Min

Min[x₁,x₂,…]

yields the numerically smallest of the x_i.

Min[{x₁,x₂,…},{y₁,…},…]

yields the smallest element of any of the lists.

Details

Min yields a definite result if all its arguments are real numbers.
In other cases, Min carries out some simplifications.
Min[] gives Infinity.
Min works on SparseArray objects.

Examples

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Basic Examples (3)

Minimum of two numbers:

Minimum of a list:

Plot over a subset of the reals:

Scope (23)

Numerical Evaluation (5)

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

The minimum of all elements of a matrix:

The minima of all rows:

The minima of all columns:

Min works with real-valued intervals:

Specific Values (5)

Values of Min at fixed points:

Values at infinity:

Evaluate symbolically:

Solve equations and inequalities:

Find a value of x for which Min[{Sin[x],Cos[x]}]1/2:

Visualization (3)

Plot the Min of several functions:

Plot Min in three dimensions:

Plot Min of three functions in three dimensions:

Function Properties (5)

Min is only defined for real-valued inputs:

The range of Min is all real numbers:

Min effectively flattens out all lists:

Basic symbolic simplification is done automatically:

Additional simplification can be done using Simplify:

Differentiation and Integration (5)

First derivative with respect to x:

Higher derivatives with respect to x:

Formula for the derivative with respect to x:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integrals:

Applications (4)

Use in bounds of iterator variables:

Cumulative minima:

Find the lowest point of a plotted curve:

Mean of the length ratio of a randomly broken stick:

R‐function-based solid modeling:

Properties & Relations (6)

With no arguments, Min returns Infinity:

Min is Flat and Orderless:

Use PiecewiseExpand to express Min and Max as explicit cases:

Use FullSimplify to simplify Min expressions:

Minimize a function containing Min:

Min can be differentiated:

Possible Issues (2)

Min flattens lists, rather than being Listable:

One‐argument form evaluates for any argument:

Neat Examples (2)

Two-dimensional sublevel sets:

Three-dimensional sublevel sets:

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Min

Details

Examples

Basic Examples (3)