> # Weiji Zheng, 09/15/2020, Assignment 1
> # OK to post Homwork

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> #Part 1 - Random Lines
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> 
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> 100+300+500;
900
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> 500-200-100;
200
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> 500-100000;
-99500
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> diff(x^6 + x*y^7*z^4, x);
y^7*z^4+6*x^5
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> factor(x^3 + 2*x*y + 3*x^5);
x*(3*x^4+x^2+2*y)
;
> isprime(17);
true
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> s := 1,640,454: s[3];
454
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> 
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> #Part 2 - Human Problem

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> #F(6) = {[1,1,1,1,1,1],[2,1,1,1,1],[1,2,1,1,1],[1,1,2,1,1],[1,1,1,2,1],[1,1,1,1,2],[2,2,1,1],[2,1,2,1],[2,1,1,2],[1,1,2,2],[1,2,1,2],[1,2,2,1]}
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> 
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> #Part 3
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> #1.To covert L1:=[Mercury,Venus,Earth] to L2:=[Mercury,Venus,Earth,Mars], Use  L->[op(L),a] where a = Mars
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> #Code:
> L1 := [Mercury,Venus,Earth];
L1 := [Mercury, Venus, Earth]
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> L2 := [op(%),Mars];
L2 := [Mercury, Venus, Earth, Mars]
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> #2.
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> #Because the function Walks(m, n) is used to calculate all the sets of possible routes from (0, 0) to (m, n) by using North and East.Thus, if either m or n or both are negative, there is no route will show up, which makes Maple shows an empty set denotes null answer.
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> #3
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> #There is still a route from (0,0) to (0,0), which is an initial condition. So we use set {[]} to show this route.
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> 
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> #Part 4
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> F:=proc(n) local W1,W2,w1,w2:
>    option remember:
> 
>    if n<0 then
>    RETURN({}):
>    fi:
> 
>    if n=0 then
>    RETURN({[]});
>    fi:
> 
>    W1:=F(n-1):
>    W2:=F(n-2):
> 
>    {seq([op(w1), 1],w1 in W1), seq([op(w2),2],w2 in W2)}:
> 
>    end:
> F(6);
{[2, 2, 2], [1, 1, 2, 2], [1, 2, 1, 2], [1, 2, 2, 1], [2, 1, 1, 2], [2, 1, 2, 1], [2, 2, 1, 1], [1, 1, 1, 1, 2], [1, 1, 1, 2, 1], [1, 1, 2, 1, 1], [1, 2, 1, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]}
;
>  #Same output as the handwrite answer
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> 
;
> #Part 5
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> 
> NuF:= proc(n) local W1,W2,w1,w2:
> option remember:
>  
> if n<0 then 
> RETURN (0):
> fi:
> 
> if n=0 then
> RETURN(1):
> fi:
>  
> W1:= NuF(n-1);
> W2:= NuF(n-2);
>  
> W1+W2:
> end:
> #check equal
;
> evalb(seq(nops(F(n)),n=0..10)=seq(NuF(n),n=0..10));
true
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> NuF(1000);
70330367711422815821835254877183549770181269836358732742604905087154537118196933579742249494562611733487750449241765991088186363265450223647106012053374121273867339111198139373125598767690091902245245323403501
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> #nops(F(1000))
;
> #this gonna be a large calculation which waste too much resources, so Maple complains.
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