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Computer Buyer 1998 October
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1997-08-26
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; ;
; Corel Ventura Default Equation Presets File ;
; =========================================== ;
; ;
; Format of the Equation Presets File : ;
; ;
; <$E .......... ,, ............ > ;
; ^ ^ ^ ^ ^ ;
; | | | | | ;
; | | | | | ;
; | Text describing Description Actual VEQN | ;
; | the preset and VEQN text for | ;
; | separator the preset | ;
; | | ;
; | | ;
; ------ Standard Ventura markup for equations ------ ;
; ;
; Notes : ;
; 1. Two successive commas cannot appear in the ;
; description string ;
; 2. All the ">" and "<" (except the ones used for the ;
; markup) characters are always in pairs (just like ;
; the text between VP4.2 equation markups) ;
; 3. ";" is used for comments. Comments can appear only ;
; outside of an equation markup i.e. outside <$E ... > ;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
<$EBayes's theorem,,
Pr(B sub j~|~A) ~=~ { Pr(B sub j~)Pr(A | B sub j~) } over
{ sum Pr(B sub i~)Pr(A | B sub i~) }
>
<$EBernoulli's equation,,
dy^/^dx ~+~ yf(x) ~=~ y sup n g(x)
>
<$EBessel functions,,
J sub n (z) ~=~ 1 over pi int from 0 to pi { cos (nt - z ^sin t) dt } =
sum from {r = 0} to inf { {{(-1)} sup r} over
{r! ~ GAMMA (n ~+~ r ~+~ 1) } } ~ { left ( z over 2 right ) } sup {n ~+~ 2r}
>
<$EBessel's equation,,
z sup 2 d sup 2 y ^/^ d z sup 2 ~~+~~ z ~ dy ^/^ dz ~+~
(z sup 2 ~-~ n sup 2~)y ~~=~~ 0
>
<$EBinomial expansion,,
{(1 ~+~ x)} sup n ~->>~ 1 ~+~ nx ~+~ [n(n ~-~ 1) ^/^ 2!] x sup 2
~+~ [n(n ~-~ 1)(n ~-~ 2) ^/^ 3!] x sup 3 ~+~~~ ...
>
<$ECauchy-Schwarz inequality ( for integrals ),,
{left ( { int {[f(x)g(x)] ^ dx } } right )} sup 2 ~~ <<= ~~
left ( { int {{[f(x)]} sup 2} dx } right ) ~~
left ( { int {{[g(x)]} sup 2} dx } right )
>
<$ECauchy-Schwarz inequality ( for sums ),,
{left ( sum (a sub i b sub i ) right )} sup 2 ~~<<=~~
left ( sum a sub i sup 2 right ) ~~~ left ( sum b sub i sup 2 right )
>
<$ECauchy-Schwarz inequality ( for sums, vector form ),,
{( fat a cdot fat b )} sup 2 ~~<<=~~ ( fat a cdot fat a ) ~~
( bold b cdot bold b )
>
<$EEuler's formula,,
GAMMA (z) ~=~ lim from { n ->> inf }{ n! ~ n sup z } over
{z(z+1)(z+2)~~...~~(z+n)}~~~(z ~!=~0, -1, -2, ... )
>
<$EEuler's infinite product,,
1 over { GAMMA (z) } ~=~ ze sup { gamma z } PI from { n = 1 } to inf
left [ left ( 1 ~+~ z over n right ) e sup { -z ^/^ n } right ]
~~~~~~~~~ left ( left | z right | << inf right )
>
<$EEinstein's equation,,
E ~=~ m c sup 2
>
<$ELaplace's equation,,
partial sup 2 italic bold V ^/^ partial x sup 2 ~~+~~
partial sup 2 italic bold V ^/^ partial y sup 2 ~~+~~
partial sup 2 bold italic V ^/^ partial z sup 2 ~~~=~~~ 0
>