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Sage 4.0.2 Release Tour

Sage 4.0.2 was released on FIXME. For the official, comprehensive release note, please refer to FIXME. A nicely formatted version of this release tour can be found at FIXME. The following points are some of the foci of this release:

Algebra

• Correct precision bound in hilbert_class_polynomial() and miscellaneous new functions (John Cremona) -- The two new functions are elliptic_j() in sage/functions/special.py, and is_primitive() in the class BinaryQF of sage/quadratic_forms/binary_qf.py. The function elliptic_j(z) returns the elliptic modular j-function evaluated at z. The function is_primitive() determines whether the binary quadratic form ax^2 + bxy + cy^2 satisfies gcd(a,b,c) = 1, i.e. that it is primitive. Here are some examples on using these new functions:

  sage: elliptic_j(CC(i))
  1728.00000000000
  sage: elliptic_j(sqrt(-2.0))
  8000.00000000000
  sage: Q = BinaryQF([6,3,9])
  sage: Q.is_primitive()
  False
  sage: Q = BinaryQF([1,1,1])
  sage: Q.is_primitive()
  True

• Efficient Lagrange interpolation polynomial (Yann Laigle-Chapuy) -- Calculating the Lagrange interpolation polynomial of a set of points is now up to 48% faster than previously. The following timing statistics were obtained using the machine sage.math:

  # BEFORE
  
  sage: R = PolynomialRing(QQ, 'x')
  sage: %timeit R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
  1000 loops, best of 3: 824 µs per loop
  sage: R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
  -23/84*x^3 - 11/84*x^2 + 13/7*x + 1
  sage: R = PolynomialRing(GF(2**3,'a'), 'x')
  sage: a = R.base_ring().gen()
  sage: timeit("R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])")
  625 loops, best of 3: 111 µs per loop
  sage: R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])
  a^2*x^2 + a^2*x + a^2
  
  
  # AFTER
  
  sage: R = PolynomialRing(QQ, 'x')
  sage: %timeit R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
  1000 loops, best of 3: 425 µs per loop
  sage: R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])
  -23/84*x^3 - 11/84*x^2 + 13/7*x + 1
  sage: R = PolynomialRing(GF(2**3,'a'), 'x')
  sage: a = R.base_ring().gen()
  sage: timeit("R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])")
  625 loops, best of 3: 86.4 µs per loop
  sage: R.lagrange_polynomial([(a^2+a,a),(a,1),(a^2,a^2+a+1)])
  a^2*x^2 + a^2*x + a^2

• Deprecate the method __len__() for a matrix group (Nicolas Thiery) -- The method __len__() of the class MatrixGroup_gap in sage/groups/matrix_gps/matrix_group.py is now deprecated and will be removed in a future release. To get the number of elements in a matrix group, users are advised to use the method cardinality() instead. The method order() is essentially the same as cardinality(), so order() will be deprecated in a future release.

Algebraic Geometry

• FIXME: summarize #6218

Basic Arithmetic

Build

• FIXME: summarize #6234
• FIXME: summarize #6170

Calculus

Coding Theory

• FIXME: summarize #6014

Combinatorics

Commutative Algebra

• FIXME: summarize #6051

Cryptography

• FIXME: summarize #6185

Graph Theory

• FIXME: summarize #5975

Graphics

Group Theory

• FIXME: summarize #6263
• FIXME: summarize #6123

Interfaces

Linear Algebra

• FIXME: summarize #6178
• FIXME: summarize #5510
• FIXME: summarize #2256

Miscellaneous

• FIXME: summarize #6089
• FIXME: summarize #6110

Modular Forms

Notebook

• FIXME: summarize #6259
• FIXME: summarize #6225
• FIXME: summarize #5371

Number Theory

• FIXME: summarize #5976
• FIXME: summarize #5842
• FIXME: summarize #6205
• FIXME: summarize #6193
• FIXME: summarize #6044
• FIXME: summarize #6046

Numerical

Packages

• Upgrade NumPy to version 1.3.0 latest upstream release (Jason Grout).

• Upgrade SciPy to version 0.7 latest upstream release (Jason Grout).

• Upgrade Singular to version 3-1-0 latest upstream release (Martin Albrecht).

• Upgrade FLINT to version 1.3.0 latest upstream release (Nick Alexander).

• Update the MPIR spkg to version mpir-1.2.p3.spkg (Nick Alexander).

• Remove Guava as a standard Sage package (David Joyner).

• FIXME: summarize #6298

Symbolics

Topology