MaplePrimes - answers and comments on Question, What's the difference between Re/Im and Re~/Im~?

elementwise

jakubi — Mon, 01 Mar 2010 00:53:55 Z

You can look at the help page ?operators,elementwise .

Oh I see now. But why does

848380 — Mon, 01 Mar 2010 01:12:00 Z

Oh I see now. But why does Re seem to work like Re~ on an Array?

elementwise

Axel Vogt — Mon, 01 Mar 2010 01:12:24 Z

I do not have Maple 13, but it seems so ... while for my taste 'map' is clearer as command then the tilde '~'

elementwise vs map

jakubi — Mon, 01 Mar 2010 02:24:52 Z

Yes, elementwise operators were introduced in Maple 13. There are some differences between map and ~:

1. Syntax. See ?operators,elementwise:

Unlike map and zip, which usually apply to the operands of their given arguments, element-wise operations treat non-container data types as single elements. For example, f~(a=b) evaluates to f(a=b), wheras map(f,a=b) breaks apart the equation applying f to each side of the equation resulting in f(x)=f(b).

2. Efficiency. See ?updates,Maple13,efficiency:

The elementwise operator syntax can be more efficient than zip or map in some cases. Specific operations have been optimized compared to the general code used by zip or map. In other cases, depending on the input, built-in hardware floating-point routines can be used directly.

If equivalent, I prefer this elementwise operator syntax as it allows typing less (important as I type slow) and have more compact input (hence visually more clear).

why

jakubi — Mon, 01 Mar 2010 03:00:55 Z

I do not know as Re is builtin, but time and memory usage seem a bit different:

restart:
`tools/bench`(Re(Array([seq(i+I,i=1..10^5)])));
                            0.156, 2517617

restart:
`tools/bench`(Re~(Array([seq(i+I,i=1..10^5)])));
                            0.203, 3217872