TIcalc site: http://www.ticalc.org/pub/92/basic/math/
! Solve n equations in n unknowns using Gauss-Jordan elimination: srref.zip
[6.24] Fast Fibonacci Numbers
The Fibonacci numbers are defined by this recurrence relation:
F
1
= 1, F
2
= 1, F
n+2
= F
n
+ F
n+1
This formula can be used to find the nth Fibonacci number:
F
n
=
1
5
1+ 5
2
n
−
1− 5
2
n
However, the 89/92+ cannot use this formula for large n, because the CAS cannot simplify the result.
Finding the numbers with a TI Basic program in recursion is quite slow, and limits n to about 255.
However, this function can find Fibonacci numbers for large n:
Define fib(n)=([[1,1][1,0]]^(n-1 ))[1,1]
(Credit to Alex Astashyn)
[6.25] Polar and rectangular coordinate conversions
The 89/92+ provide a variety of methods to convert point or vector coordinates between polar and
rectangular formats.
You can use the Vector Format setting in the Mode menu to perform conversions automatically from
the command line. If the Vector Format is set to RECTANGULAR, then coordinates entered in polar
format are converted to rectangular coordinates when the vector is entered. For example, if the mode
is RECTANGULAR and
[√(2),∠Œ/4] in polar coordinates is entered, then [1,1] is returned. If the
Vector Format is set to CYLINDRICAL or SPHERICAL and [1,1] in rectangular coordinates is entered,
then
[√(2),∠Œ/4] is returned.
You can also use the conversion functions
▶Polar and ▶Rect to convert vector coordinates. For
example,
[1,1]▶Polar returns [√(2),∠Œ/4], and [√(2),∠Œ/4]▶Rect returns [1,1]. However, note
that
▶Polar and ▶Rect are called "display-format" instructions. They only affect the display of the
vector: they do not really convert the vectors.
Finally, these functions can be used to return just one part of a converted vector:
Return angle of rectangular vector argument
✕
R▶Pθ(x,y)
Return magnitude r of rectangular vector argument
R▶Pr(x,y)
Return y-coordinate of polar vector argument
P▶Ry(r,θ)
Return x-coordinate of polar vector argument
P▶Rx(r,θ)
These functions can be used to write user functions which, unlike ▶Polar and ▶Rect, do actually
convert the input vector. These functions are:
polar(v)
6 - 26
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