simple

Search for simplest form of symbolic expression

    Note:   simple will be removed in a future release. Use simplify(S) instead of simple(S). There is no replacement for [r, how] = simple(S).

Syntax

simple(S)
simple(S,Name,Value)
r = simple(S)
r = simple(S,Name,Value)
[r,how] = simple(S)
[r,how] = simple(S,Name,Value)

Description

simple(S) applies different algebraic simplification functions and displays all resulting forms of S, and then returns the shortest form.

simple(S,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

r = simple(S) tries different algebraic simplification functions without displaying the results, and then returns the shortest form of S.

r = simple(S,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

[r,how] = simple(S) tries different algebraic simplification functions without displaying the results, and then returns the shortest form of S and a string describing the corresponding simplification method.

[r,how] = simple(S,Name,Value) uses additional options specified by one or more Name,Value pair arguments.

Input Arguments

S

Symbolic expression or symbolic matrix.

Default: false

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'IgnoreAnalyticConstraints'

If the value is true, apply purely algebraic simplifications to an expression. With IgnoreAnalyticConstraints, simple can return simpler results for expressions for which it would return more complicated results otherwise. Using IgnoreAnalyticConstraints also can lead to results that are not equivalent to the initial expression.

Default: false

Output Arguments

r

A symbolic object representing the shortest form of S

how

A string describing the simplification method that gives the shortest form of S

More About

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Tips

  • Simplification of mathematical expression is not a clearly defined subject. There is no universal idea as to which form of an expression is simplest. The form of a mathematical expression that is simplest for one problem might turn out to be complicated or even unsuitable for another problem.

  • If S is a matrix, the result represents the shortest representation of the entire matrix, which is not necessarily the shortest representation of each individual element.

Algorithms

When you use IgnoreAnalyticConstraints, simple applies these rules:

  • log(a) + log(b) = log(a·b) for all values of a and b. In particular, the following equality is valid for all values of a, b, and c:

      (a·b)c = ac·bc.

  • log(ab) = b·log(a) for all values of a and b. In particular, the following equality is valid for all values of a, b, and c:

      (ab)c = ab·c.

  • If f and g are standard mathematical functions and f(g(x)) = x for all small positive numbers, f(g(x)) = x is assumed to be valid for all complex x. In particular:

    • log(ex) = x

    • asin(sin(x)) = x, acos(cos(x)) = x, atan(tan(x)) = x

    • asinh(sinh(x)) = x, acosh(cosh(x)) = x, atanh(tanh(x)) = x

    • Wk(x·ex) = x for all values of k

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