Carl Banks wrote:
On Dec 6, 11:34 am, Anton81 <gerenu...@googlemail.com> wrote:
I do some linear algebra and whenever the prefactor of a vector turns
out to be zero, I want to remove it.
I'd like to keep the system comfortable. So basically I should write a
new class for numbers that has it's own __eq__ operator?
Is there an existing module for that?
I highly recommend against it; among other things it invalidates the
transitive property of equality:
"If a =b and b == c, then a == c."
It will also make the number non-hashable, and have several other
negative consequences. Plus, it's not something that's never
foolproof. What numbers are close enought to be condidered "equal"
depends on the calculations.
(I remember once struggling in a homework assignment over seemingly
large discrepancies in a calculation I was doing, until i realized
that the actual numbers were on the scale of 10**11, and the
difference was around 10**1, so it really didn't matter.)
Carl Banks
A few decades ago I implemented the math package (microcode) under the
machine language for a proprietary processor (this is when a processor
took 5 boards of circuitry to implement). I started with floating point
add and subtract, and continued all the way through the trig, log, and
even random functions. Anyway, a customer called asking whether a
particular problem he had was caused by his logic, or by errors in our
math. He was calculating the difference in height between an
always-level table and a perfectly flat table (between an arc of a great
circle around the earth, and a flat table that doesn't follow the
curvature.) In a couple of hundred feet of table, the difference was
measured in millionths of an inch, as I recall. Anyway it turned out
his calculation was effectively subtracting
(8000 miles plus a little bit) - (8000 miles)
and if he calculated it three different ways, he got three different
results, one was off in about the 3rd place, while the other was only
half the value. I was able to show him another way (through geometrical
transformations) to solve the problem that got the exact answer, or at
least to more digits than he could possibly measure. I think I recall
that the new solution also cancelled out the need for trig. Sometimes
the math package shouldn't hide the problem, but give it to you straight.
DaveA
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