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Ontario, Canada

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another way...

acer 32400
February 27 2017
1 3

This is not the most efficient, but is simple to use.
 

NULL

> 

c-s > (w+u-s)*(-P[A]*P[B]+P[B])+P[A]*(p-s);

(w+u-s)*(-P[A]*P[B]+P[B])+P[A]*(p-s) < c-s

> 

(w+u-s)*(-P[A]*P[B]+P[B])+P[A]*(p-s) > c-s;

c-s < (w+u-s)*(-P[A]*P[B]+P[B])+P[A]*(p-s)

> 

c-s > P[A]*P[B]*(p-s);

P[A]*P[B]*(p-s) < c-s

> 

P[A]*P[B]*(p-s) > c-s;

c-s < P[A]*P[B]*(p-s)

> 

F1 := (w+u-s)*(-P[A]*P[B]+P[B])+P[A]*(p-s)-c+s;

(w+u-s)*(-P[A]*P[B]+P[B])+P[A]*(p-s)-c+s

> 

F2 := P[A]*P[B]*(p-s)-c+s;

P[A]*P[B]*(p-s)-c+s

> 

c1 := solve(F1, P[A]);

(s*P[B]-u*P[B]-w*P[B]+c-s)/(s*P[B]-u*P[B]-w*P[B]+p-s)

> 

c2 := solve(F2, P[A]);

(c-s)/(P[B]*(p-s))

> 

wt := 4;

4

2

2

1

7

> 

cc1 := eval(c1, {c = ct, p = pt, s = st, u = ut, w = wt});

(-5*P[B]+1)/(-5*P[B]+6)

> 

cc2 := eval(c2, {c = ct, p = pt, s = st, u = ut, w = wt});

(1/6)/P[B]

> 

CC1 := piecewise(cc1 <= P[B], cc1, undefined)

piecewise((-5*P[B]+1)/(-5*P[B]+6) <= P[B], (-5*P[B]+1)/(-5*P[B]+6), undefined)

> 

CC2 := piecewise(cc2 <= P[B], cc2, undefined)

piecewise((1/6)/P[B] <= P[B], (1/6)/P[B], undefined)

> 

plot({CC1, CC2, P[B]}, P[B] = 0 .. .50, P[A] = 0 .. .50)

NULL

``


 

Download equilibrium_alt.mw

some remarks which might help...

acer 32400
February 27 2017
0 5

(Thanks to vv for Body2).

I think that the comments and a few variants might help explain some things to the OP. (I have removed output, for upload here.)

Download rotate3d.mw

proc3...

acer 32400
February 27 2017
0 3

Bring the multiplication by `s` inside the `mod` call, in the loop in `Elgamal`.

Don't call `proc3` each time you enter the loop in Elgamal`. Instead compute it once at  the start of `Elgamal`, and assign to a local (which you'll use inside the loop). Combined with the above, that brings it down to about 2 seconds, on a fast machine.

Use &^ instead of ^ inside the `mod` in `Elgamal`. (I've told you this more than three times now, in various questions and duplicates of questions you've made recently.) Combined with the above, that brings it down to about 0.2 seconds on a fast machine.


 

> 

restart;
> 

Elgamal := proc (ciphy::list, hkt, p, a, b)
               local i, icdarray, s, p3, q, x;
                 #msolve(a ^ x = b, p);
                 #p3 := subsindets(eval(x, msolve(a ^ x = b, p)),name,0);
                 p3 := proc3(a, b, p);
                 icdarray := Array(1 .. nops(ciphy));
                   for i from 1 to nops(ciphy) do
                   s := ciphy[i];
                   q := `mod`(s / hkt &^ p3, p);
                   icdarray[i] := q;
                   end do;
                   return convert(convert(icdarray,list),bytes);
                  end proc:
> 

proc3 := proc (alpha, beta, p)
                   local k, R, i, j, N, A, t;
               description "baby step giant step procedure";
                 N := floor(sqrt(p-1))+1;
                 A := Array(0 .. N);
                 for j from 0 to N do
                 A[j] := `mod`(alpha&^j, p);
                end do;
          for i from 0 to N do
             t := `mod`( ( beta * alpha &^ (-N*i) ), p);
            for k from 0 to N do
            if t = A[k]
           then return k+N*i;
         end if;
         end do;
           end do;
         end proc:
> 

header := 9681348997:
> 

ciphertext:= [12432485341, 2579085006, 13736574369, 4105371047, 9573017222,  7824534168, 10017411248, 13292180343, 2356887993,
 9573017222, 10017411248, 13765667419, 9795214235, 10017411248, 2801282019, 608404939, 4105371047, 13765667419, 11572790339,
 13765667419, 11765894302, 10017411248, 13765667419, 4549765073, 10017411248, 13736574369, 2579085006, 4549765073, 10017411248,
 4549765073, 13765667419, 2801282019, 830601952, 4105371047, 10017411248, 7824534168, 13765667419, 13736574369, 2801282019,
 7824534168, 10017411248, 830601952, 9573017222, 4327568060, 13765667419, 6076051114, 8268928194, 13292180343, 10017411248,
 7824534168, 386207926, 2801282019, 4105371047, 2579085006, 6076051114, 608404939, 13765667419, 6076051114, 830601952,
 13765667419, 4105371047, 11765894302, 10017411248, 13765667419, 13292180343, 13736574369, 10017411248, 608404939, 10017411248,
 7824534168, 2134690980, 13765667419, 4105371047, 11765894302, 2801282019, 4105371047, 13765667419, 2579085006, 608404939,
 13292180343, 11543697289, 2579085006, 7824534168, 10017411248, 4549765073, 13765667419, 4994159099, 5853854101, 6076051114,
 830601952, 4327568060, 6076051114, 5853854101, 10017411248, 7824534168, 13765667419, 4105371047, 6076051114, 13765667419,
 9573017222, 13292180343, 10017411248, 13765667419, 4105371047, 11765894302, 10017411248, 13765667419, 5853854101, 6076051114,
 7824534168, 4549765073, 13765667419, 11572790339, 13765667419, 4105371047, 11765894302, 2801282019, 4105371047, 13765667419,
 4105371047, 11765894302, 10017411248, 13765667419, 4327568060, 2801282019, 608404939, 4549765073, 13292180343, 13736574369,
 2801282019, 11543697289, 10017411248, 13765667419, 5853854101, 2801282019, 13292180343, 13765667419, 11765894302, 6076051114,
 7824534168, 7824534168, 2579085006, 8268928194, 4327568060, 2134690980, 13765667419, 11543697289, 7824534168, 10017411248,
 13736574369, 2579085006, 11543697289, 2579085006, 4105371047, 6076051114, 9573017222, 13292180343, 2385981043, 13765667419,
 3245676045, 9573017222, 2801282019, 2579085006, 608404939, 4105371047, 6105144164, 13765667419, 5853854101, 11765894302,
 10017411248, 608404939, 13765667419, 9573017222, 13292180343, 10017411248, 4549765073, 13765667419, 4105371047, 6076051114,
 13765667419, 4549765073, 10017411248, 13292180343, 13736574369, 7824534168, 2579085006, 8268928194, 10017411248, 13765667419,
 4105371047, 11765894302, 10017411248, 13765667419, 6076051114, 13736574369, 13736574369, 2801282019, 13292180343, 2579085006,
 6076051114, 608404939, 2801282019, 4327568060, 13765667419, 386207926, 2579085006, 4327568060, 4327568060, 2801282019,
 6298248127, 10017411248, 13765667419, 4105371047, 11765894302, 7824534168, 6076051114, 9573017222, 6298248127, 11765894302,
 13765667419, 5853854101, 11765894302, 2579085006, 13736574369, 11765894302, 13765667419, 4105371047, 11765894302, 10017411248,
 2134690980, 13765667419, 11543697289, 2801282019, 13292180343, 13292180343, 10017411248, 4549765073, 6105144164, 13765667419,
 9795214235, 10017411248, 2801282019, 608404939, 4105371047, 13765667419, 830601952, 10017411248, 386207926, 10017411248,
 7824534168, 11572790339, 7824534168, 2579085006, 4549765073, 4549765073, 10017411248, 608404939, 13765667419, 2801282019,
 608404939, 4549765073, 13765667419, 4105371047, 9573017222, 9795214235, 8268928194, 4327568060, 10017411248, 4549765073,
 6076051114, 5853854101, 608404939, 2385981043, 13765667419, 4994159099, 5853854101, 6076051114, 830601952, 4327568060,
 6076051114, 5853854101, 10017411248, 7824534168, 13765667419, 5853854101, 2801282019, 13292180343, 13765667419, 2801282019,
 13765667419, 4105371047, 6076051114, 9573017222, 7824534168, 2579085006, 13292180343, 4105371047, 6105144164, 13765667419,
 4105371047, 11765894302, 10017411248, 13765667419, 830601952, 2579085006, 7824534168, 13292180343, 4105371047, 13765667419,
 10017411248, 386207926, 10017411248, 7824534168, 13765667419, 13292180343, 10017411248, 10017411248, 608404939, 13765667419,
 6076051114, 608404939, 13765667419, 4105371047, 11765894302, 10017411248, 13765667419, 5438553125, 2579085006, 13292180343,
 13736574369, 5853854101, 6076051114, 7824534168, 4327568060, 4549765073, 2385981043, 13765667419, 4994159099, 6076051114,
 9573017222, 7824534168, 2579085006, 13292180343, 4105371047, 6105144164,13765667419, 8713322220, 2579085006, 608404939,
 13736574369, 10017411248, 5853854101, 2579085006, 608404939, 4549765073, 13765667419, 11765894302, 2801282019, 4549765073,
 13765667419, 4549765073, 10017411248, 13736574369, 2579085006, 4549765073, 10017411248, 4549765073, 6105144164, 13765667419,
 9795214235, 10017411248, 2801282019, 608404939, 4105371047, 13765667419, 8075824231, 2579085006, 4549765073, 2579085006,
 6076051114, 4105371047, 8075824231, 2385981043]:
> 

 

> 

Elgamal( ciphertext, header, 14654455471, 457454, 13954306945);

"Picturesque meant - he decided after careful observation of the scenery that inspired Twoflower to use the word - that the landscape was horribly precipitous. Quaint, when used to describe the occasional village through which they passed, meant fever-ridden and tumbledown. Twoflower was a tourist, the first ever seen on the Discworld. Tourist, Rincewind had decided, meant 'idiot'."

> 

 


 

Download elgamal2.mw

colon dash...

acer 32400
February 26 2017
0 4

Are you asking how you can make sure that you're always invoking the command that is not in the plots package? If so then just call it using the global name, ie.

:-changecoords

s is in eqset...

acer 32400
February 23 2017
0 6

The name `s` appears in eqset. Is that not the same global name as you're trying to use for the do-loop?

listprocedure...

acer 32400
February 16 2017
0 0

When you call dsolve (numeric) you can pass it the additonal option output=listprocedure. If you assign the result to sol then the following allows you to extract the functions individually. Eg,

sF__A := eval(F__A(V), sol):
After which you can call, 
sF__A(0.1e-4);
which should then return the single numeric value, say, HFloat(3.498873118476744e-6).

simplification...

acer 32400
February 15 2017
0 0 
restart:

targ:=(sin(t)*sin(t/n)-cos(t)*cos(t/n)) /( sin(t)*cos(t/n)+cos(t)*sin(t/n));

                         sin(t) sin(t/n) - cos(t) cos(t/n)
                 targ := ---------------------------------
                         sin(t) cos(t/n) + cos(t) sin(t/n)

res:=(cos(t/n)*sin(t/n)-sin(t)*cos(t))/(cos(t/n)^2-cos(t)^2);

                         cos(t/n) sin(t/n) - sin(t) cos(t)
                  res := ---------------------------------
                                       2         2
                               cos(t/n)  - cos(t)

simplify(targ-res);                                                                 

                                        0

normal(expand(trigsubs(numer(combine(res)))[1]
              /trigsubs(denom(combine(res)))[1]));

                        sin(t) sin(t/n) - cos(t) cos(t/n)
                        ---------------------------------
                        sin(t) cos(t/n) + cos(t) sin(t/n)

% - targ;

                                       0

alt:=convert(trigsubs(numer(combine(res)))[1]
             /trigsubs(denom(combine(res)))[1],cot);

                                     t (n + 1)
                         alt := -cot(---------)
                                         n

simplify(targ-alt);

                                       0

delay evaluation, and unapply...

acer 32400
February 15 2017
0 8


 

> 

restart;
> 

with(plots):
with(plottools):
> 

L:=[cos(0.25*t)+0.2*sin(0.25*t),
    sin(0.25*t)-0.2*cos(0.25*t),
    0.0];
> 

ff1:=unapply('display'(['line'([0, 0, 0],L,colour=red,
                               thickness=4)]),
             t):
> 

animate(ff1,[t],t=0..5,frames=100);
> 

animate(display@line,
        [[0,0,0],L,colour=red,thickness=4],
        t=0..5,frames=100);
> 

animate(display,
        ['line'([0,0,0],L,colour=red,thickness=4)],
        t=0..5,frames=100);
> 

ffp:=unapply('display'('point'(L,colour=red,
                               symbolsize=50,
                               symbol=solidsphere)),
             t):
> 

animate(ffp,[t],t=0..5,frames=100);
> 

animate(display@point,
        [L,colour=red,symbolsize=50,
         symbol=solidsphere],
        t=0..5,frames=100);
> 

animate(display,
        ['point'(L,colour=red,symbolsize=50,
                 symbol=solidsphere)],
        t=0..5,frames=100);
> 

 


 

Download delayedevaluation.mw

mod p...

acer 32400
February 10 2017
0 0

I suppose that you might be required to use a loop, or not use a system command like `msolve` for this task.


 

> 

restart;
> 

# With a loop and a table.

F:=proc(p::posint)
     local x,T;
     T:=table([]);
     for x from 0 to p-1 do
       if (x^2 = -1) mod p then
         T[x]:=x;
       end if;
     end do;
     return entries(T,':-nolist');
   end proc:
> 

F(113);

15, 98

> 

# Using `seq` and `if` instead

G:=proc(p::posint)
     seq(`if`(modp(x^2=-1,p),x,NULL),x=0..p-1);
   end proc:
> 

G(113);

15, 98

> 

gen:=proc(i::posint, f)
       local res;
       res:=[f(i)];
       if res=[] then
         return NULL;
       else
         return [i,res];
       end if;
     end proc:
> 

seq(gen(i, F), i=1..20);

[1, [0]], [2, [1]], [5, [2, 3]], [10, [3, 7]], [13, [5, 8]], [17, [4, 13]]

> 

seq(gen(i, G), i=1..20);

[1, [0]], [2, [1]], [5, [2, 3]], [10, [3, 7]], [13, [5, 8]], [17, [4, 13]]

> 

 


 

Download modp.mw

one way...

acer 32400
February 09 2017
0 6

For this example, I got this:

restart;

a:=21*arccos(RootOf(448*_Z^7+192*_Z^6-784*_Z^5-288*_Z^4
                    +392*_Z^3+108*_Z^2-49*_Z-6, index = 2))/Pi:

b:=-(21*I)*ln(RootOf(7*_Z^14+6*_Z^13+6*_Z+7, index = 2))/Pi:

evala(convert(convert(a-b,RootOf),arccos));
                                      0
Or, as it happens, 
simplify(convert(convert(a-b,RootOf),arccos));
                               0

[0,0]...

acer 32400
February 08 2017
0 1

Is your problem that any rows of the data Array which have not yet been filled with data wil make the plots (pointplot, or plot of the fitted curve) get extended down to (at the point [0,0])?

Here's a rough idea. If you want [0,0] to actually be a valid datum then enter the values as say 0.0 instead of exact 0 (the default).

augment.mw

There are other ways to go about it. Eg, perhaps using an empty string as the default fill.

 

DataTable component...

acer 32400
February 07 2017
0 1

I'm not entirely sure what you are trying to do, so this is a guess.

A DataTable component has the name of some rtable (Matrix, say) as one of it's properties. Whenever you edit the entries in the DataTable component the associated Matrix gets the new values, automatically. So a Button's Action code could simply pass the data to the LinearFit command (using data from either the whole Matrix, or just the first N rows of it, etc).

unit_free...

acer 32400
February 07 2017
1 1

@hitstudent If L is a list of inequalities (each with dimensions on the left that match those on the right), then you could try,

map(is,map2(map,convert,combine(L,':-units'),':-unit_free'));

For example,

Diameter[rør] := [273.05*Unit('mm'), 219.08*Unit('mm'),
 168.28*Unit('mm'), 114.3*Unit('mm'),
 273.05*Unit('mm'), 219.08*Unit('mm'),
 1066.8*Unit('mm'), 60.33*Unit('mm'),
 219.08*Unit('mm'), 168.28*Unit('mm'),
 168.28*Unit('mm'), 141.3*Unit('mm'),
 168.28*Unit('mm'), 114.3*Unit('mm'),
 114.3*Unit('mm'), 168.28*Unit('mm'),
 168.28*Unit('mm')]:

tm := 8.982892831*Unit('mm'),
4.189790007*Unit('mm'),.913902969*Unit('mm'),
3.620745836*Unit('mm'),4.482892831*Unit('mm'),
4.189790007*Unit('mm'),8.793627806*Unit('mm'),
3.327643012*Unit('mm'),4.189790007*Unit('mm'),
3.913902969*Unit('mm'),3.913902969*Unit('mm'),
3.767378711*Unit('mm'),3.913902969*Unit('mm'),
3.620745836*Unit('mm'),3.620745836*Unit('mm'),
3.913902969*Unit('mm'),3.913902969*Unit('mm'):

L:=[seq(tm[i] < (1/6)*Diameter[rør][i],
        i = 1 .. min(nops([tm]),nops(Diameter[rør])))]:

map(is,map2(map,convert,combine(L,':-units'),':-unit_free'));
                                                             
   [true, true, true, true, true, true, true, true, true,
    true, true, true, true, true, true, true, true]

something...

acer 32400
February 02 2017
1 7

Here's all that I could recover from one of them. The uploaded file ended in an invalid Output element. I deleted that, and then closed off (in this order) the outstanding opened Input, Group, Presentation-Block, Section, Section, and Worksheet elements.

Bygninger_energibehov.zip

[edited] And here is what I could recover from the other one. Only two sections now. If there was a third, then I could not see it. This one ended with what appeared to be a corrupted Input element (though very large...). I deleted that and it's parent Presentation-Block (then empty) and then closed off a few Sections and the Worksheet element.

Foringsveje_og_indeklina.zip

 

Maple 17...

acer 32400
February 01 2017
0 1

If you are using only Maple 17 (as indicated by your previous question) then you could use the numtheory[mlog] command.

restart;

kernelopts(version);

     Maple 17.02, X86 64 WINDOWS, Sep 5 2013, Build ID 872941

a := 3:
b := 64:
n := 137:

numtheory[mlog](b, a, n);

                            60

Do you specifically want the smallest solution, or all those less than n? Eg.

restart;
a := 5:
b := 64:
n := 1117:
numtheory[mlog](b, a, n);
                              166
raw := eval(x,msolve( a&^x = b, n ));
                         166 + 372 _Z1
cond := isolve( {raw <= n, raw >=0}, _dummy );
                {_Z1 = 0}, {_Z1 = 1}, {_Z1 = 2}
seq(eval(raw, c), c={cond});
                         166, 538, 910
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