issue with norm

[LukeOeding]

I'm having trouble getting the expected behavior from "norm".
Here's what I tried:

v = random(RR^2,RR^1)
norm(v)
norm_2 v
norm(2, v)
norm(2_RR, v)
norm(infinity, v)

Only the first one and last one execute, and both give the L^infinity norm. Of course I can implement my own 2-norm, but I would have expected this to work with any integer, certainly 2, or positive real number since the documentation says that I can do that.

[d-torrance]

I'm not sure what we want when there are at least two rows and at least two columns. For example, should norm_2 give the Frobenius norm or the spectral norm?

[LukeOeding]

I would guess that norm_2 would be the Frobenius norm, however wikipedia seems to disagree. Probably better to use the operator norm on matrices. If someone wants the vector norm on matrices, they can flatten first?

By the way, I forgot to put in the results I got:

Macaulay2, version 1.25.11
Type "help" to see useful commands

i1 : v = random(RR^2,RR^1)

o1 = | .159707 |
     | .11876  |

                2         1
o1 : Matrix RR    <-- RR
              53        53

i2 : norm(v)

o2 = .1597070215596925

o2 : RR (of precision 53)

i3 : norm_2 v
stdio:3:6:(3): error: no method found for applying norm to:
     argument 1 :  2 (of class ZZ)
     argument 2 :  | .159707 | (of class Matrix)
                   | .11876  |

i4 : norm(2, v)
stdio:4:4:(3): error: no method found for applying norm to:
     argument 1 :  2 (of class ZZ)
     argument 2 :  | .159707 | (of class Matrix)
                   | .11876  |

i5 : norm(2_RR, v)
stdio:5:4:(3): error: Lp norm only implemented for p = infinity

i6 : norm(infinity, v)

o6 = .1597070215596925

o6 : RR (of precision 53)

i7 : v = random(RR^2)

o7 = | .321267 |
     |  .59296 |

         2
o7 : RR
       53

i8 : norm(v)

o8 = .5929596345035341

o8 : RR (of precision 53)

i9 : norm_2 v
stdio:9:6:(3): error: no method found for applying norm to:
     argument 1 :  2 (of class ZZ)
                                             2
     argument 2 :  | .321267 | (of class RR   )
                   |  .59296 |             53

i10 : norm(2, v)
stdio:10:4:(3): error: no method found for applying norm to:
     argument 1 :  2 (of class ZZ)
                                             2
     argument 2 :  | .321267 | (of class RR   )
                   |  .59296 |             53

i11 : norm(2_RR, v)
stdio:11:4:(3): error: no method found for applying norm to:
     argument 1 :  2 (of class RR)
                                             2
     argument 2 :  | .321267 | (of class RR   )
                   |  .59296 |             53

i12 : norm(infinity, v)
stdio:12:4:(3): error: no method found for applying norm to:
     argument 1 :  infinity (of class InfiniteNumber)
                                             2
     argument 2 :  | .321267 | (of class RR   )
                   |  .59296 |             53

[seangrate]

I was also running into this issue in the past couple of days, so +1 for more norm functionality. I would have also expected the default to be the $2$-norm, but it seems to be the $\infty$-norm.

[d-torrance]

Mike and I just discussed this. Since the existing $\infty$-norm is the entry-wise $\infty$-norm (maximum absolute entry) and not the operator $\infty$-norm (maximum absolute row sum), we should stick with the entry-wise norms for other values of $p$ (which is easier to implement anyway).

I'll whip up something for the upcoming release.