Package: giacpy
Name:giacpySummary:A Cython frontend to the c++ library giac. (Computer Algebra System)Author:Frederic HanAuthor-email:frederic.han@imj-prg.frCopyright:2012 Frederic HanLicense:GPL v2 or aboveHome-page:https://www.imj-prg.fr/~frederic.han/xcas/giacpy/Access from python to the Computer Algebra System giac via libgiacIntroductionThis is an interface to be able to use from Python the Giac features.Giac is a general purpose Computer algebra system by Bernard Parisse released under GPLv3.http://www-fourier.ujf-grenoble.fr/~parisse/giac.htmlIt is build on C and C++ libraries:
PARI, NTL (arithmetic), CoCoA (Groebner basis), GSL (numerics),
GMP (big integers), MPFR (bigfloats)It  provides (fast) algorithms for multivariate polynomial operations (product, GCD, factorisation) andsymbolic  computations: solver, simplifications, limits/series, integration, sommation…Linear Algebra with numerical or symbolic coefficients.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.gitShort UsageExample:>>> import giacpy  # outputs various messages
Help file ... aide_cas not found
Added 0 synonyms
>>> giacpy.ifactor(2**128+1)
59649589127497217*5704689200685129054721
>>> from giacpy import giac
>>> x,y,z=giac('x,y,z')
>>> f=(x+y+z+1)**15+1
>>> g=(f*(f+1)).normal()
>>> print g.nops()
>>> print g.factor().nops()
>>> f.diff()Help:>>> help("giacpy")
>>> from giacpy import normal
>>> print(normal.__doc__) ; # to have help on some giac keyword
>>> solve.htmlhelp('fr') ; # (may be not avaible on your system) to have detailled help on some giac keyword
>>> htmlhelp()  ; # to have help the global help pages.


* Graphics 2D Output: (cf. help('giacpy') for examples)
 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)InstallTo build the extension from sources (unix):You need the giac library, gmp and python headers. Ex: giac, libgmp-dev python-devThen execute the command: python setup.py build_ext  (or try the: make or make local)If you need some options see: python setup.py build_ext –helpTo install giacpy on unix (needs libgiac): python setup.py installFor binaries of giacpy:http://webusers.imj-prg.fr/~frederic.han/xcas/giacpy/To run tests you can try: make test
or run: python -m doctest giacpy.pyx -v   (in the directory of giapy.so if it is not installed)Short Tutorial on the giac functionThis function evaluate a python object with the giac library.It creates in python a Pygen element and evaluate it with giac:>>> from giacpy import giac,pi
>>> x,y=giac('x,y');type(x)
<type 'giacpy.Pygen'>
>>> (x+2*y).cos().texpand()
cos(x)*(2*cos(y)**2-1)-sin(x)*2*cos(y)*sin(y)Coercion, Pygen and internal giac variables:The most usefull objects will be the Python object of type Pygen.>>> from giacpy import *
>>> x,y,z=giac('x,y,z')
>>> f=sum([x[i] for i in range(5)])**15/(y+z);f.coeff(x[0],12)
(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)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).>>> type(y);giac('y:=1');y
<type 'giacpy.Pygen'>
1
yThere are some natural coercion to Pygen elements:>>> pi>3.14 ; pi >3.15 ; giac(3)==3
True
False
TrueLists of Pygen and Giac lists:Here l1 is a giac list and l2 a python list of Pygen type objects.>>> l1=giac(range(10)); l2=[1/(i**2+1) for i in l1]
>>> sum(l2)
33054527/16762850So l1+l1 is done in giac and means a vector addition. But l2+l2 is done in Python so it is the list concatenation.>>> l1+l1
[0,2,4,6,8,10,12,14,16,18]
>>> l2+l2
[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]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.>>> V=[ [x[i]**j for i in range(9)] for j in range(9)]
>>> giac(V).dim()
[9,9]
>>> det_minor(V).factor()
(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]))Modular objects with %>>> V=ranm(5,5) % 2;
>>> ker(V).rowdim()+V.rank()
5
>>> a=giac(7)%3;a;a%0;7%3
1 % 3
1
1Do not confuse with the full python integers:>>> type(7%3);type(a)
<type 'int'>
<type 'giacpy.Pygen'>Syntaxes with reserved or unknown Python symbols:In general equations needs symbols such as = < > or that have another meaning in Python. So those objects must be quoted.>>> from giacpy import *
>>> x=giac('x')
>>> (1+2*sin(3*x)).solve(x)
list[-pi/3/6,7*pi/18]>>> solve('sin(3*x)>2*sin(x)',x)
Traceback (most recent call last):
...
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 ValueYou can also add some hypothesis to a giac symbol:>>> assume('x>-pi && x<pi')
x
>>> solve('sin(3*x)>2*sin(x)',x)
list[((x>((-5*pi)/6)) and (x<((-pi)/6))),((x>0) and (x<(pi/6))),((x>(5*pi/6)) and (x<pi))]To remove those hypothesis use the giac function: purge>>> purge('x')
assume[[],[line[-pi,pi]],[-pi,pi]]
>>> solve('x>0')
list[x>0]Same problems with the ..>>> from giacpy import *
>>> x=giac('x')
>>> f=1/(5+cos(4*x));f.int(x)
1/2/(2*sqrt(6))*(atan(2*tan(4*x/2)/sqrt(6))+pi*floor(4*x/2/pi+1/2))
>>> fMax(f,'x=-0..pi').simplify()
pi/4,3*pi/4
>>> fMax.help()
"Returns the abscissa of the maximum of the expression.
Expr,[Var]
fMax(-x^2+2*x+1,x)
fMin"
>>> sum(1/(1+x**2),'x=0..infinity').simplify()
(pi*exp(pi)**2+pi+exp(pi)**2-1)/(2*exp(pi)**2-2)ChangelogVersion 0.2:Add a comparison function to Pygen. (with coersion)Add a basic definition for most giac functions.Add some help.Version 0.2.1:Add __neg__ and __pos__ support for Pygen. (Ex: -pi)Change __repr__ to hide too long outputs.Make ** be the default printing for powers in giac.Version 0.2.2:Change Pygen() to Pygen(‘NULL’). (Ex: rand())Add direct acces to the python double value of a Pygen: a._doubleAdd  conversion to giac modulars via the operator %Add  ctrl-c support during list initialisation and iterationModification of __getitem__ to allow formal variables with indexes.Add htmlhelp method for Pygen objects.Improve the giac initialisation of Python long integers. (basic Horner method instead of strings)Improve  help(giac) and doctestsAdd support for the slice notation with giac listsVersion 0.2.3:Fix Pygen() None initialisation. Add crash test and improve speed in _wrap_genAdd a small MakefileAdd a GiacSettings class with some frontends to the cas settings.Add French keywordsVersion 0.2.4:Update giac 1.1 keywords.Version 0.3:Add a qt output for 2d graphics via qcas.Fixes for giac 1.1Version 0.4:Fixes for Python 3 compatibilityQt/qcas can be disabled at compilation. (cf setup.py)0.4.1:add some giac keywords.add proba_epsilon in GiacSetting.test if the html doc is present locally, otherwise open the web doc.0.4.2:add digits and epsilon in GiacSetting.Fix for interruptions of giac operators.Put all the GiacKeywords in a new class: GiacFunction to enable docstrings from giac.0.4.3:Update qcas to current version. (svg export added)New evaluation with threads to have better interruptions.0.4.4:Add sqrt and complex flags in giac settings.Add support for multi indexes. Ex A[1,2].Version 0.5:0.5.0:Put all the Qt/Graphics functions in an independant submoduleAdd a save method for Pygen and a loadgiacgen function.0.5.2:Update keywords and clean __init__.py docstring0.5.3:improve setup.py for mingw built0.5.4:update giac.dll windows binary to giac 1.2.3-57 with subsop patch
and rowreduction-R55929 patchpost1: update win64 giac.dll to fix: interface with pari; matrix mul
for integersVersion 0.6:0.6.0:add a __setitem__ for Pygen elements. Ex: A[1,2]=3add Linear algebra tutorial in the giac docstring.0.6.1:update giac keywords.0.6.2:add _repr_html_ and _repr_latex_ for jupyter outputrebuild giac.dll without ntl.0.6.3:fix for randseed, srandupdate keywordsremove qcas from tree; libqcas0.6.4:try to guess qt install from qmakeupgrade giac.dll to 1.4.9.43fix keywords update0.6.5:Add GPL-2 in MANIFEST.in0.6.6:disable include_package_data in setup.py to not install .cpp files
and remove from install directory other source files that are not needed
by python nor by cython users.windows rebuilt with giac-1.4.9-45 with NTL enabled0.6.7:udapte keywords for giac 1.5.0update windows built with giac-1.5.0-3 with NTL+glpk+nauty enabled0.6.8:udapte keywords for giac 1.5.0.53update windows built with giac-1.5.0-490.6.9:update windows built with giac-1.5.0-63doctest fix NULL ouputVersion 0.7:0.7.0:fix a build error with  giac>1.5.0-75update windows built with giac-1.5.0-850.7.1:update windows built with giac 1.9.0-28 from giacxcas binaries0.7.2:updates for cython >3.0.0 and reverse operators0.7.3:add .pyi file for some editorsuse automethods.pxi to define Pygen methods with docupdate windows built with giac 1.9.0-59