# [Maxima] Cornu spiral

Edwin Woollett woollett at charter.net
Sun Dec 14 15:25:17 CST 2008

```On Dec. 11, 2008, Edwin Woollett wrote:
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Instead of using Maxima functions, here I use expressions.
For reasons of plotting efficiency, it makes sense to use
integrate(...) once to get a symbolic expression, and
to simply use that expression to get the plot, ......
------------------------------------------------
As Robert Dodier pointed out in his description of
the two quote method, there is no loss of efficiency
in his method, since quoting him :  << In both cases, '' is
two single quotes  (not one double quote). The effect
of '' is to evaluate the integral  just once, when the
function is defined. >>
------------------------------------------------------------
Hence definitions like

fC (t) := ''(integrate (cos (s^2 * %pi/2), s, 0, t ) )\$
or

frC(t) := expand ( float ( ''(integrate (cos(s^2), s , 0, t ) ) ) )\$

are both quick and efficient methods, the latter  being useful
for looking at numerical values as well as plots.

frC (1);  --->
2.4597738442010351E-17 %i + 0.90452423790027

Ted Woollett

```