880 Appendix A: Functions and Instructions
to extend the previous example to two parallel
intersecting cylinders of radius r.
The cylinder solutions illustrate how families of
solutions might contain arbitrary constants of the
form @
k
, where
k
is an integer suffix from 1
through 255. The suffix resets to 1 when you use
ClrHome or ƒ 8:Clear Home.
For polynomial systems, computation time or
memory exhaustion may depend strongly on the
order in which you list solution variables. If your
initial choice exhausts memory or your patience,
try rearranging the variables in the equations
and/or
varOrGuess
list.
x=
r
2
and y=
3ør
2
and z=@1
or x=
r
2
and y=
ë 3ør
2
and z=@1
If you do not include any guesses and if any
equation is non-polynomial in any variable but all
equations are linear in the solution variables,
solve() uses Gaussian elimination to attempt to
determine all real solutions.
solve(x+
e
^(z)ù y=1 and xì y=sin(z),{x,y})
¸
x=
e
z
øsin(z)+1
e
z
+1
and y=
ë (sin(z)ì 1)
e
z
+1
If a system is neither polynomial in all of its
variables nor linear in its solution variables,
solve() determines at most one solution using an
approximate iterative method. To do so, the
number of solution variables must equal the
number of equations, and all other variables in
the equations must simplify to numbers.
solve(
e
^(z)ù y=1 and ë y=sin(z),{y,z})
¸
y=.041… and z=3.183…
Each solution variable starts at its guessed value
if there is one; otherwise, it starts at 0.0.
Use guesses to seek additional solutions one by
one. For convergence, a guess may have to be
rather close to a solution.
solve(
e
^(z)ù y=1 and ë y=sin(z),{y,z=2p})
¸
y=.001… and z=6.281…
SortA MATH/List menu
SortA
listName1
[,
listName2
] [,
listName3
] ...
SortA
vectorName1
[,
vectorName2
] [,
vectorName3
] ...
Sorts the elements of the first argument in
ascending order.
If you include additional arguments, sorts the
elements of each so that their new positions
match the new positions of the elements in the
first argument.
All arguments must be names of lists or vectors.
All arguments must have equal dimensions.
{2,1,4,3}! list1 ¸ {2,1,4,3}
SortA list1
¸ Done
list1
¸ {1 2 3 4}
{4,3,2,1}
! list2 ¸ {4 3 2 1}
SortA list2,list1
¸ Done
list2
¸ {1 2 3 4}
list1
¸ {4 3 2 1}
SortD MATH/List menu
SortD
listName1
[,
listName2
] [,
listName3
] ...
SortD
vectorName1
[,
vectorName 2
] [,
vectorName 3
] ...
Identical to SortA, except SortD sorts the
elements in descending order.
{2,1,4,3}! list1 ¸ {2 1 4 3}
{1,2,3,4}
! list2 ¸ {1 2 3 4}
SortD list1,list2
¸ Done
list1
¸ {4 3 2 1}
list2
¸ {3 4 1 2}
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