[2.22] Methods for some CAS functions
The descriptions below are from a file on the TI web site at
ftp://ftp.ti.com/pub/graph-ti/calc-apps/info/92algorithms.txt
These descriptions probably apply to the original TI-92, and may not accurately describe the latest
version of the 89/92+ CAS. Even so, they may be useful as a general indication of how the functions
get their results.
arcLen()
arcLen(f(x),x,a,b) is merely
¶
a
b
d
dx
(
f
(
x
))
2
+ 1 dx
avgRC()
avgRC
(
f
(
x
)
,x,h
)
=
f
(
x+h
)
−f
(
x
)
h
cFactor()
cFactor() is the same as factor() , except the domain is temporarily set to complex so that complex
factors are sought and not rejected.
comDenom()
Term by term, comDenom(a/b+c/d) reduces (a*d+b*c)/(b*d) to lowest terms, and repeats this process
for each additional term.
cSolve()
cSolve() is the same as solve() , except the domain is temporarily set to complex so that complex
solutions are sought and not rejected.
cZeros()
cZeros(expr,var) is
expr▶list(cSolve(expr=0,var),var).
() (symbolic differentiation)
() repeatedly uses the chain rule together with the well-known formulas for the derivatives of sums,
products, sinusoids, etc.
expand()
Polynomial expansion is done by repeated application of the distributive law, interleaved with use of the
associative and commutative laws to collect similar terms.
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