The ArrayTools package has been expanded to include many more commands for manipulating data inside an Array.  New operations include commands for inspecting zero and non-zero entries, element-wise operations, permutations, and expansions.

For details, see ?ArrayTools.

For information on the improvements to the DEtools package, see the Updates to Differential Equation (DE) Solvers in Maple 10 help page.

The FileTools package has four new commands: AbsolutePath, FileName, MakeDirectory, and ParentDirectory.

The gfun[rectoproc] command was rewritten to offer more flexibility to the user. A set of new options for this command was added.

The gfun[guesseqn] and gfun[guessgf] commands were accelerated.

To control global parameters of the gfun package, use the new gfun[Parameters] command.

The Groebner package implements new and faster algorithms for Groebner basis computations in the case of commutative polynomials. For more information, see Groebner[Basis], Groebner[FGLM], Groebner[Walk], and Efficiency Improvements in Maple 10.

Most of the commands in the Groebner package have been renamed and the notions of "terms" and "monomials" were changed. For more information, see Compatibility Issues in Maple 10 and Groebner/terminology.

Most commands in the Groebner package now accept radicals and RootOfs in the coefficients. The Groebner[Basis] command accepts the characteristic as an optional argument. Many commands accept PolynomialIdeal data structures as input.

New monomial orders were added, graded lexicographic order (grlex) and a constructor for products of existing monomial orders (prod).

Existing monomial orders were extended. The elimination order lexdeg now supports more than two blocks and the general matrix order matrix now supports singular matrices. For details, see MonomialOrders.

Examples

New commands FGLM and Walk:

with(Groebner):

G := Basis([x^3+x*y-y^2+1, y^3-x*y+x], tdeg(x,y));

$G≔\left[y^3-xy+x\,x^3+xy-y^2+1\right]$

FGLM(G, tdeg(x,y), plex(x,y));

$\left[y^9+y^6-3y^5+4y^4-2y^3-2y^2+3y-1\,y^8+y^7+y^6+2y^5-y^4+3y^3+x-2y+1\right]$

Walk(G, tdeg(x,y), plex(x,y));

$\left[y^9+y^6-3y^5+4y^4-2y^3-2y^2+3y-1\,y^8+y^7+y^6+2y^5-y^4+3y^3+x-2y+1\right]$

Note the new semantics of terms and monomials.

f := 3*x*y*z+2*y*z^2+5*x^3*y;

$f≔5x^{3}y+3xyz+2y{z}^2$

LeadingCoefficient(f, tdeg(x,y,z));

$5$

LeadingMonomial(f, tdeg(x,y,z));

$x^{3}y$

LeadingTerm(f, tdeg(x,y,z));

$5,x^{3}y$

New option characteristic:

Basis([x^6+x^3*y^3+y^6,x^3-y^3],plex(y),characteristic=3);

$\left[2x^3+y^3\right]$

unwith(Groebner):

Two new commands LinearFunctionalSystems[RegularSolution] and LinearFunctionalSystems[ExtendRegularSolution] were added for computing truncated asymptotic series expansions for the regular solutions of systems of linear PDEs.

A new hybrid method for computing the universal denominator for rational solutions of a system of linear PDEs was implemented.

The numapprox[chebyshev] command now accepts an operator as a first argument and a range as a second argument.

A number of features were added to the Optimization package.  These include new output and method options, integration of an integer linear programming solver and a univariate global search algorithm, and the addition of plotting capability to the Optimization Assistant.

with(Optimization):

For information on the improvements to the PDEtools package, see the Updates to Differential Equation (DE) Solvers in Maple 10 help page.

The QDifferenceEquations package has the following new commands.

The q-equivalents of factorials, binomials, the GAMMA function, and the Pochhammer symbol, as well as the q-bracket were added. For more information, see the q-Objects help page. The QDifferenceEquations[QHypergeometricSolution] command can output the solutions in terms of those new objects.

The q-analogs of the rational normal forms have been added: QDifferenceEquations[QPolynomialNormalForm], QDifferenceEquations[QRationalCanonicalForms], QDifferenceEquations[QMultiplicativeDecomposition], and QDifferenceEquations[QEfficientRepresentation].

Examples

with(QDifferenceEquations):

expand(QPochhammer(a,q,4));

$\left(1-a\right)\left(-aq+1\right)\left(-a{q}^2+1\right)\left(-a{q}^3+1\right)$

expand(QBrackets(4,q));

$\frac{q^4-1}{q-1}$

convert(QBinomial(n,k,q),'QPochhammer');

$\frac{\mathrm{QPochhammer}\left(q\,q\,n\right)}{\mathrm{QPochhammer}\left(q\,q\,k\right)\mathrm{QPochhammer}\left(q\,q\,n-k\right)}$

unwith(QDifferenceEquations):

The RandomTools package now includes various algorithms for generating pseudo-random numbers.  In addition to the Linear Congruence algorithm that was previously available as rand, RandomTools also includes the Mersenne Twister algorithm, the Blum, Blum, and Shub algorithm and a Quadratic Congruence algorithm.

The StringTools package has new commands: WrapText, ExpandTabs, Hash, Fence, and a collection of existential versions of the character class tests, such as HasDigit and HasSpace.

The Student package has undergone significant revisions to its interactive components, also known as tutors. The main result of these revisions has been to standardize the look and feel of tutors which implement similar functionality, across the package. This will reduce the time required to become familiar with tutors demonstrating different concepts, and should result in more predictable behavior.

Additionally, each of the tutors that displays a plot now has a Plot options button. Pressing this button brings up a dialog that can be used to control the presentation of the plot. For example, you can change the colors or axis style. Tutors that present concepts which are best illustrated through animations also have an Animate button. Pressing this button starts the animation, and also displays extra buttons for controlling the speed and pause/play state of the animation.

A new routine, CompleteSquare has been added to the Student[Precalculus] package. This routine can be used to rewrite quadratic subexpressions of a given expression in completed square form.

The new command SumTools[Hypergeometric][MinimalTelescoper] was added.

The new top-level command Unit now provides another means to access the Units[Unit] command for creation of expressions containing units.

The standard default context menus have been augmented with entries to assist in handling expressions containing units. Submenu entries have been added to allow simplification, removal, conversion, and introduction of units into an expression.

The new Norm command computes the norm of a Vector or VectorField.

with(VectorCalculus):

SetCoordinates(cartesian[x,y]);

${\mathrm{cartesian}}_{x,y}$

Norm(<3,4>);

$5$

n := Norm(VectorField(<x*y,x/y>),3):

n(<2,3>);

$\frac{2{730}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{3}$

The new Normalize command normalizes a Vector or VectorField.

SetCoordinates(cartesian[x,y]);

${\mathrm{cartesian}}_{x,y}$

Normalize(<3,4>);

$\left(\frac{3}{5}\right)e_x\&plus;\left(\frac{4}{5}\right)e_y$

n := Normalize(VectorField(<x*y,x/y>),3);

$n≔\left(\frac{xy\left|\frac{y}{x}\right|}{{\left({\left|y\right|}^6+1\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\right){\stackrel{\&lowbar;}{e}}_x\&plus;\left(\frac{x\left|\frac{y}{x}\right|}{y{\left({\left|y\right|}^6+1\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\right){\stackrel{\&lowbar;}{e}}_y$

simplify(evalVF(n, <2,3>));

$\left[\begin{array}{c}\frac{9{730}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{730}\\ \frac{{730}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{730}\end{array}\right]$