1 / 26

> f:= n -> [seq([n-k, n-k], k=0..n)]; f := n -> [seq([n - k, n - k], k = 0 .. n)]

> f:= n -> [seq([n-k, n-k], k=0..n)]; f := n -> [seq([n - k, n - k], k = 0 .. n)] > f(6); [[6, 6], [5, 5], [4, 4], [3, 3], [2, 2], [1, 1], [0, 0]] > h:= n -> [seq([n-k, k], k=0..n)]; h := n -> [seq([n - k, k], k = 0 .. n)] > h(6);

merle
Download Presentation

> f:= n -> [seq([n-k, n-k], k=0..n)]; f := n -> [seq([n - k, n - k], k = 0 .. n)]

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. > f:= n -> [seq([n-k, n-k], k=0..n)]; f := n -> [seq([n - k, n - k], k = 0 .. n)] > f(6); [[6, 6], [5, 5], [4, 4], [3, 3], [2, 2], [1, 1], [0, 0]] > h:= n -> [seq([n-k, k], k=0..n)]; h := n -> [seq([n - k, k], k = 0 .. n)] > h(6); [[6, 0], [5, 1], [4, 2], [3, 3], [2, 4], [1, 5], [0, 6]] > {$-4..4}; {-4, -3, -2, -1, 0, 1, 2, 3, 4} > h:= n ->[{$0..k}, k = 0..n]; h := n -> [{`$`(0 .. k)}, k = 0 .. n]

  2. > h(5); [{$(0 .. k)}, k = 0 .. 5] > g := x -> {$0..x}; > g(5); g := x -> {`$`(0 .. x)} {0, 1, 2, 3, 4, 5} > h:= n ->[g(n)]; h := n -> [g(n)] > h(6); [{0, 1, 2, 3, 4, 5, 6}] > h:= n ->[g(k),k = 0..n ]; h := n -> [g(k), k = 0 .. n]

  3. > h(6); [{$(0 .. k)}, k = 0 .. 6] > h:= n ->[{$0..k},k = 0..n]; h := n -> [{`$`(0 .. k)}, k = 0 .. n] > h(6); [{$(0 .. k)}, k = 0 .. 6] > [$-4..4]; [-4, -3, -2, -1, 0, 1, 2, 3, 4] > h := n -> [$ 0..n]; h := n -> [`$`(0 .. n)] > h(6); [0, 1, 2, 3, 4, 5, 6]

  4. > {$0..4}; {0, 1, 2, 3, 4} > {$0..0}; {0} > {$0..1}; {0, 1} > {$0..k}; {$(0 .. k)} > A := $1..12; A := 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 > h := n -> [seq({$0..k}, k=1..n)]; h := n -> [seq({`$`(0 .. k)}, k = 1 .. n)]

  5. > h(6); [{0, 1}, {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 5, 6}] > g:= x ->{$0..x}; g := x -> {`$`(0 .. x)} > g(5); {0, 1, 2, 3, 4, 5} > s:n ->[seq([g(k)], k = 0..n)]; n -> [seq([g(k)], k = 0 .. n)] > s(5); s(5) > map(abs, [-1, 3, -32, 4]); [1, 3, 32, 4] > map(abs, {1, -1, 2, -2}); {1, 2} > map(abs, [1, -1, 2, -2]); [1, 1, 2, 2] >map(f, (1, 2, 3)); 6 > map(f, {1, 2, 3}, 0, 0); {1, 4, 9}

  6. The map2 function is similar to map, except that for each operand of expr, arg1 is passed as the first argument to fcn, the operand of expr is passed as the second argument, and arg3, ..., argn are passed as the third, ..., nth arguments. • > map2(k, m, {a,b,c}); • {k(m, a), k(m, b), k(m, c)} • 2.3 • A := [a, a, b, b, b]; • B := [b, c]; • hd := x -> x[1]; // all in section 1 • > hd(A); • > map(hd,[a, b], [a, b, c], [b, d]); • [a[1], b[1]] • > map(hd,[a, b]); • [a[1], b[1]]

  7. C:=[a, b]; C := [a, b] > map(hd,C); [a[1], b[1]] > hd(C); a > map(hd,C); [a[1], b[1]] > map(hd,([a, b])); [a[1], b[1]] > map(hd,{[a, b]}); {a} > map(hd,[[a, b]]); [a] >

  8. map(tl2,[[a, b]]); # again in section 1 page 14 [[b]] > map(tl2,[[a, b]]); [[b]] > map(tl2,[a, b]); [a[2 .. 1], b[2 .. 1]] > map(tl2,[[a, b,c,d]]); [[b, c, d]] > map(tl2,[[a, b,c,d],B]);

  9. 2.3 • > C:=[a, b, c,d]; • C := [a, b, c, d] • tl2 := x -> x[2..nops(x)]; • tl2 := x -> x[2 .. nops(x)] • catLists := (x, y) -> [op(x), op(y)]; • catLists := (x, y) -> [op(x), op(y)] • > catLists([1,2,3,4],[3,4,5]); • [1, 2, 3, 4, 3, 4, 5]

  10. > • > catLists(hd(C), tl2(C)); • [a, b, c, d] • cons := catLists; • cons := catLists • > g:=x -> (hd(x), tl2(x)); • g := x -> (hd(x), tl2(x)) • > g([1,2,3,4]); • 1, [2, 3, 4] • > h := cons@g; • h := catLists@g • > h([1,2,3,4]); • [1, 2, 3, 4] • > evalb(h(C) = C); • true

  11. 2.8 • f:=x->1/(x+1); • 1 • f := x -> ----- • x + 1 • solve(f(x) = f(y), x); • y • > solve(f(x) = y, x); • -1 + y • - ------ • y • > f(%); • 1 • ------------ • -1 + y • - ------ + 1 • y

  12. > simplify(%); • y

  13. 3.1.2 > tl := x ->x[2..nops(x)]; > last := x -> if nops(x) = 1 then x else last(tl(x)) fi;

  14. 3.7 > cons := (x, S) -> [x, op(S)]; cons := (x, S) -> [x, op(S)] > cons(b,[a, b, c]); [b, a, b, c] > cons(d,[a, b, c]); [d, a, b, c]

  15. > concat := (x, y) -> if x = [ ] then y else cons(hd(x), concat(tl(x), y)) fi; concat := proc(x, y) option operator, arrow; if x = [] then y else cons(hd(x), concat(tl(x), y)) end if end proc > trace(concat); concat

  16. > concat([a, b, c], [d, e]); {--> enter concat, args = [a, b, c], [d, e] {--> enter concat, args = [b, c], [d, e] {--> enter concat, args = [c], [d, e] {--> enter concat, args = [], [d, e] <-- exit concat (now in concat) = [d, e]} <-- exit concat (now in concat) = [c, d, e]} <-- exit concat (now in concat) = [b, c, d, e]} <-- exit concat (now at top level) = [a, b, c, d, e]}

  17. 3.7.1 Recursive way hd:= x -> x[1]; hd := x -> x[1] > tl := x ->x[2..nops(x)]; tl := x -> x[2 .. nops(x)] > subset:=(x,y)->if x = {} then true > else member(hd(x),y) and subset (tl(x),y) > fi; > > A := {a,b,c,d,e}; A := {a, b, c, d, e} > B := {e,z}; B := {e, z} > C:= {a,b}; C := {a, b}

  18. > B := {e,z}; B := {e, z} > C:= {a,b}; C := {a, b} > subset(C,A); true > subset(B,A); false > subset({},A); true > subset(A,C); false

  19. 3.7.1 Non recursive version subset:=(x,y)->if `intersect`(x,y) =x then print(yes) else print(no)fi; subset := proc(x, y) option operator, arrow; if x intersect y = x then print(yes) else print(no) end if end proc > subset({d,e},{a,b,c}); no > subset({a,b},{a,b,c}); yes

  20. 3.7.2 • subset1:=(x,y)->if x = {} then true else if evalb(hd(x) in y) then subset1(tl(x),y) else false fi fi; • power:=x->if x = {} then {{}} • else power(tl(x)) union map(`union`,power(tl(x)),{hd(x)})fi;

  21. 5.1.4.b • > sum(a[n+2]*x^n, n = 0..k); • > sum(a[n]*x^(n-2), n = 2..k+2); • > simplify(sum(a[n+2]*x^n, n = 0..k)); • > evalb(simplify(sum(a[n+2]*x^n, n = 0..k))= simplify(sum(a[n]*x^(n-2), n = 2..k+2))); • False; • > sum('a[n+2]*x^n','n'=0..4); • > a[2]+a[3]*x+a[4]*x^2+a[5]*x^3+a[6]*x^4 • > sum('a[n]*x^(n-2)','n'=2..6); • > a[2]+a[3]*x+a[4]*x^2+a[5]*x^3+a[6]*x^4 • > evalb(sum('a[n+2]*x^n','n'=0..4) = sum('a[n]*x^(n-2)','n'=2..6)); • true

  22. > evalb(sum('a[n+2]*x^n','n'=0..k) = sum('a[n]*x^(n-2)','n'=2..(k+2) )); false. WHY????????????

  23. 5.2 permute({a, b, c}); [[a, b, c], [a, c, b], [b, a, c], [b, c, a], [c, a, b], [c, b, a]] > > permute([r, a, d, a, r]); [[r, a, d, a, r], [r, a, d, r, a], [r, a, a, d, r], [r, a, a, r, d], [r, a, r, d, a], [r, a, r, a, d], [r, d, a, a, r], [r, d, a, r, a], [r, d, r, a, a], [r, r, a, d, a], [r, r, a, a, d], [r, r, d, a, a], [a, r, d, a, r],

  24. [a, r, d, r, a], [a, r, a, d, r], [a, r, a, r, d], [a, r, r, d, a], [a, r, r, a, d], [a, d, r, a, r], [a, d, r, r, a], [a, d, a, r, r], [a, a, r, d, r], [a, a, r, r, d], [a, a, d, r, r], [d, r, a, a, r], [d, r, a, r, a], [d, r, r, a, a], [d, a, r, a, r], [d, a, r, r, a], [d, a, a, r, r]]

  25. 5.2.3 n:=2;numbcomb(n,n/2); n := 2 > n:=3;numbcomb(n,n/2); n := 3 Error, (in numbcomb) 2nd argument must be an integer > n:=4;numbcomb(n,n/2); n := 4 6 n:=6;numbcomb(n,n/2); n := 6 20 > numbcomb(8,4); 70

  26. 5.3.2 binomial(m, k); binomial(m, k) > m:=6; k:=2; m := 6 k := 2 evalb(binomial(m, k)=binomial(m-1, k)+binomial(m-1, k-1)); true

More Related