Release notes for SymPy 0.7.3

These are the release notes for SymPy 0.7.3, which was released on July 13, 2013. It can be downloaded from https://github.com/sympy/sympy/releases/tag/sympy-0.7.3.

This version of SymPy has been tested on Python 2.5, 2.6, 2.7, 3.2, 3.3, and PyPy.

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).

Here is an example integral that could not be computed before:

```>>> f = x*(x + 1)*(2*x*(x - (2*x**3 + 2*x**2 + x + 1)*log(x + 1))*exp(3*x**2) + (x**2*exp(2*x**2) - log(x + 1)**2)**2)/((x + 1)*log(x + 1)**2 - (x**3 + x**2)*exp(2*x**2))**2
>>> integrate(f, x)
x + x*exp(x**2)*log(x + 1)/(x**2*exp(2*x**2) - log(x + 1)**2) - log(x + 1) - log(exp(x**2) - log(x + 1)/x)/2 + log(exp(x**2) + log(x + 1)/x)/2```

ODE

• Built basic infrastructure of the PDE module (PR #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

Assumptions

Matrix expressions now support inference using the new assumptions system. New predicates include `invertible, symmetric, positive_definite, orthogonal`, ....

New Operators

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

Backwards compatibility breaks and deprecations

• 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 issue 3914.

• The `viewer='file'` option to `preview` without a file name is deprecated. Use `filename='name'` in addition to `viewer='file'`. See issue 3919.

• 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 issue 3378.

• 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 issue 3377.

• The spherical harmonics have been completely rewritten. See PR #1510.

Minor changes

Solvers

• Added enhancements and improved the methods of solving exact differential equation ((PR #1955)) and ((PR #1823))
• Support for differential equations with linear coefficients and those that can be reduced to separable and linear form ((PR #1940), (PR #1864), (PR #1883))
• Support for first order linear general PDE's with constant coefficients ((PR #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 (PR #1497)
• Various new error and inverse error functions (PR #1703)
• Use in heurisch for more symmetric and nicer results
• Gruntz for expintegrals and all new erf*
• Li, li logarithmic integrals (PR #1708)
• Integration of li/Li by heurisch (PR #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 (PR #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 (PR #2038)
• faster integer polynomial factorization (PR #2148)
• Euler-Descartes method for quartic equations (PR #1947)
• algebraic operations on tensors (PR #1700)
• tensor canonicalization (PR #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` objects
• Added DOT printing for visualization of expression trees

Authors

The following people contributed at least one patch to this release (names are given in alphabetical order by last name). A total of 85 people contributed to this release. People with a * by their names contributed a patch for the first time for this release; 56 people contributed for the first time for this release.

Thanks to everyone who contributed to this release!

• Acebulf*
• Akshit Agarwal*
• Ankit Agrawal*
• Tom Bachmann
• Raoul Bourquin
• Christian Bühler
• CJ Carey*
• Ondřej Čertík
• Mary Clark*
• Chris Conley*
• Renato Coutinho
• Björn Dahlgren*
• Christopher Dembia*
• Guru Devanla
• Rishabh Dixit*
• Alexander Eberspächer*
• Pavel Fedotov
• Benjamin Fishbein*
• Sean Ge*
• Gilbert Gede
• Brian E. Granger
• Angus Griffith*
• Chetna Gupta*
• Ananya H*
• Randy Heydon*
• Alexander Hirzel*
• Thomas Hisch*
• hm*
• Matthew Hoff*
• Case Van Horsen*
• Katja Sophie Hotz*
• Max Hutchinson*
• Sachin Irukula
• Sergiu Ivanov
• Saurabh Jha
• Sachin Joglekar*
• Varun Joshi*
• Robert Kern
• Sergey B Kirpichev*
• Stefan Krastanov
• Manoj Kumar*
• Patrick Lacasse*
• Ronan Lamy
• Colleen Lee*
• Oliver Lee*
• David Li
• Stephen Loo*
• Huijun Mai*
• Aaron Meurer
• Eric Nelson*
• Sherjil Ozair
• Mateusz Paprocki
• Tarang Patel*
• Khagesh Patel*
• Mario Pernici
• Luke Peterson
• Tyler Pirtle*
• Vasily Povalyaev*
• Seshagiri Prabhu*
• Roland Puntaier*
• Bharath M R
• Shravas K Rao*
• Thilina Rathnayake*
• Timothy Reluga*
• Julien Rioux
• Matthew Rocklin
• Christophe Saint-Jean*
• Prasoon Shukla*
• Chris Smith
• Cristóvão Sousa
• Brian Stephanik*
• Marek Šuppa*
• Tim Swast*
• Grzegorz Świrski