# norm

## Synopsis

• Usage:
norm M
norm(p,M)
• Inputs:
• M, , , , , , or a list
• p, or , specifying which norm to compute. Currently, only p=infinity is accepted.
• Outputs:
• the $L^p$-norm of M computed to the minimum of the precisions of M and of p.

## Description

 i1 : printingPrecision = 2 o1 = 2 i2 : R = RR_100 o2 = RR 100 o2 : RealField i3 : M = 10*random(R^3,R^10) o3 = | 2 5.6 1.9 4.1 3.5 2.6 6.1 5.3 .83 .44 | | 2 3.7 4.1 6.1 4.7 1.2 9 7.4 .95 1.5 | | 7.4 1.5 4.3 3.4 6.9 6 9.5 10 4.8 8 | 3 10 o3 : Matrix RR <--- RR 100 100 i4 : norm M o4 = 9.95221975867289428755563283455 o4 : RR (of precision 100) i5 : norm_(numeric_20 infinity) M o5 = 9.95222 o5 : RR (of precision 20) i6 : norm {3/2,4,-5} o6 = 5
The norm of a polynomial is the norm of the vector of its coefficients.
 i7 : RR[x] o7 = RR [x] 53 o7 : PolynomialRing i8 : (1+x)^5 5 4 3 2 o8 = x + 5x + 10x + 10x + 5x + 1 o8 : RR [x] 53 i9 : norm oo o9 = 10 o9 : RR (of precision 53)

## Ways to use norm :

• "norm(InexactField,MutableMatrix)"
• "norm(InfiniteNumber,Matrix)"
• "norm(InfiniteNumber,Number)"
• "norm(InfiniteNumber,RingElement)"
• "norm(List)"
• "norm(Matrix)"
• "norm(MutableMatrix)"
• "norm(Number)"
• "norm(RingElement)"
• "norm(RR,Matrix)"
• "norm(RR,MutableMatrix)"
• "norm(RR,Number)"
• "norm(RR,RingElement)"
• "norm(Vector)"

## For the programmer

The object norm is .