# SymPy 0.7.0¶

28 Jun 2011

## Major Changes¶

• Polys

• New internal representations of dense and sparse polynomials (see 6aecdb7, 31c9aa4)

• Implemented algorithms for real and complex root isolation and counting (see 3acac67, 4b75dae, fa1206e, 103b928, 45c9b22, 8870c8b, b348b30)

• Improved Gröbner bases algorithm (see ff65e9f, 891e4de, 310a585)

• Field isomorphism algorithm (see b097b01, 08482bf)

• Implemented efficient orthogonal polynomials (see b8fbd59)

• Added configuration framework for polys (see 33d8cdb, 7eb81c9)

• Function for computing minimal polynomials (see 88bf187, f800f95)

• Function for generating Viete’s formulas (see 1027408)

• roots() supports more classes of polynomials (e.g. cyclotomic) (see d8c8768, 75c8d2d)

• Added a function for recognizing cyclotomic polynomials (see b9c2a9a)

• Added a function for computing Horner form of polynomials (see 8d235c7)

• Added a function for computing symmetric reductions of polynomials (see 6d560f3)

• Added generators of Swinnerton-Dyer, cyclotomic, symmetric, random and interpolating polynomials (see dad03dd, 6ccf20c, dc728d6, 2f17684, 3004db8)

• Added a function computing isolation intervals of algebraic numbers (see 37a58f1)

• Polynomial division (div(), rem(), quo()) now defaults to a field (see a72d188)

• Added wrappers for numerical root finding algorithms (see 0d98945, f638fcf)

• Added symbolic capabilities to factor(), sqf() and related functions (see d521c7f, 548120b, f6f74e6, b1c49cd, 3527b64)

• together() was significantly improved (see dc327fe)

• Added support for iterable containers to gcd() and lcm() (see e920870)

• Added a function for constructing domains from coefficient containers (see a8f20e6)

• Implemented greatest factorial factorization (see d4dbbb5)

• Added partial fraction decomposition algorithm based on undetermined coefficient approach (see 9769d49, 496f08f)

• RootOf and RootSum were significantly improved (see f3e432, 4c88be6, 41502d7)

• Added support for gmpy (GNU Multiple Precision Arithmetic Library) (see 38e1683)

• Allow to compile sympy.polys with Cython (see afb3886)

• Improved configuration of variables in Poly (see 22c4061)

• Added documentation based on Wester’s examples (see 1c23792)

• Irreducibility testing over finite fields (see 17e8f1f)

• Allow symmetric and non-symmetric representations over finite fields (see 60fbff4)

• More consistent factorization forms from factor() and sqf() (see 5df77f5)

• Added support for automatic recognition algebraic extensions (see 7de602c)

• Implemented Collins’ modular algorithm for computing resultants (see 950969b)

• Implemented Berlekamp’s algorithm for factorization over finite fields (see 70353e9)

• Implemented Trager’s algorithm for factorization over algebraic number fields (see bd0be06)

• Improved Wang’s algorithm for efficient factorization of multivariate polynomials (see 425e225)

• Quantum

• Symbolic, abstract dirac notation in sympy.physics.quantum. This includes operators, states (bras and kets), commutators, anticommutators, dagger, inner products, outer products, tensor products and Hilbert spaces

• Symbolic quantum computing framework that is based on the general capabilities in sympy.physics.quantum. This includes qubits (sympy.physics.quantum.qubit), gates (sympy.physics.quantum.gate), Grover’s algorithm (sympy.physics.quantum.grover), the quantum Fourier transform (sympy.physics.quantum.qft), Shor’s algorithm (sympy.physics.quantum.shor) and circuit plotting (sympy.physics.quantum.circuitplot)

• Second quantization framework that inclues creation/anihilation operators for both Fermions and Bosons and Wick’s theorem for Fermions (sympy.physics.secondquant).

• Symbolic quantum angular momentum (spin) algebra (sympy.physics.quantum.spin)

• Hydrogen wave functions (Schroedinger) and energies (both Schroedinger and Dirac)

• Wave functions and energies for 1D harmonic oscillator

• Wave functions and energies for 3D spherically symmetric harmonic oscillator

• Wigner and Clebsch Gordan coefficients

• Everything else

• Implement symarray, providing numpy nd-arrays of symbols.

• update mpmath to 0.16

• Add a tensor module (see this report)

• A lot of stuff was being imported with from sympy import * that shouldn’t have been (like sys). This has been fixed.

• Assumptions:

• Concrete

• Finalized implementation of Gosper’s algorithm (see 0f187e5, 5888024)

• Removed redundant Sum2 and related classes (see ef1f6a7)

• Core:

• Split Atom into Atom and AtomicExpr (see 965aa91)

• Various sympify() improvements

• Added functionality for action verbs (many functions can be called both as global functions and as methods e.g. a.simplify() == simplify(a))

• Improve handling of rational strings (see 053a045, sympy/sympy#4877)

• Major changes to factoring of integers (see 273f450, sympy/sympy#5102)

• Optimized .has() (see c83c9b0, sympy/sympy#5079, d86d08f)

• Improvements to power (see c8661ef, sympy/sympy#5062)

• Added range and lexicographic syntax to symbols() and var() (see f6452a8, 9aeb220, 957745a)

• Added modulus argument to expand() (see 1ea5be8)

• Allow to convert Interval to relational form (see 4c269fe)

• SymPy won’t manipulate minus sign of expressions any more (see 6a26941, 9c6bf0f, e9f4a0a)

• Real and .is_Real were renamed to Float and .is_Float. Real and .is_Real still remain as deprecated shortcuts to Float and is_Float for backwards compatibility. (see abe1c49)

• Methods coeff and as_coefficient are now non-commutative aware. (see a4ea170)

• Geometry:

• Various improvements to Ellipse

• Updated documentation to numpy standard

• Polygon and Line improvements

• Allow all geometry objects to accept a tuple as Point args

• Integrals:

• isympy

• Fixed the -p switch (see e8cb04a)

• Caching can be disabled using -C switch (see 0d8d748)

• Ground types can be set using -t switch (see 75734f8)

• Printing ordering can be set using -o switch (see fcc6b13, 4ec9dc5)

• Logic

• implies object adheres to negative normal form

• Create new boolean class, logic.boolalg.Boolean

• Added XOR operator (^) support

• Functions:

• Spherical Bessel function of the second kind implemented

• Add series expansions of multivariate functions (see d4d351d)

• Matrices:

• Extended QR factorization for general full ranked mxn matrices

• Remove deprecated functions zero(), zeronm(), one() (see 5da0884)

• Added cholesky and LDL factorizations, and respective solves.

• Added functions for efficient triangular and diagonal solves.

• SMatrix was renamed to SparseMatrix (see acd1685)

• Printing:

• Implemented pretty printing of binomials (see 58c1dad)

• Implemented pretty printing of Sum() (see 84f2c22, 95b4321)

• sympy.printing now supports ordering of terms and factors (see 859bb33)

• Lexicographic order is now the default. Now finally things will print as x**2 + x + 1 instead of 1 + x + x**2, however series still print using reversed ordering, e.g. x - x**3/6 + O(x**5). You can get the old order (and other orderings) by setting the -o option to isympy (see 08b4932, a30c5a3)

• Series:

• Implement a function to calculate residues, residue()

• Implement nseries and lseries to handle x0 != 0, series should be more robust now (see 2c99999, sympy/sympy#5221 - sympy/sympy#5223)

• Improvements to Gruntz algorithm

• Simplify:

• Added use() (see 147c142)

• ratsimp() now uses cancel() and reduced() (see 108fb41)

• Implemented EPath (see 696139d, bf90689)

• a new keyword rational was added to nsimplify which will replace Floats with Rational approximations. (see 053a045)

• Solvers:

• Utilities:

• Improve cartes, for generating the Cartesian product (see b1b10ed)

• Added a function computing topological sort of graphs (see b2ce27b)

• Allow to setup a customized printer in lambdify() (see c1ad905)

• flatten() was significantly improved (see 31ed8d7)

• Major improvements to the Fortran code generator (see report, 3383aa3, 7ab2da2, etc)

## Compatibility breaks¶

• This will be the last release of SymPy to support Python 2.4. Dropping support for Python 2.4 will let us move forward with things like supporting Python 3, and will let us use things that were introduced in Python 2.5, like with-statement context managers.

• no longer support creating matrices without brackets (see sympy/sympy#4029)

• Renamed sum() to summation() (see 3e763a8, sympy/sympy#4475, sympy/sympy#4826). This was changed so that it no longer overrides the built-in sum(). The unevaluated summation is still called Sum().

• Renamed abs() to Abs() (see 64a12a4, sympy/sympy#4826). This was also changed so that it no longer overrides the built-in abs(). Note that because of __abs__ magic, you can still do abs(expr) with the built-in abs(), and it will return Abs(expr).

• Renamed max_() and min_() to now Max() and Min() (see 99a271e, sympy/sympy#5252)

• Changed behaviour of symbols(). symbols('xyz') gives now a single symbol ('xyz'), not three ('x', 'y' and 'z') (see f6452a8). Use symbols('x,y,z') or symbols('x y z') to get three symbols. The each_char option will still work but is being deprecated.

• Split class Basic into new classes Expr, Boolean (see a0ab479, 635d89c). Classes that are designed to be part of standard symbolic expressions (like x**2*sin(x)) should subclass from Expr. More generic objects that do not work in symbolic expressions but still want the basic SymPy structure like .args and basic methods like .subs() should only subclass from Basic.

• as_basic() method was renamed to as_expr() to reflect changes in the core (see e61819d, 80dfe91)

• Methods as_coeff_terms and as_coeff_factors were renamed to as_coeff_mul and as_coeff_add, respectively.

• Removed the trim() function. The function is redundant with the new polys. Use the cancel() function instead.

• The assume_pos_real option to logcombine() was renamed to force to be consistant with similar force options to other functions.

In addition to the more noticeable changes listed above, there have been numerous other smaller additions, improvements and bug fixes in the ~2000 commits in this release. See the git log for a full list of all changes. The command git log sympy-0.6.7..sympy-0.7.0 will show all commits made between this release and the last. You can also see the issues closed since the last release here.