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Normal

Normal[expr]
converts expr to a normal expression, from a variety of special forms.

Normal[expr] converts a power series to a normal expression by truncating higher-order terms.

Normal[expr] converts GraphicsComplex objects into ordinary lists of graphics primitives and directives.

Normal[expr] converts RootSum objects into explicit sums involving Root objects.

When additional "data types" are introduced, Normal should be defined to convert them, when possible, to normal expressions.

Create a normal dense list from a sparse array:

Create a normal expression from a series expansion:

Create a normal dense list from a sparse array:

Out[1]=

Out[2]=

Create a normal expression from a series expansion:

Out[1]=

Out[2]=

Convert RootSum objects to Root objects:

Typically the RootSum objects will give more accurate numerical values:

Convert from a GraphicsComplex object to graphics primitives:

Both forms produce the same image:

Normal will affect expressions nested inside other expressions:

Compare the actual error to the theoretical asymptotic error for a difference quotient:

Power series about

Asymptotic truncation error for small

Compare actual and asymptotic errors as a function of

for

With higher precision, the asymptotic error holds for smaller

For f that work with SparseArray objects s, often Normal[f[s]]===f[Normal[s]]: