passagemath-giac 10.4.61

passagemath: Symbolic computation with GIAC

About SageMath

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Magma, Maple, Mathematica, and MATLAB”

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SageMath fully supports all major Linux distributions, recent versions of macOS, and Windows (Windows Subsystem for Linux).

See https://doc.sagemath.org/html/en/installation/index.html for general installation instructions.

About this pip-installable distribution package

Giac/Xcas is a general purpose Computer algebra system by Bernard Parisse released under GPLv3. It has been developed since 2000 and is widely used: Giac/Xcas is the native CAS engine of the HP Prime calculators; the C++ kernel of the system, Giac, provides the CAS view of Geogebra.

This pip-installable source distribution passagemath-giac makes Giac available from Python and provides integration with the Sage Mathematical Software System.

What is included

• Cython interface to GIAC

  The Cython interface is by Frederic Han and was previously available under the name giacpy-sage. It was merged into the Sage library in 2020.

• Pexpect interface to GIAC

• see https://github.com/passagemath/passagemath/blob/main/pkgs/sagemath-giac/MANIFEST.in

• The binary wheels on PyPI ship a prebuilt copy of the Giac library.

Examples

A quick way to try it out interactively:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-giac[test]" ipython

In [1]: from sage.all__sagemath_giac import *

In [2]: x = libgiac('x')

In [3]: V = [[x[i]**j for i in range(8)] for j in range(8)]

In [4]: libgiac(V).dim()
Out[4]: [8,8]

In [5]: libgiac.det_minor(V).factor()
Out[5]: (x[6]-(x[7]))*(x[5]-(x[7]))*(x[5]-(x[6]))*(x[4]-(x[7]))*(x[4]-(x[6]))*(x[4]-(x[5]))*(x[3]-(x[7]))*(x[3]-(x[6]))*(x[3]-(x[5]))*(x[3]-(x[4]))*(x[2]-(x[7]))*(x[2]-(x[6]))*(x[2]-(x[5]))*(x[2]-(x[4]))*(x[2]-(x[3]))*(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[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]))

In [6]: (x+5)**(1/3)        # note here 1/3 is done in Python before being sent to Giac
Out[6]: (x+5)^0.333333333333

In [7]: (x+5)**QQ('1/3')    # using Sage rationals
Out[7]: (x+5)^(1/3)

In [8]: from fractions import Fraction  # using Python rationals

In [9]: (x+5)**Fraction(1,3)
Out[9]: (x+5)^(1/3)

The last example again, using the Sage REPL:

$ pipx run --pip-args="--prefer-binary" --spec "passagemath-giac[test]" sage
Warning: sage.all is not available; this is a limited REPL.

sage: from sage.all__sagemath_giac import *

sage: x = libgiac('x')

sage: (x+5)^(1/3)           # the Sage preparser translates this to (x+5)**QQ('1/3')
(x+5)^(1/3)