# 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 from`integrate()`

. For now, only transcendental elementary functions containing`exp`

or`log`

are supported. To access the algorithm directly, use`integrate(expr, x, risch=True)`

. The algorithm has the ability to prove that integrals are nonelementary. To determine if a function is nonelementary, integrate using`risch=True`

. If the resulting`Integral`

class is an instance of`NonElementaryIntegral`

, 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 not`beta`

or`MeijerG`

) and matrices. This system generally outperforms`lambdify`

and`autowrap`

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 like`SVD`

and`LU`

.

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. Use`from sympy import init_printing; init_printing()`

instead. See sympy/sympy#7013.The

`viewer='file'`

option to`preview`

without a file name is deprecated. Use`filename='name'`

in addition to`viewer='file'`

. See sympy/sympy#7018.The deprecated syntax

`Symbol('x', dummy=True)`

, which had been deprecated since 0.7.0, has been removed. Use`Dummy('x')`

or`symbols('x', cls=Dummy)`

instead. See sympy/sympy#6477.The deprecated

`Expr`

methods`as_coeff_terms`

and`as_coeff_factors`

, which have been deprecated in favor of`as_coeff_mul`

and`as_coeff_add`

, respectively (see also`as_coeff_Mul`

and`as_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 gives`Piecewise((log(x), Eq(n, -1), (x**(n + 1)/(n + 1), True))`

(previously it just gave`x**(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 on`Summation`

objectsAdded DOT printing for visualization of expression trees

Added information about solvability and nilpotency of named groups.