norm(Thing,AbstractPoint) -- p-norm of the point

Synopsis

Function: norm
Usage:

a = norm(p,pt)
Inputs:
- p, a thing, a positive real number or infinity
- pt, a point
Outputs:
- a, the p-norm of the point pt

Description

i1 : needsPackage "NumericalAlgebraicGeometry"

o1 = NumericalAlgebraicGeometry

o1 : Package

i2 : R = CC[x,y];

i3 : sols = solveSystem{x^2+y^2-3, x^3-y^3-7}

o3 = {{-1.7957-1.31322*ii, 1.7957-1.31322*ii}, {-.101284+.779159*ii,
     ------------------------------------------------------------------------
     -1.89699-.041601*ii}, {-1.7957+1.31322*ii, 1.7957+1.31322*ii},
     ------------------------------------------------------------------------
     {-.101284-.779159*ii, -1.89699+.041601*ii}, {1.89699+.041601*ii,
     ------------------------------------------------------------------------
     .101284-.779159*ii}, {1.89699-.041601*ii, .101284+.779159*ii}}

o3 : List

i4 : norm(infinity, first sols)

o4 = 2.22465672063909

o4 : RR (of precision 53)

i5 : norm(2.5, last sols) 

o5 = 1.97857011037553

o5 : RR (of precision 53)

Ways to use this method: