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author | Karl Berry <karl@freefriends.org> | 2018-12-10 22:58:44 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2018-12-10 22:58:44 +0000 |
commit | 8128a1b13f192605f1711ea4f5f7da4550d0996a (patch) | |
tree | 96bf4dc07c80082ab607d1023e59befb7f194c44 /Master/texmf-dist/doc/latex/polexpr/polexpr.txt | |
parent | e167cb1f6f6ba7c4ac582ed784d8e0a9b7d81321 (diff) |
polexpr (10dec18)
git-svn-id: svn://tug.org/texlive/trunk@49378 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/polexpr/polexpr.txt')
-rw-r--r-- | Master/texmf-dist/doc/latex/polexpr/polexpr.txt | 66 |
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: |