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<h1 class="chapter"> 5. Operators </h1>
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<h2 class="section"> 5.1 nary </h2>
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<p>An <code>nary</code> operator is used to denote a function of any number of
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arguments, each of which is separated by an occurrence of the
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operator, e.g. A+B or A+B+C. The <code>nary("x")</code> function is a syntax
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extension function to declare x to be an <code>nary</code> operator.
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extension function to declare <code>x</code> to be an <code>nary</code> operator.
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Functions may be declared to be
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<code>nary</code>. If <code>declare(j,nary);</code> is done, this tells the simplifier to
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simplify, e.g. <code>j(j(a,b),j(c,d))</code> to <code>j(a, b, c, d)</code>.
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<p>See also <code>syntax</code>.
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<p>See also <code>Syntax</code>.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<a href="maxima_93.html#Category_003a-Syntax">Syntax</a>
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<p><a name="Item_003a-nofix"></a>
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<a name="nofix"></a>
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<h2 class="section"> 5.2 nofix </h2>
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corresponding function to be evaluated. For example, when one types
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"exit;" to exit from a Maxima break, "exit" is behaving similar to a
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<code>nofix</code> operator. The function <code>nofix("x")</code> is a syntax extension
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function which declares x to be a <code>nofix</code> operator.
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<p>See also <code>syntax</code>.
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function which declares <code>x</code> to be a <code>nofix</code> operator.
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<p>See also <code>Syntax</code>.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<a href="maxima_93.html#Category_003a-Syntax">Syntax</a>
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<p><a name="Item_003a-postfix"></a>
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<a name="postfix"></a>
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<h2 class="section"> 5.3 postfix </h2>
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<p><code>postfix</code> operators like the <code>prefix</code> variety denote functions
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of a single argument, but in this case the argument immediately
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precedes an occurrence of the operator in the input string, e.g. 3! .
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The <code>postfix("x")</code> function is a syntax extension function to declare x
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The <code>postfix("x")</code> function is a syntax extension function to declare <code>x</code>
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to be a <code>postfix</code> operator.
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<p>See also <code>syntax</code>.
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<p>See also <code>Syntax</code>.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<a href="maxima_93.html#Category_003a-Syntax">Syntax</a>
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<p><a name="Item_003a-prefix"></a>
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<a name="prefix"></a>
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<h2 class="section"> 5.4 prefix </h2>
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<p>A <code>prefix</code> operator is one which signifies a function of one
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argument, which argument immediately follows an occurrence of the
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operator. <code>prefix("x")</code> is a syntax extension function to declare x to
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operator. <code>prefix("x")</code> is a syntax extension function to declare <code>x</code> to
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be a <code>prefix</code> operator.
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<p>See also <code>syntax</code>.
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<p>See also <code>Syntax</code>.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<a href="maxima_93.html#Category_003a-Syntax">Syntax</a>
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<p><a name="Item_003a-Arithmetic-operators"></a>
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<a name="Arithmetic-operators"></a>
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<h2 class="section"> 5.5 Arithmetic operators </h2>
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<p><a name="Item_003a-_002b"></a>
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<dt><u>Operator:</u> <b>+</b>
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<a name="IDX56"></a>
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<dd><p>The symbols <code>+</code> <code>*</code> <code>/</code> and <code>^</code> represent
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addition, multiplication, division, and exponentiation, respectively.
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The name of these operators are <code>"+"</code> <code>"*"</code> <code>"//"</code> and <code>"^"</code>,
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The names of these operators are <code>"+"</code> <code>"*"</code> <code>"/"</code> and <code>"^"</code>,
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which may appear where the name of a function or operator is required.
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<p>The symbols <code>+</code> and <code>-</code> represent unary addition and negation, respectively,
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<p>Division <code>a / b</code> is represented within Maxima as multiplication, <code>a * b^(- 1)</code>.
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Expressions such as <code>a * b^(- 1)</code> are displayed as division.
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Maxima recognizes <code>"//"</code> as the name of the division operator.
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Maxima recognizes <code>"/"</code> as the name of the division operator.
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<p>Addition and multiplication are n-ary, commutative operators.
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Division and exponentiation are binary, noncommutative operators.
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<p>Division and exponentiation are binary, noncommutative operators.
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The names of these operators are <code>"//"</code> and <code>"^"</code>.
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The names of these operators are <code>"/"</code> and <code>"^"</code>.
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<pre class="example">(%i1) [a / b, a ^ b];
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(%i2) [map (op, %), map (args, %)];
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(%o2) [[//, ^], [[a, b], [a, b]]]
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(%i3) [apply ("//", [a, b]), apply ("^", [a, b])];
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(%o2) [[/, ^], [[a, b], [a, b]]]
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(%i3) [apply ("/", [a, b]), apply ("^", [a, b])];
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<h2 class="section"> 5.6 Relational operators </h2>
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<p><a name="Item_003a-_003c"></a>
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<dt><u>Operator:</u> <b><</b>
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<a name="IDX62"></a>
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<dt><u>Operator:</u> <b>></b>
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<a name="IDX65"></a>
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<dd><p>The symbols <code><</code> <code><=</code> <code>>=</code> and <code>></code> represent
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less than, less than or equal, greater than or equal, and greater than, respectively.
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The names of these operators are <code>"<"</code> <code>"<="</code> <code>">="</code> and <code>">"</code>,
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which may appear where the name of a function or operator is required.
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<p>These relational operators are all binary operators;
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constructs such as <code>a < b < c</code> are not recognized by Maxima.
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<p>Relational expressions are evaluated to Boolean values
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by the functions <code>is</code> and <code>maybe</code>,
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and the programming constructs <code>if</code>, <code>while</code>, and <code>unless</code>.
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Relational expressions are not otherwise evaluated or simplified to Boolean values,
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although the arguments of relational expressions are evaluated
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(when evaluation is not otherwise prevented by quotation).
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<p>When a relational expression cannot be evaluated to <code>true</code> or <code>false</code>,
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the behavior of <code>is</code> and <code>if</code> are governed by the global flag <code>prederror</code>.
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When <code>prederror</code> is <code>true</code>,
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<code>is</code> and <code>if</code> trigger an error.
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When <code>prederror</code> is <code>false</code>,
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<code>is</code> returns <code>unknown</code>,
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and <code>if</code> returns a partially-evaluated conditional expression.
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<p><code>maybe</code> always behaves as if <code>prederror</code> were <code>false</code>,
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and <code>while</code> and <code>unless</code> always behave as if <code>prederror</code> were <code>true</code>.
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<p>Relational operators do not distribute over lists or other aggregates.
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<p>See also <code>=</code> <code>#</code> <code>equal</code> and <code>notequal</code>.
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<p>Relational expressions are evaluated to Boolean values by some functions and programming constructs.
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<pre class="example">(%i1) [x, y, z] : [123, 456, 789];
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(%o1) [123, 456, 789]
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(%i3) maybe (y > z);
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(%i4) if x >= z then 1 else 0;
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(%i5) block ([S], S : 0, for i:1 while i <= 100 do S : S + i, return (S));
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<p>Relational expressions are not otherwise evaluated or simplified to Boolean values,
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although the arguments of relational expressions are evaluated.
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<pre class="example">(%o1) [123, 456, 789]
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(%i2) [x < y, y <= z, z >= y, y > z];
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(%o2) [123 < 456, 456 <= 789, 789 >= 456, 456 > 789]
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(%o3) [true, true, true, false]
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-General-operators"></a>
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<a name="General-operators"></a>
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<a name="SEC19"></a>
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<h2 class="section"> 5.7 General operators </h2>
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<p><a name="Item_003a-_005e_005e"></a>
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<dt><u>Operator:</u> <b>^^</b>
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<a name="IDX66"></a>
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<p>For an argument <code>n</code> which is not an integer, float, or rational,
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<code>n!!</code> yields a noun form <code>genfact (n, n/2, 2)</code>.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Gamma-and-factorial-functions">Gamma and factorial functions</a>
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<a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-_0023"></a>
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<dt><u>Operator:</u> <b>#</b>
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<a name="IDX69"></a>
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(%i6) is (not a = b);
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-_002e"></a>
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<dt><u>Operator:</u> <b>.</b>
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<a name="IDX70"></a>
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<dd><p>The dot operator, for matrix (non-commutative) multiplication.
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When "." is used in this way, spaces should be left on both sides of
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it, e.g. A . B. This distinguishes it plainly from a decimal point in
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When <code>"."</code> is used in this way, spaces should be left on both sides of
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it, e.g. <code>A . B</code>. This distinguishes it plainly from a decimal point in
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a floating point number.
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<code>dotscrules</code>.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-_003a"></a>
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<dt><u>Operator:</u> <b>:</b>
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<a name="IDX71"></a>
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<dd><p>The assignment operator. E.g. A:3 sets the variable A to 3.
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<dd><p>Assignment operator.
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<p>When the left-hand side is a simple variable (not subscripted),
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<code>:</code> evaluates its right-hand side
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and associates that value with the left-hand side.
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<p>When the left-hand side is a subscripted element of a list, matrix, declared Maxima array, or Lisp array,
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the right-hand side is assigned to that element.
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The subscript must name an existing element;
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such objects cannot be extended by naming nonexistent elements.
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<p>When the left-hand side is a subscripted element of an undeclared Maxima array,
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the right-hand side is assigned to that element, if it already exists,
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or a new element is allocated, if it does not already exist.
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<p>When the left-hand side is a list of simple and/or subscripted variables,
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the right-hand side must evaluate to a list,
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and the elements of the right-hand side are assigned to the elements of the left-hand side,
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<p>See also <code>kill</code> and <code>remvalue</code>,
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which undo the association between the left-hand side and its value.
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<p>Assignment to a simple variable.
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<pre class="example">(%i1) a;
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<p>Assignment to an element of a list.
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<pre class="example">(%i1) b : [1, 2, 3];
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<p>Assignment creates an undeclared array.
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<pre class="example">(%i1) c[99] : 789;
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(%o4) [hashed, 1, [99]]
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<p>Multiple assignment.
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<pre class="example">(%i1) [a, b, c] : [45, 67, 89];
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<p>Multiple assignment is carried out in parallel.
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The values of <code>a</code> and <code>b</code> are exchanged in this example.
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<pre class="example">(%i1) [a, b] : [33, 55];
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(%i2) [a, b] : [b, a];
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Evaluation">Evaluation</a>
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<a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-_003a_003a"></a>
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<dt><u>Operator:</u> <b>::</b>
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<a name="IDX72"></a>
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<dd><p>Assignment operator. :: assigns the value of the expression
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on its right to the value of the quantity on its left, which must
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evaluate to an atomic variable or subscripted variable.
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<dd><p>Assignment operator.
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<p><code>::</code> is the same as <code>:</code> (which see)
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except that <code>::</code> evaluates its left-hand side as well as its right-hand side.
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<pre class="example">(%i1) x : 'foo;
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(%i4) x : '[a, b, c];
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(%i5) x :: [11, 22, 33];
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Evaluation">Evaluation</a>
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<a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-_003a_003a_003d"></a>
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<dt><u>Operator:</u> <b>::=</b>
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<a name="IDX73"></a>
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<p>All function definitions appear in the same namespace;
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defining a function <code>f</code> within another function <code>g</code>
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does not limit the scope of <code>f</code> to <code>g</code>.
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does not automatically limit the scope of <code>f</code> to <code>g</code>.
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However, <code>local(f)</code> makes the definition of function <code>f</code>
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effective only within the block or other compound expression in which <code>local</code> appears.
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<p>If some formal argument <var>x_k</var> is a quoted symbol,
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the function defined by <code>:=</code> does not evaluate the corresponding actual argument.
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(%i2) H (a, b, c);
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<p><code>local</code> makes a local function definition.
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<pre class="example">(%i1) foo (x) := 1 - x;
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(%o1) foo(x) := 1 - x
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(%i3) block (local (foo), foo (x) := 2 * x, foo (100));
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Function-definition">Function definition</a>
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<a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-_003d"></a>
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<dt><u>Operator:</u> <b>=</b>
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<a name="IDX75"></a>
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Otherwise, operands which do not evaluate to <code>true</code> or <code>false</code> are accepted,
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and the result is a Boolean expression.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
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<p><a name="Item_003a-abs"></a>
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<dt><u>Function:</u> <b>abs</b><i> (<var>expr</var>)</i>
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<a name="IDX79"></a>
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<dd><p>Returns the absolute value <var>expr</var>. If <var>expr</var> is complex, returns the complex
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modulus of <var>expr</var>.
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<div class=categorybox>
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<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
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<p><a name="Item_003a-additive"></a>
1073
1446
<dt><u>Keyword:</u> <b>additive</b>
1074
1447
<a name="IDX80"></a>
1130
1514
<code>symmetric</code> or <code>commutative</code>, where n is the number of interchanges of two
1131
1515
arguments necessary to convert it to that form.
1517
<div class=categorybox>
1520
<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
1522
<a href="maxima_93.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
1528
<p><a name="Item_003a-cabs"></a>
1136
1530
<dt><u>Function:</u> <b>cabs</b><i> (<var>expr</var>)</i>
1137
1531
<a name="IDX83"></a>
1139
1533
<dd><p>Returns the complex absolute value (the complex modulus) of
1140
1534
<var>expr</var>.
1536
<div class=categorybox>
1539
<p>Categories: <a href="maxima_93.html#Category_003a-Complex-variables">Complex variables</a>
1545
<p><a name="Item_003a-ceiling"></a>
1145
1547
<dt><u>Function:</u> <b>ceiling</b><i> (<var>x</var>)</i>
1146
1548
<a name="IDX84"></a>
1219
1637
simplifier that <code>h</code> is a commutative function. E.g. <code>h(x,z,y)</code> will
1220
1638
simplify to <code>h(x, y, z)</code>. This is the same as <code>symmetric</code>.
1640
<div class=categorybox>
1643
<p>Categories: <a href="maxima_93.html#Category_003a-Operators">Operators</a>
1645
<a href="maxima_93.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
1651
<p><a name="Item_003a-compare"></a>
1225
1653
<dt><u>Function:</u> <b>compare</b><i> (<var>x</var>, <var>y</var>)</i>
1226
1654
<a name="IDX87"></a>
1228
1656
<dd><p>Return a comparison operator <var>op</var>
1229
1657
(<code><</code>, <code><=</code>, <code>></code>, <code>>=</code>, <code>=</code>, or <code>#</code>) such that
1230
<code>is (<var>x</var> <var>op</var> <var>y</var>)</code> evaluates to true;
1658
<code>is (<var>x</var> <var>op</var> <var>y</var>)</code> evaluates to <code>true</code>;
1231
1659
when either <var>x</var> or <var>y</var> depends on <code>%i</code> and
1232
1660
<code><var>x</var> # <var>y</var></code>, return <code>notcomparable</code>;
1233
1661
when there is no such operator or
1257
1685
<p>The real domain of <code>acos (x^2 + 1)</code> is empty.
1687
<div class=categorybox>
1690
<p>Categories: <a href="maxima_93.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
1696
<p><a name="Item_003a-entier"></a>
1262
1698
<dt><u>Function:</u> <b>entier</b><i> (<var>x</var>)</i>
1263
1699
<a name="IDX88"></a>
1265
1701
<dd><p>Returns the largest integer less than or equal to <var>x</var> where <var>x</var> is numeric. <code>fix</code> (as in
1266
1702
<code>fixnum</code>) is a synonym for this, so <code>fix(<var>x</var>)</code> is precisely the same.
1704
<div class=categorybox>
1707
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
1713
<p><a name="Item_003a-equal"></a>
1271
1715
<dt><u>Function:</u> <b>equal</b><i> (<var>a</var>, <var>b</var>)</i>
1272
1716
<a name="IDX89"></a>
1382
1835
<p>If <var>x</var> is a constant expression (<code>10 * %pi</code>, for example),
1383
1836
<code>floor</code> evaluates <var>x</var> using big floating point numbers, and
1384
applies floor to the resulting big float. Because floor uses
1837
applies <code>floor</code> to the resulting big float. Because <code>floor</code> uses
1385
1838
floating point evaluation, it's possible, although unlikely,
1386
1839
that <code>floor</code> could return an erroneous value for constant
1387
1840
inputs. To guard against errors, the floating point evaluation
1460
1930
<code>eval</code> causes an extra evaluation of <var>expr</var>.
1461
1931
See <code>ev</code>.
1933
<div class=categorybox>
1936
<p>Categories: <a href="maxima_93.html#Category_003a-Evaluation-flags">Evaluation flags</a>
1942
<p><a name="Item_003a-evenp"></a>
1466
1944
<dt><u>Function:</u> <b>evenp</b><i> (<var>expr</var>)</i>
1467
1945
<a name="IDX93"></a>
1469
1947
<dd><p>Returns <code>true</code> if <var>expr</var> is an even integer.
1470
1948
<code>false</code> is returned in all other cases.
1950
<div class=categorybox>
1953
<p>Categories: <a href="maxima_93.html#Category_003a-Predicate-functions">Predicate functions</a>
1959
<p><a name="Item_003a-fix"></a>
1475
1961
<dt><u>Function:</u> <b>fix</b><i> (<var>x</var>)</i>
1476
1962
<a name="IDX94"></a>
1478
1964
<dd><p>A synonym for <code>entier (<var>x</var>)</code>.
1966
<div class=categorybox>
1969
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
1975
<p><a name="Item_003a-fullmap"></a>
1483
1977
<dt><u>Function:</u> <b>fullmap</b><i> (<var>f</var>, <var>expr_1</var>, ...)</i>
1484
1978
<a name="IDX95"></a>
1515
2019
<pre class="example">(%i1) fullmapl ("+", [3, [4, 5]], [[a, 1], [0, -1.5]]);
1516
2020
(%o1) [[a + 3, 4], [4, 3.5]]
2022
<div class=categorybox>
2025
<p>Categories: <a href="maxima_93.html#Category_003a-Function-application">Function application</a>
2027
<a href="maxima_93.html#Category_003a-Expressions">Expressions</a>
2033
<p><a name="Item_003a-is"></a>
1521
2035
<dt><u>Function:</u> <b>is</b><i> (<var>expr</var>)</i>
1522
2036
<a name="IDX97"></a>
1610
2144
of the absolute value of <var>x</var>,
1611
2145
which is an integer.
2147
<div class=categorybox>
2150
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2156
<p><a name="Item_003a-lmax"></a>
1616
2158
<dt><u>Function:</u> <b>lmax</b><i> (<var>L</var>)</i>
1617
2159
<a name="IDX100"></a>
1619
2161
<dd><p>When <var>L</var> is a list or a set, return <code>apply ('max, args (<var>L</var>))</code>. When <var>L</var> isn't a
1620
2162
list or a set, signal an error.
2164
<div class=categorybox>
2167
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2169
<a href="maxima_93.html#Category_003a-Lists">Lists</a>
2171
<a href="maxima_93.html#Category_003a-Sets">Sets</a>
2177
<p><a name="Item_003a-lmin"></a>
1625
2179
<dt><u>Function:</u> <b>lmin</b><i> (<var>L</var>)</i>
1626
2180
<a name="IDX101"></a>
1628
2182
<dd><p>When <var>L</var> is a list or a set, return <code>apply ('min, args (<var>L</var>))</code>. When <var>L</var> isn't a
1629
2183
list or a set, signal an error.
2185
<div class=categorybox>
2188
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2190
<a href="maxima_93.html#Category_003a-Lists">Lists</a>
2192
<a href="maxima_93.html#Category_003a-Sets">Sets</a>
2198
<p><a name="Item_003a-max"></a>
1634
2200
<dt><u>Function:</u> <b>max</b><i> (<var>x_1</var>, ..., <var>x_n</var>)</i>
1635
2201
<a name="IDX102"></a>
1641
2207
<code>max (x, 2*x, 3*x) --> max (x, 3*x)</code>. To set the value of <code>trylevel</code> to 2, use
1642
2208
<code>put (trylevel, 2, maxmin)</code>.
2210
<div class=categorybox>
2213
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2219
<p><a name="Item_003a-min"></a>
1647
2221
<dt><u>Function:</u> <b>min</b><i> (<var>x_1</var>, ..., <var>x_n</var>)</i>
1648
2222
<a name="IDX103"></a>
1654
2228
<code>min (x, 2*x, 3*x) --> min (x, 3*x)</code>. To set the value of <code>trylevel</code> to 2, use
1655
2229
<code>put (trylevel, 2, maxmin)</code>.
2231
<div class=categorybox>
2234
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2240
<p><a name="Item_003a-polymod"></a>
1660
2242
<dt><u>Function:</u> <b>polymod</b><i> (<var>p</var>)</i>
1661
2243
<a name="IDX104"></a>
1705
2295
(%i3) mod (0, x);
2298
<div class=categorybox>
2301
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2307
<p><a name="Item_003a-oddp"></a>
1711
2309
<dt><u>Function:</u> <b>oddp</b><i> (<var>expr</var>)</i>
1712
2310
<a name="IDX107"></a>
1714
2312
<dd><p>is <code>true</code> if <var>expr</var> is an odd integer.
1715
2313
<code>false</code> is returned in all other cases.
2315
<div class=categorybox>
2318
<p>Categories: <a href="maxima_93.html#Category_003a-Predicate-functions">Predicate functions</a>
2324
<p><a name="Item_003a-pred"></a>
1720
2326
<dt><u>Operator:</u> <b>pred</b>
1721
2327
<a name="IDX108"></a>
2534
<div class=categorybox>
2537
<p>Categories: <a href="maxima_93.html#Category_003a-Numerical-evaluation">Numerical evaluation</a>
2543
<p><a name="Item_003a-round"></a>
2545
<dt><u>Function:</u> <b>round</b><i> (<var>x</var>)</i>
2546
<a name="IDX116"></a>
2548
<dd><p>When <var>x</var> is a real number, returns the closest integer
2549
to <var>x</var>. Multiples of 1/2 are rounded to the nearest
2550
even integer. Evaluation of <var>x</var> is similar to
2551
<code>floor</code> and <code>ceiling</code>.
2553
<div class=categorybox>
2556
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2563
<p><a name="Item_003a-sign"></a>
1896
2565
<dt><u>Function:</u> <b>sign</b><i> (<var>expr</var>)</i>
1897
<a name="IDX116"></a>
2566
<a name="IDX117"></a>
1899
2568
<dd><p>Attempts to determine the sign of <var>expr</var>
1900
2569
on the basis of the facts in the current data base. It returns one of
1902
2571
(positive or zero), <code>nz</code> (negative or zero), <code>pn</code> (positive or negative),
1903
2572
or <code>pnz</code> (positive, negative, or zero, i.e. nothing known).
2574
<div class=categorybox>
2577
<p>Categories: <a href="maxima_93.html#Category_003a-Declarations-and-inferences">Declarations and inferences</a>
2583
<p><a name="Item_003a-signum"></a>
1908
2585
<dt><u>Function:</u> <b>signum</b><i> (<var>x</var>)</i>
1909
<a name="IDX117"></a>
2586
<a name="IDX118"></a>
1911
2588
<dd><p>For numeric <var>x</var>, returns 0 if <var>x</var> is 0, otherwise returns -1 or +1
1912
2589
as <var>x</var> is less than or greater than 0, respectively.
1914
2591
<p>If <var>x</var> is not numeric then a simplified but equivalent form is returned.
1915
2592
For example, <code>signum(-x)</code> gives <code>-signum(x)</code>.
2594
<div class=categorybox>
2597
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2603
<p><a name="Item_003a-sort"></a>
1920
2605
<dt><u>Function:</u> <b>sort</b><i> (<var>L</var>, <var>P</var>)</i>
1921
<a name="IDX118"></a>
2606
<a name="IDX119"></a>
1923
2608
<dt><u>Function:</u> <b>sort</b><i> (<var>L</var>)</i>
1924
<a name="IDX119"></a>
2609
<a name="IDX120"></a>
1926
2611
<dd><p>Sorts a list <var>L</var> according to a predicate <code>P</code> of two arguments,
1927
2612
such that <code><var>P</var> (<var>L</var>[k], <var>L</var>[k + 1])</code> is <code>true</code>
1973
2658
reverse (b))));
1974
2659
(%o7) [[%pi, %e], [ee, cc], [zz, xx, mm, cc], [aa, hh, uu]]
2661
<div class=categorybox>
2664
<p>Categories: <a href="maxima_93.html#Category_003a-Lists">Lists</a>
2670
<p><a name="Item_003a-sqrt"></a>
1979
2672
<dt><u>Function:</u> <b>sqrt</b><i> (<var>x</var>)</i>
1980
<a name="IDX120"></a>
2673
<a name="IDX121"></a>
1982
2675
<dd><p>The square root of <var>x</var>. It is represented internally by
1983
2676
<code><var>x</var>^(1/2)</code>. See also <code>rootscontract</code>.
1986
2679
which are powers of n to be pulled outside of the radical, e.g.
1987
2680
<code>sqrt(16*x^2)</code> will become <code>4*x</code> only if <code>radexpand</code> is <code>true</code>.
2682
<div class=categorybox>
2685
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2691
<p><a name="Item_003a-sqrtdispflag"></a>
1992
2693
<dt><u>Option variable:</u> <b>sqrtdispflag</b>
1993
<a name="IDX121"></a>
2694
<a name="IDX122"></a>
1995
2696
<dd><p>Default value: <code>true</code>
1997
2698
<p>When <code>sqrtdispflag</code> is <code>false</code>,
1998
2699
causes <code>sqrt</code> to display with exponent 1/2.
2701
<div class=categorybox>
2704
<p>Categories: <a href="maxima_93.html#Category_003a-Mathematical-functions">Mathematical functions</a>
2706
<a href="maxima_93.html#Category_003a-Display-flags-and-variables">Display flags and variables</a>
2713
<p><a name="Item_003a-sublis"></a>
2003
2715
<dt><u>Function:</u> <b>sublis</b><i> (<var>list</var>, <var>expr</var>)</i>
2004
<a name="IDX122"></a>
2716
<a name="IDX123"></a>
2006
2718
<dd><p>Makes multiple parallel substitutions into an expression.
2029
2749
(%i2) sublist (L, evenp);
2030
2750
(%o2) [2, 4, 6]
2752
<div class=categorybox>
2755
<p>Categories: <a href="maxima_93.html#Category_003a-Lists">Lists</a>
2761
<p><a name="Item_003a-sublis_005fapply_005flambda"></a>
2035
2763
<dt><u>Option variable:</u> <b>sublis_apply_lambda</b>
2036
<a name="IDX124"></a>
2764
<a name="IDX125"></a>
2038
<dd><p>Default value: <code>true</code> - controls whether <code>lambda</code>'s
2766
<dd><p>Default value: <code>true</code>
2768
<p>Controls whether <code>lambda</code>'s
2039
2769
substituted are applied in simplification after <code>sublis</code> is used or
2040
2770
whether you have to do an <code>ev</code> to get things to apply. <code>true</code> means do the
2773
<div class=categorybox>
2776
<p>Categories: <a href="maxima_93.html#Category_003a-Expressions">Expressions</a>
2783
<p><a name="Item_003a-subst"></a>
2046
2785
<dt><u>Function:</u> <b>subst</b><i> (<var>a</var>, <var>b</var>, <var>c</var>)</i>
2047
<a name="IDX125"></a>
2786
<a name="IDX126"></a>
2049
2788
<dd><p>Substitutes <var>a</var> for <var>b</var> in <var>c</var>. <var>b</var> must be an atom or a
2050
2789
complete subexpression of <var>c</var>. For example, <code>x+y+z</code> is a complete
2085
2824
<p>For further examples, do <code>example (subst)</code>.
2826
<div class=categorybox>
2829
<p>Categories: <a href="maxima_93.html#Category_003a-Expressions">Expressions</a>
2835
<p><a name="Item_003a-substinpart"></a>
2090
2837
<dt><u>Function:</u> <b>substinpart</b><i> (<var>x</var>, <var>expr</var>, <var>n_1</var>, ..., <var>n_k</var>)</i>
2091
<a name="IDX126"></a>
2838
<a name="IDX127"></a>
2093
2840
<dd><p>Similar to <code>substpart</code>, but <code>substinpart</code> works on the
2094
2841
internal representation of <var>expr</var>.
2144
2891
<p>Also, setting the option <code>inflag</code> to <code>true</code> and calling <code>part</code> or <code>substpart</code> is
2145
2892
the same as calling <code>inpart</code> or <code>substinpart</code>.
2894
<div class=categorybox>
2897
<p>Categories: <a href="maxima_93.html#Category_003a-Expressions">Expressions</a>
2903
<p><a name="Item_003a-substpart"></a>
2150
2905
<dt><u>Function:</u> <b>substpart</b><i> (<var>x</var>, <var>expr</var>, <var>n_1</var>, ..., <var>n_k</var>)</i>
2151
<a name="IDX127"></a>
2906
<a name="IDX128"></a>
2153
2908
<dd><p>Substitutes <var>x</var> for the subexpression
2154
2909
picked out by the rest of the arguments as in <code>part</code>. It returns the
2174
2929
<p>Also, setting the option <code>inflag</code> to <code>true</code> and calling <code>part</code> or <code>substpart</code> is
2175
2930
the same as calling <code>inpart</code> or <code>substinpart</code>.
2932
<div class=categorybox>
2935
<p>Categories: <a href="maxima_93.html#Category_003a-Expressions">Expressions</a>
2941
<p><a name="Item_003a-subvarp"></a>
2180
2943
<dt><u>Function:</u> <b>subvarp</b><i> (<var>expr</var>)</i>
2181
<a name="IDX128"></a>
2944
<a name="IDX129"></a>
2183
2946
<dd><p>Returns <code>true</code> if <var>expr</var> is a subscripted variable, for example
2184
2947
<code>a[i]</code>.
2949
<div class=categorybox>
2952
<p>Categories: <a href="maxima_93.html#Category_003a-Predicate-functions">Predicate functions</a>
2958
<p><a name="Item_003a-symbolp"></a>
2189
2960
<dt><u>Function:</u> <b>symbolp</b><i> (<var>expr</var>)</i>
2190
<a name="IDX129"></a>
2961
<a name="IDX130"></a>
2192
2963
<dd><p>Returns <code>true</code> if <var>expr</var> is a symbol, else <code>false</code>.
2193
2964
In effect, <code>symbolp(x)</code> is equivalent to the predicate <code>atom(x) and not numberp(x)</code>.
2195
<p>See also <a href="maxima_6.html#SEC25">Identifiers</a>.
2966
<p>See also <a href="maxima_6.html#SEC24">Identifiers</a>.
2968
<div class=categorybox>
2971
<p>Categories: <a href="maxima_93.html#Category_003a-Predicate-functions">Predicate functions</a>
2977
<p><a name="Item_003a-unorder"></a>
2200
2979
<dt><u>Function:</u> <b>unorder</b><i> ()</i>
2201
<a name="IDX130"></a>
2980
<a name="IDX131"></a>
2203
2982
<dd><p>Disables the aliasing created by the last use of the ordering
2204
2983
commands <code>ordergreat</code> and <code>orderless</code>. <code>ordergreat</code> and <code>orderless</code> may not
2298
3101
On the other hand <code>zeroequiv (log(a*b) - log(a) - log(b), a)</code> returns <code>dontknow</code> because
2299
3102
of the presence of an extra parameter <code>b</code>.
3104
<div class=categorybox>
3107
<p>Categories: <a href="maxima_93.html#Category_003a-Predicate-functions">Predicate functions</a>
3113
<p><a name="Item_003a-Expressions"></a>
2304
3115
<table cellpadding="1" cellspacing="1" border="0">
2305
3116
<tr><td valign="middle" align="left">[<a href="#SEC12" title="Beginning of this chapter or previous chapter"> << </a>]</td>
2306
3117
<td valign="middle" align="left">[<a href="maxima_6.html#SEC20" title="Next chapter"> >> </a>]</td>
2311
3122
<td valign="middle" align="left"> </td>
2312
3123
<td valign="middle" align="left">[<a href="maxima.html#SEC_Top" title="Cover (top) of document">Top</a>]</td>
2313
3124
<td valign="middle" align="left">[<a href="maxima_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>
2314
<td valign="middle" align="left">[<a href="maxima_77.html#SEC300" title="Index">Index</a>]</td>
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<td valign="middle" align="left">[<a href="maxima_79.html#SEC320" title="Index">Index</a>]</td>
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<td valign="middle" align="left">[<a href="maxima_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
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This document was generated by <em>Robert Dodier</em> on <em>August, 25 2007</em> using <a href="http://texi2html.cvshome.org/"><em>texi2html 1.76</em></a>.
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This document was generated by <em>Robert Dodier</em> on <em>December, 14 2008</em> using <a href="http://texi2html.cvshome.org/"><em>texi2html 1.76</em></a>.
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