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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html lang="en" xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="content-type" content="text/html;charset=UTF-8"/>
<link rel="icon" type="image/gif" href="/favicon.gif"/>
<link rel="apple-touch-icon" sizes="120x120" href="touch-icon-iphone-retina.png" />
<link rel="apple-touch-icon" sizes="152x152" href="touch-icon-ipad-retina.png" />
<title>Lorem Ipsum</title>
<script type="text/javascript"
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<style type="text/css" id="internal-style">
@import url(hyperpolyglot.css);
</style>
<meta http-equiv="content-type" content="text/html;charset=UTF-8"/>
<meta http-equiv="content-language" content="en"/>
</head>
<body>
<div id="container-wrap-wrap">
<div id="container-wrap">
<div id="container">
<div id="header">
<h1><a href="/"><span>Hyperpolyglot</span></a></h1>
</div>
<div id="content-wrap">
<div id="main-content">
<div id="page-title">Lorem Ipsum</div>
<div id="page-content">
<p><em>a side-by-side reference sheet</em></p>
<p><strong>sheet one:</strong> <a href="#grammar-invocation">grammar and invocation</a> | <a href="#var-expr">variables and expressions</a> | <a href="#arithmetic-logic">arithmetic and logic</a> | <a href="#strings">strings</a> | <a href="#arrays">arrays</a> | <a href="#sets">sets</a> | <a href="#arith-seq">arithmetic sequences</a> | <a href="#dictionaries">dictionaries</a> | <a href="#functions">functions</a> | <a href="#execution-control">execution control</a> | <a href="#exceptions">exceptions</a> | <a href="#streams">streams</a> | <a href="#files">files</a> | <a href="#directories">directories</a> | <a href="#libraries-namespaces">libraries and namespaces</a> | <a href="#reflection">reflection</a></p>
<p><strong><a href="/computer-algebra2">sheet two:</a></strong> <a href="/computer-algebra2#symbolic-expr">symbolic expressions</a> | <a href="/computer-algebra2#calculus">calculus</a> | <a href="/computer-algebra2#equations-unknowns">equations and unknowns</a> | <a href="/computer-algebra2#optimization">optimization</a> | <a href="/computer-algebra2#vectors">vectors</a> | <a href="/computer-algebra2#matrices">matrices</a> | <a href="/computer-algebra2#combinatorics">combinatorics</a> | <a href="/computer-algebra2#number-theory">number theory</a> | <a href="/computer-algebra2#polynomials">polynomials</a> | <a href="/computer-algebra2#trigonometry">trigonometry</a> | <a href="/computer-algebra2#special-functions">special functions</a> | <a href="/computer-algebra2#permutations">permutations</a> | <a href="/computer-algebra2#descriptive-statistics">descriptive statistics</a> | <a href="/computer-algebra2#distributions">distributions</a> | <a href="/computer-algebra2#statistical-tests">statistical tests</a></p>
<p><a href="/computer-algebra2#bar-charts">bar charts</a> | <a href="/computer-algebra2#scatter-plots">scatter plots</a> | <a href="/computer-algebra2#line-charts">line charts</a> | <a href="/computer-algebra2#surface-charts">surface charts</a> | <a href="/computer-algebra2#chart-options">chart options</a></p>
<table class="wiki-content-table">
<tr>
<th></th>
<th><a href="#mathematica">mathematica</a></th>
<th><a href="#sympy">sympy</a></th>
<th><a href="#sage">sage</a></th>
<th><a href="#maxima">maxima</a></th>
</tr>
<tr>
<td><a name="version-used"></a><a href="#version-used-note">version used</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>10.0</em></span></td>
<td><span style="color: gray"><em>Python 2.7; SymPy 0.7</em></span></td>
<td><span style="color: gray"><em>6.10</em></span></td>
<td><span style="color: gray"><em>5.37</em></span></td>
</tr>
<tr>
<td><a name="show-version"></a><a href="#show-version-note">show version</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>select</em> About Mathematica <em>in</em> Mathematica <em>menu</em></span></td>
<td><span style="white-space: pre-wrap;">sympy.__version__</span></td>
<td>$ sage <span style="white-space: pre-wrap;">--</span>version<br />
<br />
<span style="color: gray"><em>also displayed on worksheet</em></span></td>
<td>$ maxima <span style="white-space: pre-wrap;">--</span>version</td>
</tr>
<tr>
<td><a name="implicit-prologue"></a><a href="#implicit-prologue-note">implicit prologue</a></td>
<td> </td>
<td>from sympy import *<br />
<br />
<span style="color: gray"># enable LaTeX rendering in Jupyter notebook:</span><br />
init_printing()<br />
<br />
<span style="color: gray"># unknown variables must be declared:</span><br />
x, y = symbols('x y')</td>
<td><span style="color: gray"># unknowns other than x must be declared:</span><br />
y = var('y')</td>
<td> </td>
</tr>
<tr>
<th colspan="5"><a name="grammar-invocation"></a><a href="#grammar-invocation-note">grammar and invocation</a></th>
</tr>
<tr>
<th></th>
<th>mathematica</th>
<th>sympy</th>
<th>sage</th>
<th>maxima</th>
</tr>
<tr>
<td><a name="interpreter"></a><a href="#interpreter-note">interpreter</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>$ cat <span style="white-space: pre-wrap;">></span> hello.m<br />
Print["Hello, World!"]<br />
<br />
$ MathKernel -script hello.m</td>
<td><span style="color: gray"><em>if</em> foo.py <em>imports sympy:</em></span><br />
$ python <span style="color: gray"><em>foo</em></span>.py</td>
<td>$ cat > hello.sage<br />
print("Hello, World!")<br />
<br />
$ sage hello.sage</td>
<td>$ cat <span style="white-space: pre-wrap;">>></span> hello.max<br />
print("Hello, world!");<br />
<br />
$ maxima -b hello.maxima</td>
</tr>
<tr>
<td><a name="repl"></a><a href="#repl-note">repl</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>$ MathKernel</td>
<td>$ python<br />
<span style="white-space: pre-wrap;">>>></span> from sympy import *</td>
<td>$ sage</td>
<td>$ maxima</td>
</tr>
<tr>
<td><a name="block-delimiters"></a><a href="#block-delimiters-note">block delimiters</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>( <span style="color: gray"><em>stmt</em></span>; <span style="color: gray"><em>...</em></span>)</td>
<td>: <span style="color: gray"><em>and offside rule</em></span></td>
<td>: <span style="color: gray"><em>and offside rule</em></span></td>
<td>block([x: 3, y: 4], x + y);<br />
<br />
<span style="color: gray">/* Multiple stmts are separated by commas; a list of assignments can be used to set variables local to the block. */</span></td>
</tr>
<tr>
<td><a name="stmt-separator"></a><a href="#stmt-separator-note">statement separator</a></td>
<td>; <span style="color: gray"><em>or sometimes newline</em></span><br />
<br />
<span style="color: gray"><em>A semicolon suppresses echoing value of previous expression.</em></span></td>
<td><span style="color: gray"><em>newline or</em></span> ;<br />
<br />
<span style="color: gray">//newlines not separators inside (), [], {}, triple quote literals, or after backslash: <span style="white-space: pre-wrap;">\</span>//</span>//</td>
<td><span style="color: gray"><em>newline or</em></span> ;<br />
<br />
<span style="color: gray">//newlines not separators inside (), [], {}, triple quote literals, or after backslash: <span style="white-space: pre-wrap;">\</span>//</span>//</td>
<td>; <span style="color: gray"><em>or</em></span> $<br />
<br />
<span style="color: gray"><em>The dollar sign</em> $ <em>suppresses output.</em></span></td>
</tr>
<tr>
<td><a name="eol-comment"></a><a href="#eol-comment-note">end-of-line comment</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>none</em></span></td>
<td>1 + 1 <span style="color: gray"># addition</span></td>
<td>1 + 1 <span style="color: gray"># addition</span></td>
<td><span style="color: gray"><em>none</em></span></td>
</tr>
<tr>
<td><a name="multiple-line-comment"></a><a href="#multiple-line-comment-note">multiple line comment</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>1 + <span style="color: gray">(* addition *)</span> 1</td>
<td><span style="color: gray"><em>none</em></span></td>
<td><span style="color: gray"><em>none</em></span></td>
<td>1 + <span style="color: gray">/* addition */</span> 1;</td>
</tr>
<tr>
<th colspan="5"><a name="var-expr"></a><a href="#var-expr-note">variables and expressions</a></th>
</tr>
<tr>
<th></th>
<th>mathematica</th>
<th>sympy</th>
<th>sage</th>
<th>maxima</th>
</tr>
<tr>
<td><a name="assignment"></a><a href="#assignment-note">assignment</a></td>
<td>a = 3<br />
Set[a, 3]<br />
<br />
<span style="color: gray">(* rhs evaluated each time a is accessed: *)</span><br />
a := x + 3<br />
SetDelayed[a, x + 3]</td>
<td>a = 3</td>
<td>a = 3</td>
<td>a: 3;</td>
</tr>
<tr>
<td><a name="parallel-assignment"></a><a href="#parallel-assignment-note">parallel assignment</a></td>
<td>{a, b} = {3, 4}<br />
Set[{a, b}, {3, 4}]</td>
<td>a, b = 3, 4</td>
<td>a, b = 3, 4</td>
<td>[a, b]: [3, 4]</td>
</tr>
<tr>
<td><a name="compound-assignment"></a><a href="#compound-assignment-note">compound assignment</a></td>
<td>+= -= *= /=<br />
<span style="color: gray"><em>corresponding functions:</em></span><br />
AddTo SubtractFrom TimeBy DivideBy</td>
<td>+= -= *= /= <span style="white-space: pre-wrap;">//=</span> %= ^= <span style="white-space: pre-wrap;">**=</span></td>
<td>+= -= *= /= <span style="white-space: pre-wrap;">//=</span> %= <span style="white-space: pre-wrap;">**=</span></td>
<td><span style="color: gray"><em>none</em></span></td>
</tr>
<tr>
<td><a name="incr-decr"></a><a href="#incr-decr-note">increment and decrement</a></td>
<td>++x <span style="white-space: pre-wrap;">--</span>x<br />
PreIncrement[x] PreDecrement[x]<br />
x++ x<span style="white-space: pre-wrap;">--</span><br />
Increment[x] Decrement[x]</td>
<td><span style="color: gray"><em>none</em></span></td>
<td><span style="color: gray"><em>none</em></span></td>
<td><span style="color: gray"><em>none</em></span></td>
</tr>
<tr>
<td><a name="non-referential-id"></a><a href="#non-referential-id-note">non-referential identifier</a></td>
<td><span style="color: gray"><em>any unassigned identifier is non-referential</em></span></td>
<td>x, y, z, w = symbols('x y z w')</td>
<td>y, z, w = var('y z w')<br />
<br />
<span style="color: gray"># x is non-referential unless assigned a value</span></td>
<td><span style="color: gray"><em>any unassigned identifier is non-referential</em></span></td>
</tr>
<tr>
<td><a name="id-as-val"></a><a href="#id-as-val-note">identifier as value</a></td>
<td>x = 3<br />
y = HoldForm[x]</td>
<td> </td>
<td> </td>
<td>x: 3;<br />
y: 'x;</td>
</tr>
<tr>
<td><a name="global-var"></a><a href="#global-var-note">global variable</a></td>
<td><span style="color: gray"><em>variables are global by default</em></span></td>
<td>g1, g2 = 7, 8<br />
<br />
def swap_globals():<br />
<span style="white-space: pre-wrap;"> </span>global g1, g2<br />
<span style="white-space: pre-wrap;"> </span>g1, g2 = g2, g1</td>
<td>g1, g2 = 7, 8<br />
<br />
def swap_globals():<br />
<span style="white-space: pre-wrap;"> </span>global g1, g2<br />
<span style="white-space: pre-wrap;"> </span>g1, g2 = g2, g1</td>
<td><span style="color: gray"><em>variables are global by default</em></span></td>
</tr>
<tr>
<td><a name="local-var"></a><a href="#local-var-note">local variable</a></td>
<td>Module[{x = 3, y = 4}, Print[x + y]]<br />
<br />
<span style="color: gray">(* makes x and y read-only: *)</span><br />
With[{x = 3, y = 4}, Print[x + y]]<br />
<br />
<span style="color: gray">(* Block[ ] declares dynamic scope *)</span></td>
<td><span style="color: gray"><em>assignments inside functions are to local variables by default</em></span></td>
<td><span style="color: gray"><em>assignments inside functions are to local variables by default</em></span></td>
<td>block([x: 3, y: 4], print(x + y));</td>
</tr>
<tr>
<td><a name="null"></a><a href="#null-note">null</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Null</td>
<td>None</td>
<td>None</td>
<td><span style="color: gray"><em>no null value</em></span></td>
</tr>
<tr>
<td><a name="null-test"></a><a href="#null-test-note">null test</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>x == Null</td>
<td>x is None</td>
<td>x is None</td>
<td><span style="color: gray"><em>no null value</em></span></td>
</tr>
<tr>
<td><a name="undef-var"></a><a href="#undef-var-note">undefined variable access</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>treated as an unknown number</em></span></td>
<td><span style="color: gray"><em>raises</em> NameError</span></td>
<td><span style="color: gray"><em>raises</em> NameError</span></td>
<td><span style="color: gray"><em>treated as an unknown number</em></span></td>
</tr>
<tr>
<td><a name="rm-var-binding"></a><a href="#rm-var-binding-note">remove variable binding</a></td>
<td>Clear[x]<br />
Remove[x]</td>
<td>del x</td>
<td>del x</td>
<td>kill(x);</td>
</tr>
<tr>
<td><a name="cond-expr"></a><a href="#cond-expr-note">conditional expression</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>If[x > 0, x, -x]</td>
<td>x if x > 0 else -x</td>
<td>x if x > 0 else -x</td>
<td>if x < 0 then -x else x;</td>
</tr>
<tr>
<th colspan="5"><a name="arithmetic-logic"></a><a href="#arithmetic-logic-note">arithmetic and logic</a></th>
</tr>
<tr>
<th></th>
<th>mathematica</th>
<th>sympy</th>
<th>sage</th>
<th>maxima</th>
</tr>
<tr>
<td><a name="true-false"></a><a href="#true-false-note">true and false</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>True False</td>
<td>True False</td>
<td>True False</td>
<td>true false</td>
</tr>
<tr>
<td><a name="falsehoods"></a><a href="#falsehoods-note">falsehoods</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>False</td>
<td>False 0 0.0</td>
<td>False None 0 0.0 '' [] {}</td>
<td> </td>
</tr>
<tr>
<td><a name="logical-op"></a><a href="#logical-op-note">logical operators</a></td>
<td>! True @</td>
<td>@@ (True && False)<br />
Or[Not[True], And[True, False]]</td>
<td>Or(Not(True), And(True, False))<br />
<br />
<span style="color: gray"># when arguments are symbols:</span><br />
<span style="white-space: pre-wrap;">~ x | (y & z)</span></td>
<td> </td>
<td>and or not</td>
</tr>
<tr>
<td><a name="relational-expr"></a><a href="#relational-expr-note">relational expression</a></td>
<td>1 < 2</td>
<td> </td>
<td> </td>
<td>is(1 < 2);</td>
</tr>
<tr>
<td><a name="relational-op"></a><a href="#relational-op-note">relational operators</a></td>
<td>== != > < >= <=<br />
<span style="color: gray"><em>corresponding functions:</em></span><br />
Equal Unequal Greater Less GreaterEqual LessEqual</td>
<td>Eq Ne Gt Lt Ge Le<br />
<br />
<span style="color: gray"># when arguments are symbols:</span><br />
== != > < >= <=</td>
<td>== != > < >= <=</td>
<td><span style="white-space: pre-wrap;">=</span> # > < >= <=</td>
</tr>
<tr>
<td><a name="arith-op"></a><a href="#arith-op-note">arithmetic operators</a></td>
<td>+ - * / Quotient Mod<br />
<span style="color: gray"><em>adjacent terms are multiplied, so * is not necessary.</em> Quotient <em>and</em> Mod <em>are functions, not binary infix operators. These functions are also available:</em></span><br />
Plus Subtract Times Divide</td>
<td>+ - * / <span style="color: gray"><em>??</em></span> %<br />
<br />
<span style="color: gray"><em>if an expression contains a symbol, then the above operators are rewritten using the following classes:</em></span><br />
Add Mul Pow Mod</td>
<td>+ - * / <span style="white-space: pre-wrap;">//</span> %</td>
<td>+ - * / quotitent() mod()<br />
<br />
<span style="color: gray">quotient <em>and</em> mod <em>are functions, not binary infix operators.</em></span></td>
</tr>
<tr>
<td><a name="int-div"></a><a href="#int-div-note">integer division</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Quotient[a, b]</td>
<td> </td>
<td>7 <span style="white-space: pre-wrap;">//</span> 3</td>
<td>quotient(7, 3);</td>
</tr>
<tr>
<td><a name="int-div-zero"></a><a href="#int-div-zero-note">integer division by zero</a></td>
<td><span style="color: gray"><em>dividend is zero:</em></span><br />
Indeterminate<br />
<span style="color: gray"><em>otherwise:</em></span><br />
ComplexInfinity</td>
<td> </td>
<td><span style="color: gray"><em>raises</em> ZeroDivisionError</span></td>
<td><span style="color: gray"><em>error</em></span></td>
</tr>
<tr>
<td><a name="float-div"></a><a href="#float-div-note">float division</a></td>
<td><span style="color: gray"><em>exact division:</em></span><br />
a / b</td>
<td> </td>
<td> </td>
<td>a / b</td>
</tr>
<tr>
<td><a name="float-div-zero"></a><a href="#float-div-zero-note">float division by zero</a></td>
<td><span style="color: gray"><em>dividend is zero:</em></span><br />
Indeterminate<br />
<span style="color: gray"><em>otherwise:</em></span><br />
ComplexInfinity</td>
<td> </td>
<td> </td>
<td><span style="color: gray"><em>error</em></span></td>
</tr>
<tr>
<td><a name="power"></a><a href="#power-note">power</a></td>
<td>2 ^ 32<br />
Power[2, 32]</td>
<td>2 <span style="white-space: pre-wrap;">**</span> 32<br />
Pow(2, 32)</td>
<td>2 ^ 32<br />
2 <span style="white-space: pre-wrap;">**</span> 32</td>
<td>2 ^ 32;<br />
2 <span style="white-space: pre-wrap;">**</span> 32;</td>
</tr>
<tr>
<td><a name="sqrt"></a><a href="#sqrt-note">sqrt</a></td>
<td><span style="color: gray"><em>returns symbolic expression:</em></span><br />
Sqrt[2]</td>
<td>sqrt(2)</td>
<td>sqrt(2)</td>
<td>sqrt(2);</td>
</tr>
<tr>
<td><a name="sqrt-negative-one"></a><a href="#sqrt-negative-one-note">sqrt -1</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>I</td>
<td>I</td>
<td>I</td>
<td>%i</td>
</tr>
<tr>
<td><a name="transcendental-func"></a><a href="#transcendental-func-note">transcendental functions</a></td>
<td>Exp Log<br />
Sin Cos Tan<br />
ArcSin ArcCos ArcTan<br />
ArcTan<br />
<span style="color: gray">ArcTan <em>accepts 1 or 2 arguments</em></span></td>
<td>exp log<br />
sin cos tan<br />
asin acos atan<br />
atan2</td>
<td>exp log<br />
sin cos tan<br />
asin acos atan<br />
atan2</td>
<td>exp log<br />
sin cos tan<br />
asin acos atan<br />
atan2</td>
</tr>
<tr>
<td><a name="transcendental-const"></a><a href="#transcendental-const-note">transcendental constants</a><br />
<span style="color: gray"><em>π and Euler's number</em></span></td>
<td>Pi E EulerGamma</td>
<td>pi E</td>
<td>pi e euler_gamma</td>
<td>%pi %e %gamma</td>
</tr>
<tr>
<td><a name="float-truncation"></a><a href="#float-truncation-note">float truncation</a><br />
<span style="color: gray"><em>round towards zero, round to nearest integer, round down, round up</em></span></td>
<td>IntegerPart Round Floor Ceiling</td>
<td>floor<br />
ceiling</td>
<td>int<br />
round<br />
floor<br />
ceil</td>
<td>truncate<br />
round<br />
floor<br />
ceiling</td>
</tr>
<tr>
<td><a name="absolute-val"></a><a href="#absolute-val-note">absolute value</a><br />
<span style="color: gray"><em>and signum</em></span></td>
<td>Abs Sign</td>
<td>Abs sign</td>
<td>abs sign</td>
<td>abs sign<br />
<br />
<span style="color: gray">sign <em>returns</em> pos, neg, <em>or</em> zero</span></td>
</tr>
<tr>
<td><a name="int-overflow"></a><a href="#int-overflow-note">integer overflow</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>none, has arbitrary length integer type</em></span></td>
<td><span style="color: gray"><em>none, has arbitrary length integer type</em></span></td>
<td><span style="color: gray"><em>none, has arbitrary length integer type</em></span></td>
<td><span style="color: gray"><em>none, has arbitrary length integer type</em></span></td>
</tr>
<tr>
<td><a name="float-overflow"></a><a href="#float-overflow-note">float overflow</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>none</em></span></td>
<td> </td>
<td> </td>
<td><span style="color: gray"><em>none</em></span></td>
</tr>
<tr>
<td><a name="rational-construction"></a><a href="#rational-construction-note">rational construction</a></td>
<td>2 / 7</td>
<td>Mul(2, Pow(7, -1))<br />
Rational(2, 7)</td>
<td>2 / 7</td>
<td>2 / 7</td>
</tr>
<tr>
<td><a name="rational-decomposition"></a><a href="#rational-decomposition-note">rational decomposition</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Numerator[2 / 7]<br />
Denominator[2 / 7]</td>
<td>numer, denom = fraction(Rational(2, 7))</td>
<td>numerator(2 / 7)<br />
denominator(2 / 7)</td>
<td>num(2 / 7);<br />
denom(2 / 7);</td>
</tr>
<tr>
<td><a name="decimal-approx"></a><a href="#decimal-approx-note">decimal approximation</a></td>
<td>N[2 / 7]<br />
2 / 7 + 0.<br />
2 / 7 <span style="white-space: pre-wrap;">//</span> N<br />
N[2 / 7, 100]</td>
<td>N(Rational(2, 7))<br />
N(Rational(2, 7), 100)</td>
<td>n(2 / 7)<br />
n(2 / 7, 100)<br />
<br />
<span style="color: gray"># synonyms for n:</span><br />
N(2 / 7)<br />
numerical_approx(2 / 7)</td>
<td>2 / 7, numer;</td>
</tr>
<tr>
<td><a name="complex-construction"></a><a href="#complex-construction-note">complex construction</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>1 + 3I</td>
<td>1 + 3 * I</td>
<td>1 + 3 * I</td>
<td>1 + 3 * %i;</td>
</tr>
<tr>
<td><a name="complex-decomposition"></a><a href="#complex-decomposition-note">complex decomposition</a><br />
<span style="color: gray"><em>real and imaginary part, argument and modulus, conjugate</em></span></td>
<td>Re Im<br />
Arg Abs<br />
Conjugate</td>
<td>re im<br />
Abs arg<br />
conjugate</td>
<td>(3 + I).real()<br />
(3 + I).imag()<br />
abs(3 + I)<br />
arg(3 + I)<br />
(3 + I).conjugate()</td>
<td>realpart imagpart<br />
cabs carg<br />
conjugate</td>
</tr>
<tr>
<td><a name="random-num"></a><a href="#random-num-note">random number</a><br />
<span style="color: gray"><em>uniform integer, uniform float</em></span></td>
<td>RandomInteger[{0, 99}]<br />
RandomReal[]</td>
<td> </td>
<td> </td>
<td>random(100);<br />
random(1.0);</td>
</tr>
<tr>
<td><a name="random-seed"></a><a href="#random-seed-note">random seed</a><br />
<span style="color: gray"><em>set, get</em></span></td>
<td>SeedRandom[17]<br />
<span style="color: gray"><em>??</em></span></td>
<td> </td>
<td> </td>
<td>set_random_state(make_random_state(17));<br />
<span style="color: gray"><em>??</em></span></td>
</tr>
<tr>
<td><a name="bit-op"></a><a href="#bit-op-note">bit operators</a></td>
<td>BitAnd[5, 1]<br />
BitOr[5, 1]<br />
BitXor[5, 1]<br />
BitNot[5]<br />
BitShiftLeft[5, 1]<br />
BitShiftRight[5, 1]</td>
<td> </td>
<td> </td>
<td><span style="color: gray"><em>none</em></span></td>
</tr>
<tr>
<td><a name="binary-octal-hex-literals"></a><a href="#binary-octal-hex-literals-note">binary, octal, and hex literals</a></td>
<td>2<span style="white-space: pre-wrap;">^^</span>101010<br />
8<span style="white-space: pre-wrap;">^^</span>52<br />
16<span style="white-space: pre-wrap;">^^</span>2a</td>
<td> </td>
<td> </td>
<td>ibase: 2;<br />
101010;<br />
<br />
ibase: 8;<br />
52;<br />
<br />
<span style="color: gray">/* If first hex digit is a letter, prefix a zero: */</span><br />
ibase: 16;<br />
2a;</td>
</tr>
<tr>
<td><a name="radix"></a><a href="#radix-note">radix</a></td>
<td>BaseForm[42, 7]<br />
BaseForm[7^^60, 10]</td>
<td> </td>
<td> </td>
<td>obase: 7;<br />
42;</td>
</tr>
<tr>
<td><a name="to-array-of-digits"></a><a href="#to-array-of-digits-note">to array of digits</a></td>
<td><span style="color: gray">(* base 10: *)</span><br />
IntegerDigits[1234]<br />
<span style="color: gray">(* base 2: *)</span><br />
IntegerDigits[1234, 2]</td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<th colspan="5"><a name="strings"></a><a href="#strings-note">strings</a></th>
</tr>
<tr>
<th></th>
<th>mathematica</th>
<th>sympy</th>
<th>sage</th>
<th>maxima</th>
</tr>
<tr>
<td><a name="str-literal"></a><a href="#str-literal-note">string literal</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>"don't say \"no\""</td>
<td><span style="color: gray"><em>use</em></span> <a href="/scripting#strings">Python strings</a></td>
<td><span style="color: gray"><em>use</em></span> <a href="/scripting#strings">Python strings</a></td>
<td>"don't say \"no\""</td>
</tr>
<tr>
<td><a name="newline-in-str-literal"></a><a href="#newline-in-str-literal-note">newline in literal</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>yes</em></span></td>
<td> </td>
<td> </td>
<td><span style="color: gray"><em>Newlines are inserted into strings by continuing the string on the next line. However, if the last character on a line inside a string is a backslash, the backslash and the following newline are omitted.</em></span></td>
</tr>
<tr>
<td><a name="str-literal-esc"></a><a href="#str-literal-esc-note">literal escapes</a></td>
<td>\\ \" \b \f \n \r \t \<span style="color: gray"><em>ooo</em></span></td>
<td> </td>
<td> </td>
<td>\" \\</td>
</tr>
<tr>
<td><a name="str-concat"></a><a href="#str-concat-note">concatenate</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>"one " <> "two " <> "three"</td>
<td> </td>
<td> </td>
<td>concat("one ", "two ", "three");</td>
</tr>
<tr>
<td><a name="translate-case"></a><a href="#translate-case-note">translate case</a></td>
<td>ToUpperCase["foo"]<br />
ToLowerCase["FOO"]</td>
<td> </td>
<td> </td>
<td>supcase("foo");<br />
sdowncase("FOO");</td>
</tr>
<tr>
<td><a name="trim"></a><a href="#trim-note">trim</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>StringTrim[" foo "]</td>
<td> </td>
<td> </td>
<td>strim(" ", " foo ");</td>
</tr>
<tr>
<td><a name="num-to-str"></a><a href="#num-to-str-note">number to string</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>"value: " <> ToString[8]</td>
<td> </td>
<td> </td>
<td>concat("value: ", 8);</td>
</tr>
<tr>
<td><a name="str-to-num"></a><a href="#str-to-num-note">string to number</a></td>
<td>7 + ToExpression["12"]<br />
73.9 + ToExpression[".037"]</td>
<td> </td>
<td> </td>
<td>7 + parse_string("12");<br />
73.9 + parse_string(".037");<br />
<br />
<span style="color: gray">/* parse_string raises error if the string does<br />
not contain valid Maxima code. Use numberp<br />
predicate to verify that the return value is<br />
numeric. */</span></td>
</tr>
<tr>
<td><a name="str-join"></a><a href="#str-join-note">string join</a></td>
<td>StringJoin[Riffle[{"foo", "bar", "baz"}, ","]]</td>
<td> </td>
<td> </td>
<td>simplode(["foo", "bar", "baz"], ",");</td>
</tr>
<tr>
<td><a name="split"></a><a href="#split-note">split</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>StringSplit["foo,bar,baz", ","]</td>
<td> </td>
<td> </td>
<td>split("foo,bar,baz", ",");</td>
</tr>
<tr>
<td><a name="str-subst"></a><a href="#str-subst-note">substitute</a><br />
<br />
<span style="color: gray"><em>first occurrence, all occurences</em></span> </td>
<td>s = "do re mi mi"<br />
re = RegularExpression["mi"]<br />
<br />
StringReplace[s, re -> "ma", 1]<br />
StringReplace[s, re -> "ma"]</td>
<td> </td>
<td> </td>
<td>ssubst("mi", "ma", "do re mi mi mi");<br />
ssubstfirst("mi", "ma", "do re mi mi mi");</td>
</tr>
<tr>
<td><a name="str-len"></a><a href="#str-len-note">length</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>StringLength["hello"]</td>
<td> </td>
<td> </td>
<td>slength("hello");</td>
</tr>
<tr>
<td><a name="index-substr"></a><a href="#index-substr-note">index of substring</a></td>
<td>StringPosition["hello", "el"][[1]][[1]]<br />
<br />
<span style="color: gray">(* The index of the first character is 1.*)</span><br />
<br />
<span style="color: gray">(* StringPosition returns an array of pairs, one for each occurrence of the substring. Each pair contains the index of the first and last character of the occurrence. *)</span></td>
<td> </td>
<td> </td>
<td>ssearch("el", "hello");<br />
<br />
<span style="color: gray">/* 1 is index of first character;<br />
returns false if substring not found */</span> _</td>
</tr>
<tr>
<td><a name="extract-substr"></a><a href="#extract-substr-note">extract substring</a></td>
<td><span style="color: gray">(* "el": *)</span><br />
StringTake["hello", {2, 3}]</td>
<td> </td>
<td> </td>
<td>substring("hello", 2, 4);</td>
</tr>
<tr>
<td><a name="char-literal"></a><a href="#char-literal-note">character literal</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td><span style="color: gray"><em>none</em></span></td>
<td> </td>
<td> </td>
<td><span style="color: gray"><em>none</em></span></td>
</tr>
<tr>
<td><a name="lookup-char"></a><a href="#lookup-char-note">character lookup</a></td>
<td>Characters["hello"][[1]]</td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td><a name="chr-ord"></a><a href="#chr-ord-note">chr and ord</a></td>
<td>FromCharacterCode[{65}]<br />
ToCharacterCode["A"][[1]]</td>
<td> </td>
<td> </td>
<td>ascii(65);<br />
cint("A");</td>
</tr>
<tr>
<td><a name="delete-char"></a><a href="#delete-char-note">delete characters</a></td>
<td>rules = {"a" -> "", "e" -> "", "i" -> "",<br />
<span style="white-space: pre-wrap;"> </span>"o" -> "", "u" -> ""}<br />
StringReplace["disemvowel me", rules]</td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<th colspan="5"><a name="arrays"></a><a href="#arrays-note">arrays</a></th>
</tr>
<tr>
<th></th>
<th>mathematica</th>
<th>sympy</th>
<th>sage</th>
<th>maxima</th>
</tr>
<tr>
<td><a name="array-literal"></a><a href="#array-literal-note">literal</a></td>
<td>{1, 2, 3}<br />
<br />
List[1, 2, 3]</td>
<td><span style="color: gray"><em>use</em></span> <a href="/scripting#arrays">Python lists</a></td>
<td><span style="color: gray"><em>use</em></span> <a href="/scripting#arrays">Python lists</a></td>
<td>[1, 2, 3];</td>
</tr>
<tr>
<td><a name="array-size"></a><a href="#array-size-note">size</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Length[{1, 2, 3}]</td>
<td> </td>
<td> </td>
<td>length([1, 2, 3]);</td>
</tr>
<tr>
<td><a name="array-lookup"></a><a href="#array-lookup-note">lookup</a></td>
<td><span style="color: gray">(* access time is O(1) *)</span><br />
<span style="color: gray">(* indices start at one: *)</span><br />
{1, 2, 3}[[1]]<br />
<br />
Part[{1, 2, 3}, 1]</td>
<td> </td>
<td> </td>
<td>a: [6, 7, 8];<br />
a[1];</td>
</tr>
<tr>
<td><a name="array-update"></a><a href="#array-update-note">update</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>a[[1]] = 7</td>
<td> </td>
<td> </td>
<td>a[1]: 7;</td>
</tr>
<tr>
<td><a name="array-out-of-bounds"></a><a href="#array-out-of-bounds-note">out-of-bounds behavior</a></td>
<td><span style="color: gray"><em>left as unevaluated</em> Part[] <em>expression</em></span></td>
<td> </td>
<td> </td>
<td><span style="color: gray"><em>Error for both lookup and update.</em></span></td>
</tr>
<tr>
<td><a name="array-element-index"></a><a href="#array-element-index-note">element index</a></td>
<td><span style="color: gray">(* Position returns list of all positions: *)</span><br />
First /@ Position[{7, 8, 9, 9}, 9]</td>
<td> </td>
<td> </td>
<td>a: [7, 8, 9, 9];<br />
first(sublist_indices(a, lambda([x], x = 9)));</td>
</tr>
<tr>
<td><a name="array-slice"></a><a href="#array-slice-note">slice</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>{1, 2, 3}[[1 ;; 2]]</td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td><a name="array-of-integers-as-index"></a><a href="#array-of-integers-as-index-note">array of integers as index</a></td>
<td><span style="color: gray">(* evaluates to {7, 9, 9} *)</span><br />
{7, 8, 9}[[{1, 3, 3}]]</td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td><a name="array-back"></a><a href="#array-back-note">manipulate back</a></td>
<td>a = {6,7,8}<br />
AppendTo[a, 9]<br />
elem = a[[Length[a]]]<br />
a = Delete[a, Length[a]]<br />
elem</td>
<td> </td>
<td> </td>
<td> </td>
</tr>
<tr>
<td><a name="array-front"></a><a href="#array-front-note">manipulate front</a></td>
<td>a = {6, 7, 8}<br />
PrependTo[a, 5]<br />
elem = a[[1]]<br />
a = Delete[a, 1]<br />
elem</td>
<td> </td>
<td> </td>
<td>a: [6, 7, 8];<br />
push(5, a);<br />
elem: pop(a);</td>
</tr>
<tr>
<td><a name="array-head"></a><a href="#array-head-note">head</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>First[{1, 2, 3}]</td>
<td> </td>
<td> </td>
<td>first([1, 2, 3]);</td>
</tr>
<tr>
<td><a name="array-tail"></a><a href="#array-tail-note">tail</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Rest[{1, 2, 3}]</td>
<td> </td>
<td> </td>
<td>rest([1, 2, 3]);</td>
</tr>
<tr>
<td><a name="array-cons"></a><a href="#array-cons-note">cons</a></td>
<td><span style="color: gray">(* first arg must be an array *)</span><br />
Prepend[{2, 3}, 1]</td>
<td> </td>
<td> </td>
<td>cons(1, [2, 3]);</td>
</tr>
<tr>
<td><a name="array-concatenate"></a><a href="#array-concatenate-note">concatenate</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Join[{1, 2, 3}, {4, 5, 6}]</td>
<td> </td>
<td> </td>
<td>append([1, 2, 3], [4, 5, 6]);</td>
</tr>
<tr>
<td><a name="array-replicate"></a><a href="#array-replicate-note">replicate</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>tenZeros = Table[0, {i, 0, 9}]</td>
<td> </td>
<td> </td>
<td>ten_zeros: makelist(0, 10);</td>
</tr>
<tr>
<td><a name="copy-array"></a><a href="#copy-array-note">copy</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>a2 = a</td>
<td> </td>
<td> </td>
<td>a2: copylist(a);</td>
</tr>
<tr>
<td><a name="iterate-over-array"></a><a href="#iterate-over-array-note">iterate</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Do[Print[i], {i, {1, 2, 3]</td>
<td> </td>
<td> </td>
<td>for i in [1, 2, 3] do print(i);</td>
</tr>
<tr>
<td><a name="reverse-array"></a><a href="#reverse-array-note">reverse</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>Reverse[{1, 2, 3}]</td>
<td> </td>
<td> </td>
<td>reverse([1, 2, 3]);</td>
</tr>
<tr>
<td><a name="sort-array"></a><a href="#sort-array-note">sort</a></td>
<td><span style="color: gray">(* original list not modified: *)</span><br />
a = Sort[{3, 1, 4, 2}]</td>
<td> </td>
<td> </td>
<td>sort([3, 1, 4, 2]);</td>
</tr>
<tr>
<td><a name="dedupe-array"></a><a href="#dedupe-array-note">dedupe</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>DeleteDuplicates[{1, 2, 2, 3}]</td>
<td> </td>
<td> </td>
<td>unique([1, 2, 2, 3]);</td>
</tr>
<tr>
<td><a name="membership"></a><a href="#membership-note">membership</a><br />
<span style="white-space: pre-wrap;"> </span></td>
<td>MemberQ[{1, 2, 3}, 2]</td>
<td> </td>
<td> </td>
<td>member(7, {1, 2, 3});<br />
evalb(7 in {1, 2, 3});</td>
</tr>
<tr>
<td><a name="map"></a><a href="#map-note">map</a></td>
<td>Map[Function[x, x x], {1, 2, 3}]<br />
<br />
Function[x, x x] /@ {1, 2, 3}<br />
<br />
<span style="color: gray">(* if function has Listable attribute, Map is unnecessary: *)</span><br />
sqr[x_] := x * x<br />
SetAttributes[sqr, Listable]<br />
sqr[{1, 2, 3, 4}]</td>
<td> </td>
<td> </td>
<td>map(lambda([x], x * x), [1, 2, 3]);</td>