norm

Usage:

norm M

norm(p,M)
Inputs:
- M, a mutable matrix, a matrix, a ring element, a number, a vector, or a list
- p, a real number or an infinite number, 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 = 9.952219758672894287555632834552

o4 : RR (of precision 100)

i5 : norm_(numeric_20 infinity) M

o5 = 9.952225

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 a method function.

The source of this document is in Macaulay2Doc/ov_analytic_functions.m2:542:0.