Owner's Manual

802 Appendix A: Functions and Instructions
You can also include unknown variables that do
not appear in the expressions. These zeros show
how families of zeros 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 unknowns. If your initial
choice exhausts memory or your patience, try
rearranging the variables in the expressions
and/or
varOrGuess list.
cZeros({u_ù v_ì u_ì v_,v_^2+u_},
{u_,v_,w_}) ¸
⎣
⎣⎣
⎣
⎢
⎢⎢
⎢
⎡
⎡⎡
⎡
⎦
⎦⎦
⎦
⎥
⎥⎥
⎥
⎤
⎤⎤
⎤
1/2 ì
3
2
ø i
ii
i 1/2 +
3
2
ø i
ii
i @1
1/2 +
3
2
ø i
ii
i 1/2 ì
3
2
ø i
ii
i @1
0
0 @1
If you do not include any guesses and if any
expression is non-polynomial in any variable but
all expressions are linear in all unknowns,
cZeros() uses Gaussian elimination to attempt to
determine all zeros.
cZeros({u_+v_ì e ^(w_),u_ì v_ì i },
{u_,v_}) ¸
⎣
⎣⎣
⎣
⎡
⎡⎡
⎡
⎦
⎦⎦
⎦
⎤
⎤⎤
⎤
e
w_
2
+1/2ø i
ii
i
e
w_
ì i
ii
i
2
If a system is neither polynomial in all of its
variables nor linear in its unknowns,
cZeros()
determines at most one zero using an
approximate iterative method. To do so, the
number of unknowns must equal the number of
expressions, and all other variables in the
expressions must simplify to numbers.
cZeros({ e ^(z_)ì w_,w_ì z_^2},
{w_,z_}) ¸
[]
.494… ë.703…
A non-real guess is often necessary to determine
a non-real zero. For convergence, a guess might
have to be rather close to a zero.
cZeros({ e ^(z_)ì w_,w_ì z_^2},
{w_,z_=1+
i }) ¸
[]
.149…+4.89…ø i
ii
i 1.588…+1.540…ø i
ii
i
d () 2=key or MATH/Calculus menu
d ( expression1 , var [, order ]) ⇒
⇒⇒
⇒ expression
d
( list1,var [, order ]) ⇒
⇒⇒
⇒ list
d ( matrix1,var [, order ]) ⇒
⇒⇒
⇒ matrix
Returns the first derivative of expression1 with
respect to variable
var . expression1 can be a list or
a matrix.
order , if included, must be an integer. If the order
is less than zero, the result will be an anti-
derivative.
d () does not follow the normal evaluation
mechanism of fully simplifying its arguments and
then applying the function definition to these
fully simplified arguments. Instead,
d () performs
the following steps:
1. Simplify the second argument only to the
extent that it does not lead to a non-
variable.
2. Simplify the first argument only to the extent
that it does recall any stored value for the
variable determined by step 1.
3. Determine the symbolic derivative of the
result of step 2 with respect to the variable
from step 1.
4. If the variable from step 1 has a stored value
or a value specified by a “with” (|) operator,
substitute that value into the result from
step 3.
d (3x^3ì x+7,x) ¸ 9xñì1
d (3x^3ì x+7,x,2) ¸ 18ø x
d (f(x)ù g(x),x) ¸
d
d
x
(f(x))ø g(x) +
d
d
x
(g(x))ø f(x)
d (sin(f(x)),x) ¸
cos(f(x))
d
d
x
(f(x))
d (x^3,x)|x=5 ¸ 75
d ( d (x^2ù y^3,x),y) ¸ 6ø yñøx
d (x^2,x,ë 1) ¸
xò
3
d ({x^2,x^3,x^4},x) ¸
{2ø x 3ø xñ 4ø xò }