converting any rational operands to floating-point. In other words, floating-point is
"infectious." For example:
transforms to
1/2
-
1/3
but
transforms to
0.5
-
1/3
This floating-point infection does not leap over barriers such as undefined variables or
between elements of lists or matrices. For example:
(1/2
-
1/3) x + (0.5
and
{1/2
-
1/3, 0.5
-
In the AUTO setting, functions such as
exactly, and then use approximate numerical methods if necessary to determine
additional solutions. Similarly, ä (integrate) uses approximate numerical methods if
appropriate where exact symbolic methods fail.
Advantages
You see exact results when practical,
and approximate numeric results
when exact results are impractical.
You can often control the format of a
result by choosing to enter some
coefficients as either rational or
floating-point numbers.
Symbolic Manipulation
1/6
.16666666666667
transforms to
-
1/3) y
transforms to
1/3}
Disadvantages
If you are interested only in exact
results, some time may be wasted
seeking approximate results.
If you are interested only in
approximate results, some time may
be wasted seeking exact results.
Moreover, you might exhaust the
memory seeking those exact results.
x/6 + .16666666666667 y
{1/6, .16666666666667}
determine as many solutions as possible
solve
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