Useful and Efficient Commands

Examples

evalf - evaluate using floating-point arithmetic

$\ln \left(2\right)$ = $\ln \left(2\right)$$$

$\mathrm{evalf}\left(\ln \left(2\right)\right)$ = $0.6931471806$$$

evalb- evaluate as a Boolean expression

$\mathrm{evalb}\left(-11\>0\right)$ = $\mathrm{false}$$$

$a≔2\:$

$b≔2\:$

$\mathrm{evalb}\left(a\=b\right)$ = $\mathrm{true}$$$

sort - sort a list of values or a polynomial

$\mathrm{sort}\left(\left[2\, 1\, 3\, 1\right]\right)$ = $\left[1\,1\,2\,3\right]$$$

$\mathrm{sort}\left(1\+2 x^4\+3 x\+x^3\right)$ = $2x^4+x^3+3x+1$$$

seq - create a sequence

$\mathrm{seq}\left(1..4\right)$ = $1,2,3,4$$$

$\mathrm{seq}\left(i^3\,i\=1..4\right)$ = $1,8,27,64$$$

map - apply a procedure to each operand of an expression

zip - zip together two data sets by applying a binary function to the components of the two data sets

The function iquo returns the quotient of two integers.

$\mathrm{map}\left(\ln \,\left[1\,2\,3\,4\right]\right)$ = $\left[0\,\ln \left(2\right)\,\ln \left(3\right)\,2\ln \left(2\right)\right]$$$

$\mathrm{zip}\left(\mathrm{iquo}\,\left[207\,241\,345\, 1235\right]\,\left[17\,21\,30\,44\right]\right)$ = $\left[12\,11\,11\,28\right]$$$

select, remove, and selectremove - selection or removal from an expression

Those elements which satisfy the Boolean-valued command are returned.  Here, we use the Boolean-valued command issqr, which tests if an integer is a perfect square.  

$\mathrm{select}\left(\mathrm{issqr}\,\left\{42\, 53\, 64\right\}\right)$ = $\left\{64\right\}$$$

indets - find the indeterminates of an expression

Expressions such as ${\ⅇ}^y$ are considered indeterminates.  Use the type `name` to return only variable names.

$\mathrm{indets}\left(x\cdot y\+z-x\cdot {\ⅇ}^y\right)$ = $\left\{x\,y\,z\,{\ⅇ}^y\right\}$$$

$\mathrm{indets}\left(x\cdot y\+z-x\cdot {\ⅇ}^y\,\mathrm{name}\right)$ = $\left\{x\,y\,z\right\}$$$

Package

Purpose

CodeGeneration

tools for translating Maple code to other languages

combinat

combinatorial functions, including commands for calculating permutations and combinations of lists and partitions of integers

CurveFitting

commands that support curve-fitting

DEtools

tools for manipulating, solving, and plotting systems of differential equations

DiscreteTransforms

commands for computing transforms of discrete data

DynamicSystems

commands for creating, manipulating, simulating, and plotting linear systems objects

LinearAlgebra

commands for manipulating Matrices and Vectors and performing Linear Algebra

Optimization

commands for numerically solving optimization theory problems

plots

commands for displaying graphical representations

Statistics

tools for mathematical statistics and data analysis

StringTools

optimized commands for string manipulation

Steps

Result

Example:

Use the Minimize command from the Optimization package to minimize $4\cdot x^2-\ln \left(x\right)$, given the initial point $x\=.5$.

First, we will use the long form by calling Optimization:-Minimize.

The minimum is given, followed by the $x$-value for which this minimum is attained.

$\mathrm{expr}≔4\cdot x^2-\ln \left(x\right)\:$

$\mathrm{Optimization}:-\mathrm{Minimize}\left(\mathrm{expr}\,\mathrm{initialpoint}\=\left\{x\=.5\right\}\right)$

Now, enter with(Optimization).

A list of all the commands in the package is returned.  (To suppress the display of this list, use a colon (:) after this command.)

Now, all these commands can be used by just entering the command name.  This is the short form of the calling sequence.

Example:

Redo the problem, using the short form.

Tip:  Packages can also be loaded from the Tools menu.

$\mathrm{with}\left(\mathrm{Optimization}\right)$

$\mathrm{Minimize}\left(\mathrm{expr}\,\mathrm{initialpoint}\=\left\{x\=.5\right\}\right)$