SymPy 0.7.3
13 Jul 2013
Major changes
Integration
This release includes Risch integration algorithm from Aaron Meurer’s 2010 Google Summer of Code project. This makes
integrate
much more powerful and much faster for the supported functions. The algorithm is called automatically fromintegrate()
. For now, only transcendental elementary functions containingexp
orlog
are supported. To access the algorithm directly, useintegrate(expr, x, risch=True)
. The algorithm has the ability to prove that integrals are nonelementary. To determine if a function is nonelementary, integrate usingrisch=True
. If the resultingIntegral
class is an instance ofNonElementaryIntegral
, then it is not elementary (otherwise, that part of the algorithm has just not been implemented yet).
ODE
Built basic infrastructure of the PDE module (sympy/sympy#1970)
Theano Interaction
SymPy expressions can now be translated into Theano expressions for numeric evaluation. This includes most standard scalar operations (e.g.
sin
,exp
,gamma
, but notbeta
orMeijerG
) and matrices. This system generally outperformslambdify
andautowrap
but does require Theano to be installed.
Matrix Expressions
Matrix expressions now support inference using the new assumptions system. New predicates include
invertible
,symmetric
,positive_definite
,orthogonal
, ….New operators include
Adjoint
,HadamardProduct
,Determinant
,MatrixSlice
,DFT
. Also, preliminary support exists for factorizations likeSVD
andLU
.
Context manager for New Assumptions
Added the
with assuming(*facts)
context manager for new assumptions. See blogpost.
Compatibility breaks
This is the last version of SymPy to support Python 2.5.
The IPython extension, i.e.,
%load_ext sympy.interactive.ipythonprinting
is deprecated. Usefrom sympy import init_printing; init_printing()
instead. See sympy/sympy#7013.The
viewer='file'
option topreview
without a file name is deprecated. Usefilename='name'
in addition toviewer='file'
. See sympy/sympy#7018.The deprecated syntax
Symbol('x', dummy=True)
, which had been deprecated since 0.7.0, has been removed. UseDummy('x')
orsymbols('x', cls=Dummy)
instead. See sympy/sympy#6477.The deprecated
Expr
methodsas_coeff_terms
andas_coeff_factors
, which have been deprecated in favor ofas_coeff_mul
andas_coeff_add
, respectively (see alsoas_coeff_Mul
andas_coeff_Add
), were removed. The methods had been deprecated since SymPy 0.7.0. See sympy/sympy#6476.The spherical harmonics have been completely rewritten. See sympy/sympy#1510.
Minor changes
Solvers
Added enhancements and improved the methods of solving exact differential equation. See sympy/sympy#1955 and sympy/sympy#1823.
Support for differential equations with linear coefficients and those that can be reduced to separable and linear form. See sympy/sympy#1940, sympy/sympy#1864 and sympy/sympy#1883.
Support for first order linear general PDE’s with constant coefficients (sympy/sympy#2109).
Return all found independent solutions for underdetermined systems.
Handle recursive problems for which
y(0) = 0
.Handle matrix equations.
Integration
integrate
will split out integrals into Piecewise expressions when conditions must hold for the answer to be true. For example,integrate(x**n, x)
now givesPiecewise((log(x), Eq(n, -1), (x**(n + 1)/(n + 1), True))
(previously it just gavex**(n + 1)/(n + 1)
).Calculate Gauss-Legendre and Gauss-Laguerre points and weights (sympy/sympy#1497).
Various new error and inverse error functions (sympy/sympy#1703).
Use in heurisch for more symmetric and nicer results.
Gruntz for expintegrals and all new erf*.
Li, li logarithmic integrals (sympy/sympy#1708).
Integration of li/Li by heurisch (sympy/sympy#1712).
elliptic integrals, complete and incomplete.
Integration of complete elliptic integrals by meijerg.
Integration of Piecewise with symbolic conditions.
Fixed many wrong results of DiracDelta integrals.
Logic
Addition of SOPform and POSform functions to sympy.logic to generate boolean expressions from truth tables.
Addition of simplify_logic function and enabling
simplify()
to reduce logic expressions to their simplest forms.Addition of bool_equals function to check equality of boolean expressions and return a mapping of variables from one expr to other that leads to the equality.
Addition of disjunctive normal form methods - to_dnf, is_dnf
Others
gmpy version 2 is now supported
Added
is_algebraic_expr()
method (sympy/sympy#2176).Many improvements to the handling of noncommutative symbols:
Better support in simplification functions, e.g.
factor
,trigsimp
Better integration with
Order()
Better pattern matching
Improved pattern matching including matching the identity.
normalizes Jacobi polynomials
Quadrature rules for orthogonal polynomials in arbitrary precision (hermite, laguerre, legendre, gen_legendre, jacobi)
summation of harmonic numbers
Many improvements of the polygamma functions
evaluation at special arguments
Connections to harmonic numbers
structured full partial fraction decomposition (mainly interesting for developers)
besselsimp improvements
Karr summation convention
New spherical harmonics
improved minimal_polynomial using composition of algebraic numbers (sympy/sympy#2038).
faster integer polynomial factorization (sympy/sympy#2148).
Euler-Descartes method for quartic equations (sympy/sympy#1947)
algebraic operations on tensors (sympy/sympy#1700).
tensor canonicalization (sympy/sympy#1644).
Handle the simplification of summations and products over a KroneckerDelta.
Implemented LaTeX printing of DiracDelta, Heaviside, KroneckerDelta and LeviCivita, also many Matrix expressions.
Improved LaTeX printing of fractions, Mul in general.
IPython integration and printing issues have been ironed out.
Stats now supports discrete distributions (e.g.
Poisson
) by relying onSummation
objectsAdded DOT printing for visualization of expression trees
Added information about solvability and nilpotency of named groups.