| Name: | giacpy |
|---|---|
| Summary: | A Cython frontend to the c++ library giac. (Computer Algebra System) |
| Author: | Frederic Han |
| Author-email: | han@math.jussieu.fr |
| Copyright: | 2012 Frederic Han |
| License: | GPL v2 or above |
| Home-page: | http://www.math.jussieu.fr/~han/xcas/giacpy/ |
Access from python to the Computer Algebra System giac via libgiac
This 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.html
- It 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) and
- symbolic 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/?p=qcas/qcas.git
Example:
>>> 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.help() ; # to have help on some giac keyword
>>> solve.htmlhelp('fr') ; # 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)
To build the extension from sources:
- You need the giac library, gmp and python headers. Ex: giac, libgmp-dev python-dev
- Then 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 --help
- To install giacpy on unix (needs libgiac): python setup.py install
For binaries of giacpy: http://www.math.jussieu.fr/~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)
This 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)
- 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 y
- There are some natural coercion to Pygen elements:
>>> pi>3.14 ; pi >3.15 ; giac(3)==3 True False True
- 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'>
- 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 Value
- You 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)
- Version 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._double
- Add conversion to giac modulars via the operator %
- Add ctrl-c support during list initialisation and iteration
- Modification 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 doctests
- Add support for the slice notation with giac lists
- Version 0.2.3:
- Fix Pygen() None initialisation. Add crash test and improve speed in _wrap_gen
- Add a small Makefile
- Add a GiacSettings class with some frontends to the cas settings.
- Add French keywords
- Version 0.2.4:
- Update giac 1.1 keywords.
- Version 0.3:
- Add a qt output for 2d graphics via qcas.
- Fixes for giac 1.1
- Version 0.4:
Fixes for Python 3 compatibility
Qt/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.