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/* eval_when([translate,load,loadfile,batch,demo],
matchdeclare(a,nonzeroandfreeof(x),[b,c],freeof(x)))$ */
define_variable(takegcd,true,boolean,"used in gcdivide to decide the
gcd choice");
rempart&& rempart(exp,n):=
?append(rest(exp, /* combine two parts of exp
first part is beginning to part to be removed
specify that the first l-1 parts are retained */
(if listp(n) then n[1] else n)-1-length(exp)),
block([t], /* last part is from removed part to end */
if atom(t:rest(exp, /* last m-1 parts are retained */
if listp(n) then n[2] else n))
then ?list(t) else ?cdr(t)))$
wronskian&& wronskian(functlist,var):=block([end],
end:length(functlist)-1,
functlist:[functlist],
thru end do functlist:endcons(map(lambda([x],diff(x,var)),
last(functlist)),functlist),
apply('matrix,functlist))$
tracematrix&& tracematrix(m):=block([sum,len],sum:0,len:length(m),
for i:1 thru len do sum:sum+part(m,i,i),sum)$
rational&& rational(z):=block([n,d,cd,ratfac],
ratfac:false,
n:ratdisrep(ratnumer(z)*(cd:conjugate(d:ratdenom(z)))),
d:rat(n/ratdisrep(d*cd)),
if ratp(z) then d else ratdisrep(d))$
logical&& logand(x,y):=?boole(1,x,y)$
logor(x,y):=?boole(7,x,y)$
logxor(x,y):=?boole(6,x,y)$
nonzeroandfreeof&& nonzeroandfreeof(x,e):=is(e#0 and freeof(x,e))$
/* linear&& matchdeclare(a,nonzeroandfreeof(x),[b,c],freeof(x))$
defmatch(linearize,a*x+b,x)$
defmatch(quadraticize,a*x^2+b*x+c,x)$
linear(exp,x):=block([a,b],if linearize(exp,x)=false then exp else
a*x+b)$
quadratic(exp,x):=block([a,b,c],if quadraticize(exp,x)=false then
exp else a*x^2+b*x+c)$ */
lcm&& lcm([list]):=block([listconstvars:false],if listofvars(list)=[] then
lcm1(list) else factor(lcm1(list)))$
lcm1(list):=if list=[] then 1 else block([rlist:rest(list),flist:first(list),
frlist,partswitch:true,inflag:true,piece], if rlist=[] then flist else
lcm1(cons(flist*(frlist:first(rlist))/gcd(flist,frlist),rest(rlist))))$
gcdivide&& gcdivide(poly1,poly2):=block([gcdlist],
gcdlist:if takegcd then ezgcd(poly1,poly2)
else [1,poly1,poly2],
gcdlist[2]/gcdlist[3])$
series&& arithmetic(a,d,n):=a+(n-1)*d$
geometric(a,r,n):=a*r^(n-1)$
harmonic(a,b,c,n):=a/(b+(n-1)*c)$
arithsum(a,d,n):=n*(a+(n-1)*d/2)$
geosum(a,r,n):=block([],
if r=1
then if n='inf
then return(limit(i*a,i,'inf))
else return(n*a),
if r=-1
then error("The series is not convergent"),
if n='inf
then if abs(r) < 1
then a/(1-r)
else limit(a*(1-r^i)/(1-r),i,'inf)
else a*(1-r^n)/(1-r) )$
gauss&& gaussprob(x):=1/sqrt(2*%pi)*%e^(-x^2/2)$
/* See, for example, http://en.wikipedia.org/wiki/Gudermannian_function */
gd&& gd(x):=2*atan(%e^x)-%pi/2$
agd(x):=log(tan(%pi/4+x/2))$
trig&& vers(x):=1-cos(x)$
covers(x):=1-sin(x)$
exsec(x):=sec(x)-1$
hav(x):=(1-cos(x))/2$
combination&& combination(n,r):=binomial(n,r)$
permutation(n,r):=binomial(n,r)*r!$
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