Comments (2)
Mmh that's quite interesting in terms of pedagogy. I haven't really thought about it but at first it seems we could have a sort-of tree structure for equations with "AND" and "OR" nodes, and operate on that tree in steps in the same way you currently operate on expression trees.
For example, starting from a single root node |x| + 3 = 4
, we would transform it to an "OR" node with left branch x + 3 = 4
and right branch -x + 3 = 4
.
You could also imagine a slightly more complex example. Say we start with the system
|x| = 3
x >= 0
The initial tree structure would be
AND(|x| = 3, x >= 0)
The first step would deal with the absolute value and we would get
AND(
OR(x = 3, -x = 3),
x >= 0
)
then we could distribute the conjunction over the disjunction to get
OR(
AND(x = 3, x >= 0),
AND(-x = 3, x >= 0),
)
We would then eliminate the right branch of the "OR" node because -x = 3
and x >= 0
are not satisfiable, and somehow contract x = 3
and x >= 0
(since they contain redundant information) to the single equation x = 3
.
In a short example like this it seems it would work and be easy to follow, but in this specific case the reasoning "x >= 0 so I can just remove the absolute value" would also be correct (and shorter).
What do you think?
from mathsteps.
I hadn't thought about it much yet, but that sounds quite reasonable! Since this will be a pretty big decision, I think it's worth doing research into what other CAS do as well.
from mathsteps.
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from mathsteps.