diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/polexpr/polexpr.txt')
| -rw-r--r-- | Master/texmf-dist/doc/latex/polexpr/polexpr.txt | 85 |
1 files changed, 57 insertions, 28 deletions
diff --git a/Master/texmf-dist/doc/latex/polexpr/polexpr.txt b/Master/texmf-dist/doc/latex/polexpr/polexpr.txt index dd2ab246900..7b792ed8ca0 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 =============================== -0.5 (2018/04/08) -================ +0.5.1 (2018/04/22) +================== .. contents:: @@ -16,9 +16,26 @@ The syntax is:: \poldef polname(x):= expression in variable x; -where in place of ``x`` an arbitrary *dummy variable* is authorized -(i.e. per default any of ``[a-z|A-Z]``; more letters can be declared -under Unicode engines.) One can also issue:: +where: + +- in place of ``x`` an arbitrary *dummy variable* is authorized, + i.e. per default any of ``[a-z|A-Z]`` (more letters can be declared + under Unicode engines.) + +- ``polname`` consists of letters, digits, and the ``_`` and + ``'`` characters. It must start with a letter. + +.. attention:: + + The ``'`` is authorized since ``0.5.1``. As a result some constructs + recognized by the ``\xintexpr`` parser, such as ``var1 'and' var2`` + will get misinterpreted and cause errors. However these constructs + are unlikely to be frequently needed in polynomial expressions, and + the ``\xintexpr`` syntax offers alternatives, so it was deemed a + small evil. Of course the ``\xintexpr`` parser is modified only + temporarily during execution of ``\poldef``. + +One can also issue:: \PolDef{polname}{expression in variable x} @@ -27,7 +44,8 @@ from its default ``x``. ``\poldef f(x):= 1-x+x^2;`` defines polynomial ``f``. Polynomial names must start with a - letter and may contain letters, digits, and underscores. The + letter and may contain letters, digits, underscores and the right + tick character. The variable must be a single letter. The colon character is optional. The semi-colon at end of expression is mandatory. @@ -50,23 +68,29 @@ from its default ``x``. should now define the zero polynomial... Let's check: ``\[ k(z) = \PolTypeset[z]{k} \]`` -``\PolDiff{f}{df_dx}`` - sets ``df_dx`` to the derivative of ``f``. +``\PolDiff{f}{f'}`` + sets ``f'`` to the derivative of ``f``. The name doesn't have to be + ``f'`` (in fact the ``'`` is licit only since ``0.5.1``). -``\PolDiff{df_dx}{f_xx}`` +.. important:: + + This is not done automatically. If some new definition needs to use + the derivative of some available polynomial, that derivative + polynomial must have been defined via ``\PolDiff``: something like + ``T'(x)^2`` will not work without a prior ``\PolDiff{T}{T'}``. + +``\PolDiff{f}{f''}`` obtains second derivative. -``\PolDiff[3]{f}{d3f_dx3}`` - computes directly the third derivative. Its name does not have to be - chosen so complicated ``:)``, but the right quote ``'`` is not - allowed in polynomial names (currently). +``\PolDiff[3]{f}{f'''}`` + computes the third derivative. :: $f(z) = \PolTypeset[z]{f} $\newline - $f'(z) = \PolTypeset[z]{df_dx}$\newline - $f''(z) = \PolTypeset[z]{f_xx}$\newline - $f'''(z)= \PolTypeset[z]{d3f_dx3}$\par + $f'(z) = \PolTypeset[z]{f'} $\newline + $f''(z) = \PolTypeset[z]{f''} $\newline + $f'''(z)= \PolTypeset[z]{f'''} $\par .. important:: @@ -184,16 +208,16 @@ was no further reduction. \PolEnsureIntervalLengths{f_1}{-10}% Here they are with ten digits after decimal mark: \PolPrintIntervals[W]{f_1} - \PolDiff{f_1}{f_xx} - \PolToSturm{f_xx}{f_xx} - \PolSturmIsolateZeros{f_xx} - The second derivative is \PolTypeset{f_xx}. - It has \PolSturmNbOfIsolatedZeros{f_xx} distinct real + \PolDiff{f_1}{f''} + \PolToSturm{f''}{f''} + \PolSturmIsolateZeros{f''} + The second derivative is \PolTypeset{f''}. + It has \PolSturmNbOfIsolatedZeros{f''} distinct real roots: - \PolPrintIntervals[X]{f_xx} + \PolPrintIntervals[X]{f''} Here is the positive one with 20 digits after decimal mark: - \PolEnsureIntervalLength{f_xx}{2}{-20}% - \[X_2 = \PolSturmIsolatedZeroLeft{f_xx}{2}\dots\] + \PolEnsureIntervalLength{f''}{2}{-20}% + \[X_2 = \PolSturmIsolatedZeroLeft{f''}{2}\dots\] The more mathematically advanced among our dear readers will be able to give the exact value for $X_2$! @@ -367,8 +391,9 @@ Non-expandable macros in a private structure accessible later via other package macros, under the user-chosen ``polname``. Of course the *expression* can use other previously defined polynomials. Names must start with a - letter and are constituted of letters, digits and underscore - characters. The whole xintexpr_ syntax is authorized:: + letter and are constituted of letters, digits, underscores and + (since ``0.5.1``) the right tick ``'``. + The whole xintexpr_ syntax is authorized:: \poldef sin(z) := add((-1)^i z^(2i+1)/(2i+1)!, i = 0..10); @@ -1810,14 +1835,18 @@ CHANGE LOG degree 41 polynomial with -2, -1.9, -1.8, ..., 0, 0.1, ..., 1.9, 2 as roots`_ for usage). It will presumably be replaced in future by an interval specification. - * new non-expandable macros: + * new non-expandable macro: - `\\PolMakePrimitive`_ - * new expandable macros: + * new expandable macro: - `\\PolIContent`_ +- v0.5.1 (2018/04/22) + + * new feature: + - the character ``'`` can be used in polynomial names. Acknowledgments --------------- |