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-rw-r--r--Master/texmf-dist/doc/latex/polexpr/polexpr.txt40
1 files changed, 23 insertions, 17 deletions
diff --git a/Master/texmf-dist/doc/latex/polexpr/polexpr.txt b/Master/texmf-dist/doc/latex/polexpr/polexpr.txt
index 3e064bc769e..fe99d075a49 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
===============================
-0.4 (2018/02/16)
-================
+0.4.1 (2018/03/01)
+==================
.. contents::
@@ -145,6 +145,12 @@ First some remarks about auxiliaries.
A typical example
~~~~~~~~~~~~~~~~~
+In this example the polynomial is square-free; we can make sure of that by
+comparing the degree of the first element of the Sturm chain with the
+degree of the original polynomial. In such case the second element of
+the Sturm chain is still the polynomial first derivative, because there
+was no further reduction.
+
::
\poldef f(x) := x^7 - x^6 - 2x + 1;
@@ -160,7 +166,8 @@ A typical example
And here is the first root with twenty digits after decimal mark:
\PolEnsureIntervalLength{f}{1}{-20}
\[\PolSturmIsolatedZeroLeft{f}{1}<Z_1<\PolSturmIsolatedZeroRight{f}{1}\]
- The derivative polynomial is \PolTypeset{f_1}.
+ The derivative polynomial is \PolTypeset{f_1} (from
+ $\PolDegree{f_0}=7$ we know that original polynomial was square-free).
\PolToSturm{f_1}{f_1}\PolSturmIsolateZeros{f_1}%
It has \PolSturmNbOfIsolatedZeros{f_1} distinct real
roots:
@@ -1461,24 +1468,19 @@ More precisely, they can be used within the replacement texts of the
``\PolDecToString{decimal number}``
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- This is a utility macro to print decimal numbers. Indeed for legacy
- reasons, xintfrac_ does not yet have user-level ready-to-use macros
- handling specifically the printing of decimal numbers from their
- internal representations such as ``A/1[N]``.
+ This is a utility macro to print decimal numbers. It has been
+ backported to xintfrac_ (release ``1.3`` of ``2018/03/01``) under
+ the name ``\xintDecToString``, and the ``polexpr`` macro is simply
+ now an alias to it.
For example
``\PolDecToString{123.456e-8}`` will expand to ``0.00000123456``
- and ``\PolDecToString{123.450e-8}`` to ``0.00000123450``. This
- illustrates that trailing zeros are not trimmed (to achieve that one
- can use ``\PolDecToString{\xintREZ{#1}}``.)
-
- The macro does not try to identify if the fraction has a denominator
- consisting only of two's and five's; such a denominator will be left
- at right-end of output.
+ and ``\PolDecToString{123.450e-8}`` to ``0.00000123450`` which
+ illustrates that trailing zeros are not trimmed. To trim trailing
+ zeroes, one can use ``\PolDecToString{\xintREZ{#1}}``.
- This utility macro will presumably be incorporated (possibly in a
- more powerful form) to xintfrac_ (or rather to a decimal module) in
- a future xint_ release.
+ The exact behaviour of this macro may evolve in future releases of
+ xint_.
Booleans (with default setting as indicated)
--------------------------------------------
@@ -1737,6 +1739,10 @@ CHANGE LOG
for localization of the real roots of polynomials.
+- v0.4.1 (2018/03/01)
+
+ Synced with xint 1.3.
+
Acknowledgments
---------------