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        "description": "=============\nGiacpy\n=============\n\n:Name: giacpy\n:Summary: A Cython frontend to the c++ library giac. (Computer Algebra System)\n:Author: Frederic Han\n:Author-email: frederic.han@imj-prg.fr\n:Copyright: 2012 Frederic Han\n:License:  GPL v2 or above\n:Home-page: https://www.imj-prg.fr/~frederic.han/xcas/giacpy/\n\n\n\nAccess from python to the Computer Algebra System giac via libgiac\n\n------------\nIntroduction\n------------\n\nThis is an interface to be able to use from Python the Giac features.\n\n   * Giac is a general purpose Computer algebra system by Bernard Parisse released under GPLv3.\n\n      - http://www-fourier.ujf-grenoble.fr/~parisse/giac.html\n      - It is build on C and C++ libraries:\n        PARI, NTL (arithmetic), CoCoA (Groebner basis), GSL (numerics),\n        GMP (big integers), MPFR (bigfloats)\n      - It  provides (fast) algorithms for multivariate polynomial operations (product, GCD, factorisation) and\n      - symbolic  computations: solver, simplifications, limits/series, integration, sommation...\n      - Linear Algebra with numerical or symbolic coefficients.\n\n\n   * giacpy is an interface to this library. It is built with cython. Graphic output is obtained with qcas by Loic Lecoq:  http://git.tuxfamily.org/qcas/qcas.git\n\n\n-----------\nShort Usage\n-----------\n\nExample::\n\n    >>> import giacpy  # outputs various messages\n    Help file ... aide_cas not found\n    Added 0 synonyms\n    >>> giacpy.ifactor(2**128+1)\n    59649589127497217*5704689200685129054721\n    >>> from giacpy import giac\n    >>> x,y,z=giac('x,y,z')\n    >>> f=(x+y+z+1)**15+1\n    >>> g=(f*(f+1)).normal()\n    >>> print g.nops()\n    >>> print g.factor().nops()\n    >>> f.diff()\n\nHelp::\n\n    >>> help(\"giacpy\")\n    >>> from giacpy import normal\n    >>> print(normal.__doc__) ; # to have help on some giac keyword\n    >>> solve.htmlhelp('fr') ; # (may be not avaible on your system) to have detailled help on some giac keyword\n    >>> htmlhelp()  ; # to have help the global help pages.\n\n\n    * Graphics 2D Output: (cf. help('giacpy') for examples)\n     If your version of giacpy has qt support, you can send graphics to qcas with the .qcas() method. For experimental interactive geometry see: help(qcas)\n\n\n-------\nInstall\n-------\n\n   * To build the extension from sources (unix):\n\n      - You need the giac library, gmp and python headers. Ex: giac, libgmp-dev python-dev\n\n      - Then execute the command: python setup.py build_ext  (or try the: make or make local)\n\n      - If you need some options see: python setup.py build_ext --help\n\n      - To install giacpy on unix (needs libgiac): python setup.py install\n\n   * For binaries of giacpy: http://webusers.imj-prg.fr/~frederic.han/xcas/giacpy/\n\n   * To run tests you can try: make test\n     or run: python -m doctest giacpy.pyx -v   (in the directory of giapy.so if it is not installed)\n\n\n-----------------------------------\nShort Tutorial on the giac function\n-----------------------------------\n\n    This function evaluate a python object with the giac library.\n\n    * It creates in python a Pygen element and evaluate it with giac:\n\n\n     >>> from giacpy import giac,pi\n     >>> x,y=giac('x,y');type(x)\n     <type 'giacpy.Pygen'>\n     >>> (x+2*y).cos().texpand()\n     cos(x)*(2*cos(y)**2-1)-sin(x)*2*cos(y)*sin(y)\n\n\nCoercion, Pygen and internal giac variables:\n--------------------------------------------\n\n   * The most usefull objects will be the Python object of type Pygen.\n\n    >>> from giacpy import *\n    >>> x,y,z=giac('x,y,z')\n    >>> f=sum([x[i] for i in range(5)])**15/(y+z);f.coeff(x[0],12)\n    (455*(x[1])**3+1365*(x[1])**2*x[2]+1365*(x[1])**2*x[3]+1365*(x[1])**2*x[4]+1365*x[1]*(x[2])**2+2730*x[1]*x[2]*x[3]+2730*x[1]*x[2]*x[4]+1365*x[1]*(x[3])**2+2730*x[1]*x[3]*x[4]+1365*x[1]*(x[4])**2+455*(x[2])**3+1365*(x[2])**2*x[3]+1365*(x[2])**2*x[4]+1365*x[2]*(x[3])**2+2730*x[2]*x[3]*x[4]+1365*x[2]*(x[4])**2+455*(x[3])**3+1365*(x[3])**2*x[4]+1365*x[3]*(x[4])**2+455*(x[4])**3)/(y+z)\n\n\n   * The Python object y of type Pygen is not an internal giac variable. (Most of the time you won't need to use internal giac variables).\n\n    >>> type(y);giac('y:=1');y\n    <type 'giacpy.Pygen'>\n    1\n    y\n\n   * There are some natural coercion to Pygen elements:\n\n    >>> pi>3.14 ; pi >3.15 ; giac(3)==3\n    True\n    False\n    True\n\n\nLists of Pygen and Giac lists:\n------------------------------\n\n   * Here l1 is a giac list and l2 a python list of Pygen type objects.\n\n    >>> l1=giac(range(10)); l2=[1/(i**2+1) for i in l1]\n    >>> sum(l2)\n    33054527/16762850\n\n    So l1+l1 is done in giac and means a vector addition. But l2+l2 is done in Python so it is the list concatenation.\n\n    >>> l1+l1\n    [0,2,4,6,8,10,12,14,16,18]\n    >>> l2+l2\n    [1, 1/2, 1/5, 1/10, 1/17, 1/26, 1/37, 1/50, 1/65, 1/82, 1, 1/2, 1/5, 1/10, 1/17, 1/26, 1/37, 1/50, 1/65, 1/82]\n\n\n   * Here V is not a Pygen element. We need to push it to giac to use a giac method like dim, or we need to use an imported function.\n\n    >>> V=[ [x[i]**j for i in range(9)] for j in range(9)]\n    >>> giac(V).dim()\n    [9,9]\n    >>> det_minor(V).factor()\n    (x[7]-(x[8]))*(x[6]-(x[8]))*(x[6]-(x[7]))*(x[5]-(x[8]))*(x[5]-(x[7]))*(x[5]-(x[6]))*(x[4]-(x[8]))*(x[4]-(x[7]))*(x[4]-(x[6]))*(x[4]-(x[5]))*(x[3]-(x[8]))*(x[3]-(x[7]))*(x[3]-(x[6]))*(x[3]-(x[5]))*(x[3]-(x[4]))*(x[2]-(x[8]))*(x[2]-(x[7]))*(x[2]-(x[6]))*(x[2]-(x[5]))*(x[2]-(x[4]))*(x[2]-(x[3]))*(x[1]-(x[8]))*(x[1]-(x[7]))*(x[1]-(x[6]))*(x[1]-(x[5]))*(x[1]-(x[4]))*(x[1]-(x[3]))*(x[1]-(x[2]))*(x[0]-(x[8]))*(x[0]-(x[7]))*(x[0]-(x[6]))*(x[0]-(x[5]))*(x[0]-(x[4]))*(x[0]-(x[3]))*(x[0]-(x[2]))*(x[0]-(x[1]))\n\n   * Modular objects with %\n\n    >>> V=ranm(5,5) % 2;\n    >>> ker(V).rowdim()+V.rank()\n    5\n    >>> a=giac(7)%3;a;a%0;7%3\n    1 % 3\n    1\n    1\n\n   Do not confuse with the full python integers:\n\n    >>> type(7%3);type(a)\n    <type 'int'>\n    <type 'giacpy.Pygen'>\n\nSyntaxes with reserved or unknown Python symbols:\n-------------------------------------------------\n\n   * In general equations needs symbols such as = < > or that have another meaning in Python. So those objects must be quoted.\n\n    >>> from giacpy import *\n    >>> x=giac('x')\n    >>> (1+2*sin(3*x)).solve(x)\n    list[-pi/3/6,7*pi/18]\n\n    >>> solve('sin(3*x)>2*sin(x)',x)\n    Traceback (most recent call last):\n    ...\n    RuntimeError: Unable to find numeric values solving equation. For trigonometric equations this may be solved using assumptions, e.g. assume(x>-pi && x<pi) Error: Bad Argument Value\n\n\n   * You can also add some hypothesis to a giac symbol:\n\n    >>> assume('x>-pi && x<pi')\n    x\n    >>> solve('sin(3*x)>2*sin(x)',x)\n    list[((x>((-5*pi)/6)) and (x<((-pi)/6))),((x>0) and (x<(pi/6))),((x>(5*pi/6)) and (x<pi))]\n\n   * To remove those hypothesis use the giac function: purge\n\n    >>> purge('x')\n    assume[[],[line[-pi,pi]],[-pi,pi]]\n    >>> solve('x>0')\n    list[x>0]\n\n\n   * Same problems with the ..\n\n    >>> from giacpy import *\n    >>> x=giac('x')\n    >>> f=1/(5+cos(4*x));f.int(x)\n    1/2/(2*sqrt(6))*(atan(2*tan(4*x/2)/sqrt(6))+pi*floor(4*x/2/pi+1/2))\n    >>> fMax(f,'x=-0..pi').simplify()\n    pi/4,3*pi/4\n    >>> fMax.help()\n    \"Returns the abscissa of the maximum of the expression.\n    Expr,[Var]\n    fMax(-x^2+2*x+1,x)\n    fMin\"\n    >>> sum(1/(1+x**2),'x=0..infinity').simplify()\n    (pi*exp(pi)**2+pi+exp(pi)**2-1)/(2*exp(pi)**2-2)\n\n\n\n\n\n---------\nChangelog\n---------\n\n\n   * Version 0.2:\n      - Add a comparison function to Pygen. (with coersion)\n      - Add a basic definition for most giac functions.\n      - Add some help.\n\n   * Version 0.2.1:\n      - Add __neg__ and __pos__ support for Pygen. (Ex: -pi)\n      - Change __repr__ to hide too long outputs.\n      - Make ** be the default printing for powers in giac.\n\n   * Version 0.2.2:\n      - Change Pygen() to Pygen('NULL'). (Ex: rand())\n      - Add direct acces to the python double value of a Pygen: a._double\n      - Add  conversion to giac modulars via the operator %\n      - Add  ctrl-c support during list initialisation and iteration\n      - Modification of __getitem__ to allow formal variables with indexes.\n      - Add htmlhelp method for Pygen objects.\n      - Improve the giac initialisation of Python long integers. (basic Horner method instead of strings)\n      - Improve  help(giac) and doctests\n      - Add support for the slice notation with giac lists\n\n   * Version 0.2.3:\n      - Fix Pygen() None initialisation. Add crash test and improve speed in _wrap_gen\n      - Add a small Makefile\n      - Add a GiacSettings class with some frontends to the cas settings.\n      - Add French keywords\n\n   * Version 0.2.4:\n      - Update giac 1.1 keywords.\n\n   * Version 0.3:\n      - Add a qt output for 2d graphics via qcas.\n      - Fixes for giac 1.1\n\n   * Version 0.4:\n      - Fixes for Python 3 compatibility\n      - Qt/qcas can be disabled at compilation. (cf setup.py)\n      - 0.4.1:\n\t  + add some giac keywords.\n      \t  + add proba_epsilon in GiacSetting.\n\t  + test if the html doc is present locally, otherwise open the web doc.\n      - 0.4.2:\n          + add digits and epsilon in GiacSetting.\n\t  + Fix for interruptions of giac operators.\n\t  + Put all the GiacKeywords in a new class: GiacFunction to enable docstrings from giac.\n      - 0.4.3:\n\t  + Update qcas to current version. (svg export added)\n\t  + New evaluation with threads to have better interruptions.\n      - 0.4.4:\n          + Add sqrt and complex flags in giac settings.\n\t  + Add support for multi indexes. Ex A[1,2].\n\n   * Version 0.5:\n      - 0.5.0:\n          + Put all the Qt/Graphics functions in an independant submodule\n          + Add a save method for Pygen and a loadgiacgen function.\n      - 0.5.2:\n          + Update keywords and clean __init__.py docstring\n      - 0.5.3:\n          + improve setup.py for mingw built\n      - 0.5.4:\n          + update giac.dll windows binary to giac 1.2.3-57 with subsop patch\n\t    and rowreduction-R55929 patch\n          + post1: update win64 giac.dll to fix: interface with pari; matrix mul\n            for integers\n\n   * Version 0.6:\n      - 0.6.0:\n          + add a __setitem__ for Pygen elements. Ex: A[1,2]=3\n\t  + add Linear algebra tutorial in the giac docstring.\n      - 0.6.1:\n          + update giac keywords.\n      - 0.6.2:\n          + add _repr_html_ and _repr_latex_ for jupyter output\n\t  + rebuild giac.dll without ntl.\n      - 0.6.3:\n          + fix for randseed, srand\n\t  + update keywords\n\t  + remove qcas from tree; libqcas\n      - 0.6.4:\n\t  + try to guess qt install from qmake\n\t  + upgrade giac.dll to 1.4.9.43\n\t  + fix keywords update\n      - 0.6.5:\n\t  + Add GPL-2 in MANIFEST.in\n      - 0.6.6:\n          + disable include_package_data in setup.py to not install .cpp files\n\t    and remove from install directory other source files that are not needed\n\t    by python nor by cython users.\n\t  + windows rebuilt with giac-1.4.9-45 with NTL enabled\n      - 0.6.7:\n          + udapte keywords for giac 1.5.0\n\t  + update windows built with giac-1.5.0-3 with NTL+glpk+nauty enabled\n      - 0.6.8:\n          + udapte keywords for giac 1.5.0.53\n\t  + update windows built with giac-1.5.0-49\n      - 0.6.9:\n\t  + update windows built with giac-1.5.0-63\n          + doctest fix NULL ouput",
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