norm

Synopsis

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 = | 9.1 2.9 .6  .55 4.4 1.9 4.5 7.7 2.8 8.2 |
     | 3.1 2.1 8   6.9 7.7 9.6 8.8 .86 9.3 7.8 |
     | 8.7 8.5 2.4 7.8 .8  2.9 6.4 9   2.4 5.4 |

             3       10
o3 : Matrix R  <--- R

i4 : norm M

o4 = 9.58375675924518436104525675063

o4 : RR (of precision 100)

i5 : norm_(numeric_20 infinity) M

o5 = 9.58376

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)
norm(Thing,List) (missing documentation)

norm

Synopsis

Description

Ways to use norm :

Ways to use `norm` :