• ← Chop
• → Piecewise

N

WMA link

N[expr, prec]

evaluates expr numerically with a precision of prec digits.

• • N[Pi, 50]

• • N[1/7]

• • N[1/7, 5]

You can manually assign numerical values to symbols.

When you do not specify a precision, MachinePrecision is taken.

• • N[a] = 10.9

• • a

N automatically threads over expressions, except when a symbol has
attributes NHoldAll, NHoldFirst, or NHoldRest.

• • N[a + b]

• • N[a, 20]

• • N[a, 20] = 11;

• • N[a + b, 20]

• • N[f[a, b]]

• • SetAttributes[f, NHoldAll]

• • N[f[a, b]]

The precision can be a pattern:

• • N[c, p_?(#>10&)] := p

• • N[c, 3]

• • N[c, 11]

You can also use UpSet or TagSet to specify values for N:

• • N[d] ^= 5;

However, the value will not be stored in UpValues, but
in NValues (as for Set):

• • UpValues[d]

• • NValues[d]

• • e /: N[e] = 6;

• • N[e]

Values for N[expr] must be associated with the head of expr:

• • f /: N[e[f]] = 7;

You can use Condition:

• • N[g[x_, y_], p_] := x + y * Pi /; x + y > 3

• • SetAttributes[g, NHoldRest]

• • N[g[1, 1]]

• • N[g[2, 2]] // InputForm

The precision of the result is no higher than the precision of the input

• • N[Exp[0.1], 100]

• • % // Precision

• • N[Exp[1/10], 100]

• • % // Precision

• • N[Exp[1.0`20], 100]

• • % // Precision

N can also accept an option “Method”. This establishes what is the prefrered underlying method to compute numerical values:

• • N[F[Pi], 30, Method->"numpy"]

• • N[F[Pi], 30, Method->"sympy"]