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|
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<Task-category name="<default>">
</Task-category>
</Task-table>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure "na\303\257ve"</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Cette proc\303\251dure calcule les coefficients de Fourier par une m\303\251thode dite "naive".</Font></Text-field>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TFDSimple:=proc(x)
local n,X:
n:=nops(x):
X:=[seq(sum(x[j]*exp(-2*I*(j-1)*(k-1)*Pi/n),j=1..n),k=1..n)];
end proc:</Text-field>
</Input>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure r\303\251cursive</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Cette proc\303\251dure prend en entr\303\251e une liste repr\303\251sentant les coefficients d'un polyn\303\264me dont on cherche \303\240 calculer les coefficients de Fourier.</Font></Text-field>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TFDRecur:=proc(x)
local N,CoefFFT,xp,xi,u,v,omega:
N:=nops(x):
if N=1 then CoefFFT:=x:
else
xp:=[seq(x[2*i],i=1..N/2)]:
xi:=[seq(x[2*i-1],i=1..N/2)]:
u:=TFDRecur(xp):
v:=TFDRecur(xi):
omega:=exp(-2*I*Pi/N):
CoefFFT:=[seq(omega^(k-1)*u[k]+v[k],k=1..N/2),seq(-omega^(k-1)*u[k]+v[k],k=1..N/2)];
end if:
CoefFFT;
end proc:</Text-field><Pagebreak></Pagebreak>
</Input>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par it\303\251ration</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va utiliser l'\303\251criture des divers coefficients en binaire.</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TFDIter:=proc(x)
local n,i,j,k,a,b,p,l,z,w,h,m,tmp:
n:=nops(x):
l:=Array(1..n):
l:=Array(x):
p:=n/2:<Font encoding="UTF-8">#p: puissance de 2 dans d\303\251composition.
</Font>
while p>=1 do
<Font encoding="UTF-8"> z:=1: #premi\303\250re valeur de omega.
</Font> w:=exp(-I*Pi/p): #c'est omega.
<Font encoding="UTF-8"> for h from 1 to p do #Variable servant \303\240 la d\303\251composition
</Font> for m from 1 to n/(2*p) do
#On va calculer le signal xm
<Font encoding="UTF-8"> a:=h+2*(m-1)*p: #Premi\303\250re valeur du signal x_(m-1)
</Font> b:=a+p: #Seconde valeur du signal x_(m-1)
tmp:=(l[a]-l[b])*z:
l[a]:=l[a]+l[b]: #x_m(a) = x_(m-1)(a)+x_(m-1)(b)
l[b]:=tmp: #x_m(b) = (x_(m-1)(a)-x_(m-1)(b))*z
end do:
#On passe au signal m+1 -> w<-w^(m+1)
z:=z*w:
end do:
p:=p/2:
end do:
#On a maintenant notre liste contenant les signaux x_r
<Font encoding="UTF-8">#Il reste \303\240 remettre les signaux dans le bon ordre.</Font>
j:=1:
for i from 1 to n do
if j>i then tmp:=l[j]:
l[j]:=l[i]:
l[i]:=tmp:
end if:
p:=n/2:
while p>=2 and j>p do
j:=j-p:
p:=p/2:
end do:
j:=j+p:
end do:
l;
end proc:</Text-field><Pagebreak></Pagebreak>
</Input>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la Transform\303\251e Inverse.</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">De m\303\252me, il est possible d'effectuer deux m\303\251thodes pour calculer la transform\303\251e inverse de Fourier :</Font></Text-field>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode na\303\257ve</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">En utilisant le m\303\252me algorithme, on obtient : </Font></Text-field>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TFDISimple:=proc(X)
local n,F:
n:=nops(X):
F:=[seq((1/n)*sum(X[i]*exp(2*I*(j-1)*(i-1)*Pi/(n)),i=1..n),j=1..n)];
end proc:</Text-field>
</Input>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode r\303\251cursive</Font></Text-field></Title>
<Text-field style="Text" layout="Normal">Attention : Pour que l'on puisse retrouver les valeurs initiales, </Text-field>
<Text-field style="Text" layout="Normal">il ne faut pas oublier de diviser par le nombre de valeurs.</Text-field>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TFDIRecur:=proc(X)
local Coef,N,Xi,Xp,U,V,Omega,k;
N:=nops(X);
if N=1 then Coef:=X:
else
Xi:=[seq(X[2*k-1],k=1..N/2)];
Xp:=[seq(X[2*k],k=1..N/2)];
U:=TFDIRecur(Xi);
V:=TFDIRecur(Xp);
Omega:=exp(2*I*Pi/N);
Coef:=[seq(U[k]+Omega^(k-1)*V[k],k=1..N/2),seq(U[k]-Omega^(k-1)*V[k],k=1..N/2)]:
end if;
Coef;
end proc:</Text-field><Pagebreak></Pagebreak>
</Input>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode it\303\251rative</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">TFDIIter:=proc(x)
local n,i,j,k,a,b,p,l,z,w,h,m,tmp:
n:=nops(x):
l:=Array(1..n):
l:=Array(x):
p:=n/2:
while p>=1 do
z:=1:
<Font encoding="UTF-8"> w:=exp(I*Pi/p); #C'est la diff\303\251rence
</Font>
for h from 1 to p do
for m from 1 to n/(2*p) do
a:=h+2*(m-1)*p:
b:=a+p:
tmp:=(l[a]-l[b])*z:
l[a]:=l[a]+l[b]:
l[b]:=tmp:
end do:
z:=z*w:
end do:
p:=p/2:
end do:
j:=1:
for i from 1 to n do
if j>i then tmp:=l[j]:
l[j]:=l[i]:
l[i]:=tmp:
end if:
p:=n/2:
while p>=2 and j>p do
j:=j-p:
p:=p/2:
end do:
j:=j+p:
end do:
for i from 1 to n do
l[i]:=l[i]/n:
end do:
return l;
end proc:</Text-field><Pagebreak></Pagebreak>
</Input>
</Group>
</Section>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Mesure du temps de calcul</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va ici s'int\303\251resser \303\240 la mesure du temps n\303\251cessaire pour calculer les coefficients de Fourier (Transform\303\251e Directe) pour n "grand", par exemple n=2^5, n=2^10,... .
Pour cela, on va d\303\251finir la liste de nos coefficients par une m\303\251thode "pseudo-al\303\251atoire" : </Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">with(RandomTools[MersenneTwister]):
A:=[seq(GenerateFloat(),i=1..2^8)]:</Text-field>
</Input>
</Group>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode na\303\257ve</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On effectue le calcul pour la m\303\251thode na\303\257ve : </Font></Text-field>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">t:=time():
TFDSimple(A):
Temps := time()-t;</Text-field>
</Input>
<Output>
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</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode r\303\251cursive</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Calcul pour la m\303\251thode r\303\251cursive : </Font></Text-field>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">t:=time():
TFDRecur(A):
Temps := time()-t;</Text-field>
</Input>
<Output>
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</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode it\303\251rative</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Mesure pour la m\303\251thode it\303\251rative :</Font></Text-field>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">t:=time():
TFDIter(A):
Temps:= time()-t;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field><Pagebreak></Pagebreak>
</Output>
</Group>
</Section>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Multiplication de polyn\303\264mes</Font></Text-field></Title>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Algorithme</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va prendre en entr\303\251e deux listes contenant les coefficients des deux polyn\303\264mes dont on cherche \303\240 calculer le produit.</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Il faut prendre des pr\303\251cautions, car la proc\303\251dure ne v\303\251rifie pas si les deux polyn\303\264mes sont de m\303\252me degr\303\251, qui doit \303\252tre une puissance de 2, si l'on souhaite utiliser la m\303\251thode r\303\251cursive ou it\303\251rative.</Font></Text-field>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Multiplication:=proc(P,Q)
local n,N,R,A,B,i,j,k:
n:=nops(P):
N:=2*n:
<Font encoding="UTF-8">#On cr\303\251e la liste des coefficients \303\251tendus \303\240 2n \303\251l\303\251ments.
</Font>A:=[seq(P[k],k=1..n),seq(0,k=n+1..N)];
B:=[seq(Q[k],k=1..n),seq(0,k=n+1..N)];
#On calcule la TFD de chacune de ces listes.
A:=TFDIter(A):
B:=TFDIter(B):
#On effectue les produits
R:=[seq(A[k]*B[k],k=1..N)]:
<Font encoding="UTF-8">#On r\303\251cup\303\250re les coefficients.
</Font>TFDIIter(R);
end proc:</Text-field><Pagebreak></Pagebreak>
</Input>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Exemple</Text-field></Title>
<Text-field style="Text" layout="Normal">On va poser <Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mi("P"), Typesetting:-mo(":=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-munderover(Typesetting:-mo("\342\210\221", form = "prefix", fence = "false", separator = "false", lspace = "0em", rspace = "thinmathspace", stretchy = "true", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "true", movablelimits = "true", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mi("i"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("0"), Typesetting:-mi("")), Typesetting:-mn("7"), accent = "false", accentunder = "false"), Typesetting:-mi(""), Typesetting:-msup(Typesetting:-mi("iX"), Typesetting:-mi("i"), superscriptshift = "0"), Typesetting:-mi("")), Typesetting:-mi(""))">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</Equation> et <Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mi("Q"), Typesetting:-mo(":=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-munderover(Typesetting:-mo("\342\210\221", form = "prefix", fence = "false", separator = "false", lspace = "0em", rspace = "thinmathspace", stretchy = "true", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "true", movablelimits = "true", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mi("i"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("0")), Typesetting:-mn("7"), accent = "false", accentunder = "false"), Typesetting:-mi(""), Typesetting:-msup(Typesetting:-mi("i"), Typesetting:-mi("i"), superscriptshift = "0"), Typesetting:-mi(""), Typesetting:-msup(Typesetting:-mi("X"), Typesetting:-mi("i"), superscriptshift = "0"), Typesetting:-mi("")), Typesetting:-mi(""))">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</Equation> donc<Equation executable="false" style="2D Math" input-equation="Typesetting:-mrow(Typesetting:-mo(" ", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mi("n"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-mn("8"), Typesetting:-mo("=", form = "infix", fence = "false", separator = "false", lspace = "thickmathspace", rspace = "thickmathspace", stretchy = "false", symmetric = "false", maxsize = "infinity", minsize = "1", largeop = "false", movablelimits = "false", accent = "false", font_style_name = "2D Math", size = "12", foreground = "[0,0,0]", background = "[255,255,255]"), Typesetting:-msup(Typesetting:-mn("2"), Typesetting:-mn("3."), superscriptshift = "0"), Typesetting:-mi(""))">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</Equation></Text-field>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">Algo</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va demander la liste des coefficients du polyn\303\264me R=P*Q. Pour une lecture plus facile, nous en prendrons les valeurs arrondies.</Font></Text-field>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">P:=[seq(i,i=0..7)]:</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Q:=[seq(i^i,i=0..7)]:</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R:=evalf(Multiplication(P,Q)):</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">[seq(R[j],j=1..2*nops(P))];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R:=[seq(round(R[j]),j=1..2*nops(P))];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">Maple</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">On va evaluer le polyn\303\264me P*Q :</Font></Text-field>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">P:=sum(i*X^i,i=0..7):</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Q:=sum(i^i*X^i,i=0..7):</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">sort(expand(P*Q),X,ascending);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Section>
</Section>
</Section>
</Worksheet>
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