zeros()
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variable
– or –
variable = real or non-real number
For example, x is valid and so is x=3.
If all of the expressions are polynomials and
if you do NOT specify any initial guesses,
zeros() uses the lexical Gröbner/Buchberger
elimination method to attempt to
determine all real zeros.
For example, suppose you have a circle of
radius r at the origin and another circle of
radius r centered where the first circle
crosses the positive x-axis. Use zeros() to
find the intersections.
As illustrated by r in the example to the
right, simultaneous polynomial expressions
can have extra variables that have no
values, but represent given numeric values
that could be substituted later.
Each row of the resulting matrix represents
an alternate zero, with the components
ordered the same as the varOrGuess list.
To extract a row, index the matrix by [row].
Extract row 2:
You can also (or instead) include unknowns
that do not appear in the expressions. For
example, you can include z as an unknown
to extend the previous example to two
parallel intersecting cylinders of radius r.
The cylinder zeros illustrate how families of
zeros might contain arbitrary constants in
the form ck, where k is an integer suffix
from 1 through 255.
For polynomial systems, computation time
or memory exhaustion may depend strongly
on the order in which you list unknowns. If
your initial choice exhausts memory or your
patience, try rearranging the variables in
the expressions and/or varOrGuess list.
Alphabetical Listing 199
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