**-23`` change in one
+coefficient.
+
+Here is the output (with release 0.7.2)::
+
+ Z_1 = 0.00000095367431640625
+ Z_2 = 0.0000019073486328125
+ Z_3 = 0.000003814697265625
+ Z_4 = 0.00000762939453125
+ Z_5 = 0.0000152587890625
+ Z_6 = 0.000030517578125
+ Z_7 = 0.00006103515625
+ Z_8 = 0.0001220703125
+ Z_9 = 1/4096
+ Z_10 = 1/2048
+ Z_11 = 1/1024
+ Z_12 = 1/512
+ Z_13 = 1/256
+ Z_14 = 1/128
+ Z_15 = 0.015625
+ Z_16 = 0.03125
+ Z_17 = 0.0625
+ Z_18 = 0.125
+ Z_19 = 0.25
+ Z_20 = 0.5
+
+There is some incoherence in output format which has its source in the
+fact that some roots are found in branches which can only find decimal
+roots, whereas some are found in branches which could find general
+fractions and they use ``\xintIrr`` before storage of the found root.
+This may evolve in future.
+
The degree 41 polynomial with -2, -1.9, -1.8, ..., 0, 0.1, ..., 1.9, 2 as roots
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -961,7 +1011,7 @@ Non-expandable macros
The polynomials ``sturmname_k`` main utility is for the execution of
`\\PolSturmIsolateZeros{sturmname}`_. Be careful not to use these
names ``sturmname_0``, ``sturmname_1``, etc... for defining other
- polynomials after having done ``\PolToSturm{polname}{sturmname} and
+ polynomials after having done ``\PolToSturm{polname}{sturmname}`` and
before executing ``\PolSturmIsolateZeros{sturmname}`` else the
latter will behave erroneously.
@@ -2448,7 +2498,11 @@ CHANGE LOG
- `\\PolSturmNbWithMultOfRootsOf{sturmname}\\LessThanOrEqualTo{value}`_
- `\\PolSturmNbWithMultOfRootsOf{sturmname}\\LessThanOrEqualToExpr{expression}`_
-- v0.7 (2018/12/08)
+- v0.7 (2018/12/08) (not released)
+
+- v0.7.1 (2018/12/09) (bugfix)
+
+- v0.7.2 (2018/12/09)
* breaking changes: