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norm

Synopsis

Description

i1 : printingPrecision = 2

o1 = 2
i2 : R = RR_100

o2 = RR
       100

o2 : RealField
i3 : M = 10*random(R^3,R^10)

o3 = | 2.9 3.2 3.8 3.4 5   2.4 7.9 5   3.5 4.2 |
     | .77 8   9.9 6.3 4.4 4.4 6.7 9.6 7   2.6 |
     | 3.3 5.2 5.6 1.5 9.9 7.4 1.2 5.7 2.6 9.3 |

             3       10
o3 : Matrix R  <--- R
i4 : norm M

o4 = 9.93969526810272331546124470928

o4 : RR (of precision 100)
i5 : norm_(numeric_20 infinity) M

o5 = 9.9397

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 :