Christian Wolinski

MaplePrimes Activity


These are replies submitted by Christian Wolinski

@vv The query is(Q, OrProp(A,B)); is explicitly:
can it be proven that: Q is A is true or Q is A is false.
can it be proven that: Q is B is true or Q is B is false.
All of the above fails and the result follows. OrProp is not part of the lattice and does not discern in any other way.

@vv Why do you post

is(Pi + exp(1), OrProp(rational, irrational));


as ???. The result is very clear and proper.

@Muhammad Usman To fix that replace set by a list in Sol. As the contents of the set vary, its representation varies also and op(i, Sol) does not have the desired effect. Also consider assign(op(Sol)); inplace of the loop.

@mmcdara 

restart:

N   := 3:
P   := 2:

niv := [seq(Z[i], i=1..N)];
f   := Matrix(N^P, P, (i,j) -> `if`(j=P, niv[(i mod N)+1], niv[iquo(i-1,N)+1]));
ds := subs(niv =~ [$0..N-1], f);

vs := [ seq(V__||i, i=1..P)]:
es := unapply( sort( [ seq( mul(vs ^~ [entries(ds[i,..], nolist)]), i=1..N^P) ] ), vs);

ff := convert([ seq(es(entries(f[i,..], nolist)), i=1..N^P) ], Matrix);

R := RootOf(NumberTheory:-CyclotomicPolynomial(N, x), x);
alias(alpha = R);
UnityRoots := map2(op, 1, roots(x^N-1, x, R));

F := evala(subs(niv =~ UnityRoots, ff)) /~ sqrt(N^P);
evala(1/F - subs(R = 1/R, F^+));
convert(%, set);

@mmcdara For the record I have no idea what you actually need here.... :(

The operator you seek is : F ^ *, F ^ %H rather than F ^ +, F ^ %T, indicated by Maple Help pages. So that should be simplify(F^ * . F);

If the above code was ever successfully valuated to a procedure code then please post it in .mw form. Otherwise, know that the above is so badly written it is useless.

Maple 2017.3 gives the correct answer. Perhaps you should try it with a restart?

@ogunmiloro Replace the definitions You gave with:
B[0] := .50; C[0] := .30; DD[0] := .21; E[0] := .14; F[0] := .70; G[0] := .45; H[0] := .14;

Did You initialize B,C,DD,E,F,G,H at 0?

Re is a builtin function. You should not use it as a variable.

Please post source text or maple worksheet.
Which parameter is to vary? Is it phi?
 

  restart;
  with(plots);
  local O;
  P := b*x*cos(phi) + a*y*sin(phi) - a . b = 0;
  Q := a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi) = 0;
  M := op(solve([P, Q], [x, y]));
  X := `&-+`((P)/(sqrt(b^2*cos(phi)^2 + a^2*sin(phi)^2)));
  Y := `&-+`((Q)/(sqrt(b^2*cos(phi)^2 + a^2*sin(phi)^2)));
  (P^2)/(A*(b^2*cos(phi)^2 + a^2*sin(phi)^2))
   + (Q^2)/(B*(b^2*cos(phi)^2 + a^2*sin(phi)^2)) - 1 = 0;
  a := 10;
  b := 7;
  c := sqrt(a^2 - b^2);
  phi := 4/5*Pi;
  Ell := plots:-implicitplot((x^2)/(a^2) + (y^2)/(b^2) - 1 = 0, x = -11 .. 11, 
  y = -8 .. 8, color = grey);
  O := [0, 0];
  M := [a*cos(phi), b*sin(phi)];
  vec := plot([O, M], color = black, thickness = 1);
  P := plots:-implicitplot(P, x = -20 .. 20, y = -20 .. 20, color = aquamarine);
  Q := plots:-implicitplot(Q, x = -20 .. 20, y = -20 .. 20);
  F1 := [(a + b)*cos(phi), (a + b)*sin(phi)];
  F2 := [2*M[1] - F1[1], 2*M[2] - F1[2]];
  F1F2 := plot([F1, F2], color = green, thickness = 3);
  ELL := plots:-implicitplot(((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))^2)/(
  a^2*(b^2*cos(phi)^2 + a^2*sin(phi)^2)) + (
  (a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))^2)/(c^2*cos(phi)^2*(
  b^2*cos(phi)^2 + a^2*sin(phi)^2)) - 1 = 0, x = -20 .. 20, y = -20 .. 20, 
  color = blue, thickness = 3);
  Hyp := plots:-implicitplot(((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))^2)/(
  b^2*(b^2*cos(phi)^2 + a^2*sin(phi)^2)) - (
  (a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))^2)/(c^2*sin(phi)^2*(
  b^2*cos(phi)^2 + a^2*sin(phi)^2)) - 1 = 0, x = -20 .. 20, y = -20 .. 20, 
  color = black);
  dF1 := plottools[disk](F1, 0.3, color = red);
  dF2 := plottools[disk](F2, 0.3, color = red);
  cir1 := plots:-implicitplot(x^2 + y^2 = (a + b)^2, x = -20 .. 20, 
  y = -18 .. 18, color = pink);
  cir2 := plots:-implicitplot(x^2 + y^2 = (a - b)^2, x = -10 .. 10, 
  y = -4 .. 4, color = coral);
  asym1 := plots:-implicitplot((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))/(b)
   + (a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, 
  x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT);
  asym2 := plots:-implicitplot((b*x*cos(phi) + a*y*sin(phi) - `.`(a, b))/(b)
   - (a*x*sin(phi) - b*y*cos(phi) - c^2*sin(phi)*cos(phi))/(c*sin(phi)) = 0, 
  x = -20 .. 20, y = -18 .. 18, color = black, linestyle = DOT);
  tp := plots:-textplot([[M[1], M[2] + 0.8, "M"], [F1[1] - 0.8, F1[2], "F1"], 
  [F2[1] + 0.8, F2[2] + 0.3, "F2"], [5, 15, "axe P"], [8, -10, "axe Q"]]);
  plots:-display(
  [Ell, vec, P, Q, F1F2, cir1, cir2, ELL, Hyp, dF1, dF2, asym1, asym2, tp], 
  scaling = constrained, axes = normal, 
  axis = [gridlines = [1, color = blue]], xtickmarks = 0, ytickmarks = 0, 
  view = [-20 .. 20, -20 .. 20], size = [500, 500]);

@Adam Ledger I think these are trending in recent weeks.

@Rouben Rostamian  It appears somewhere in the procedure returned an expression diff(?, t) is utilised. So diff(?, 1) is an error once t is assigned.

The last output is as expected. If you wanted a sequence of 1s then change the w for loop to:
for w from 1 by 1 to TOTAL do

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