Advanced Search

acer

32348 Reputation

29 Badges

19 years, 329 days
Ontario, Canada

Social Networks and Content at Maplesoft.com

Contact acer

MaplePrimes Activity


These are replies submitted by acer

pardon...

acer 32348
August 27 2020
0 0

@dharr I suspect that he already was able to create the posted plot, and wanted it to differ from that.

 

ok...

acer 32348
August 27 2020
0 0

@Reshu Gupta That was not at all clear in your original question.

The following both display with literal Nu instead of the capital Greek letter, in upright roman, and the a appears as a subscript.

   labels=[eta,Typesetting:-mo("Nu")[a](eta)]

   labels=[eta,`#mo("Nu");`[a](eta)]

For example,

plot(axes=box,gridlines,size=[375,300],
     labelfont=["Tahoma",bold,14],
     labeldirections=[horizontal,vertical],
     labels=[eta,`#mo("Nu");`[a](eta)]);

If you want the Nu in italics then you could do it like this,

    labels=[eta,`#mrow(mi("N"),mi("u"));`[a](eta)]

For example,

plot(axes=box,gridlines,size=[375,300],
     labelfont=["Tahoma",bold,14],
     labeldirections=[horizontal,vertical],
     labels=[eta,`#mrow(mi("N"),mi("u"));`[a](eta)]);

documentation...

acer 32348
August 27 2020
0 0

@animeplot A good place to start is by reading the Help (documentation) that comes bundled inside Maple.

You could look at the Help page for topic,
   DocumentTools,Tabulate

Or you could look at Examples on the Embedded Components Help pages, and in particular,
   PlotComponent
   MathContainer
and you could even call you first worksheet and push the results into those components using,
   ButtonComponent

 

f(0)?...

acer 32348
August 25 2020
0 0

What is the rationale for specifying f(0) as 0?

Why that value, instead of, oh, say, 0.0031 or 0.003043455 or something else?

Is there something you expect to happen at f(1)? Some value such as, say, oh, 0.007 that f might approach?

I am just curious about the origin of the problem.

Why did you force method=ck45?

ps. It's not helpful to post only an image of the code. You can upload and attach your worksheet using the green up-arrow in the Mapleprimes editor.

I changed your query from a Post to a Question.

what condition number?...

acer 32348
August 21 2020
0 0

@petit loup How did you compute "the" condition number?

(What computations did you do, altogether, that is also to the point.)

blank portions...

acer 32348
August 21 2020
0 0

Why does your Question (and followup Reply to vv) contain various blank portions? Are those supposed to contain missing details?

sigh...

acer 32348
August 21 2020
0 0

@mary120 Why did you not mention before that you are using Maple 11!  That was released thirteeen years ago, and is now 13 major releases out of date.

You could try one of these options:

   legend=('n[`0p`]'/'n[`0i`]'=0.1)

or,

   legend=`#mfrac(msub(mi("n"),mi("0p")),msub(mi("n"),mi("0i")))`

   

legend...

acer 32348
August 20 2020
0 0

@mary120 You could use options such as,

  legend=typeset(n__0p/n__0n=0.1), legendstyle=[font=[Helvetica,10]]

where you adjust the font name as size as desired. Note that I used a double-underscore to get the subscripting.

comments...

acer 32348
August 19 2020
0 0

@faizfrhn Please don't submit the question more than once.

You've incorrectly used square-brackets [...] instead of round-brackets (...) as delimiters in your expression for eq3.

Also, did you mean Pi/4 instead of 90? Maple's trig sommands work with radians.

Also, in the term sin(((beta + 90 + delta) - beta) + phi)) there is a +beta added to a -beta. Is that intentional, or did you mean something else?

 

followup question...

acer 32348
August 18 2020
0 0

[edited] Put your followup questions as Comments here, instead of in a separate Question thread.

more programmatic...

acer 32348
August 18 2020
0 0

Here is something more programmatic (ie. hopefully more systematic and less ad hoc). I'm trying to keep in mind the OP's mention of pulling out the H (akin to factoring in some sense).

I expect there is room for improvement. I tried to make it not expand terms. I didn't stress-test it.

The main idea is to not have to determine visually (and specifiy manually) which multiplicative term to adjust, or by what power of H.

At the end, for fun, it's also used to pull out other "factors".

> 

restart;
> 

eq := W__1 + W__2 = -sin(-beta + alpha)*((H^2 - h^2)*gamma
                    + h^2*psi)/(2*sin(beta)*sin(alpha));

W__1+W__2 = -(1/2)*sin(-beta+alpha)*((H^2-h^2)*gamma+h^2*psi)/(sin(beta)*sin(alpha))

> 

targ := W__1 + W__2 = -H^2*sin(-beta + alpha)*((1 - h^2/H^2)*gamma
                    + h^2*psi/H^2)/(2*sin(beta)*sin(alpha));
 

W__1+W__2 = -(1/2)*H^2*sin(-beta+alpha)*((1-h^2/H^2)*gamma+h^2*psi/H^2)/(sin(beta)*sin(alpha))

> 

F := proc(ee::`*`,T::name)
  local a,c,count,d,o,p,P,q;
  (a,o) := selectremove(type,[op(ee)],
                    And(`+`,polynom(anything,T),
                        satisfies(p->degree(p,T)>0)));
  count:=0; P:=1;
  if nops(a)>0 then
    for p in a do
      d := degree(p,T); count := count+d;
      (c,q) := selectremove(type,[op(p)],`*`);
      P := P*`+`(op(map(`/`,q,T^d)),map(u->F(u,T)/T^d,c)[]);
    end do;
  end if;
  `*`(P,T^count,op(o));
end proc:
> 

 

> 

answer := lhs(eq) = F(rhs(eq), H);

W__1+W__2 = -(1/2)*H^2*sin(-beta+alpha)*((1-h^2/H^2)*gamma+h^2*psi/H^2)/(sin(beta)*sin(alpha))

> 

evalb(simplify(answer-eq)), evalb(answer=targ);

true, true

> 

# for fun...
lhs(eq) = F(rhs(eq), h); evalb(simplify(%-eq));
lhs(eq) = F(rhs(eq), gamma); evalb(simplify(%-eq));
lhs(eq) = F(rhs(eq), psi); evalb(simplify(%-eq));

W__1+W__2 = -(1/2)*((H^2/h^2-1)*gamma+psi)*h^2*sin(-beta+alpha)/(sin(beta)*sin(alpha))

true

W__1+W__2 = -(1/2)*(H^2-h^2+h^2*psi/gamma)*gamma*sin(-beta+alpha)/(sin(beta)*sin(alpha))

true

W__1+W__2 = -(1/2)*((H^2-h^2)*gamma/psi+h^2)*psi*sin(-beta+alpha)/(sin(beta)*sin(alpha))

true

> 

 

Download manipulation.mw

 

ok...

acer 32348
August 15 2020
0 0

@nguyenhuyenag I never claimed that it would work for every other problem you concocted. That's why I wrote particular in italics.

If you are trying to ask something else, something more general, then ask it clearly.

another...

acer 32348
August 15 2020
0 0

In a related way that happens to work quickly for this particular example (but without reliance on identify),

> 

restart;
> 

L := {m[4]+4*m[7]+m[10]+m[13]+m[16]+m[19]+m[22] = 2*sqrt(2)+7,
 m[15]+3*m[18]+11*m[21]+m[6]+9*m[12]+2*m[3]-2*sqrt(2)*m[18]+6*sqrt(2)*m[21]
 -4*sqrt(2)*m[12]+m[24] = 2*sqrt(2)+61, -4*sqrt(2)*m[14]+6*m[14]+m[17]
 +11*m[20]+m[2]+4*m[5]+18*m[8]+6*sqrt(2)*m[20]-8*sqrt(2)*m[8]+m[23]
 = 2*sqrt(2)+34, m[27]-2*sqrt(2)*m[19]+4*sqrt(2)*m[7]+2*sqrt(2)*m[13]
 -2*m[16]+m[17]-6*m[19]-4*m[4]+m[5]+m[20]-16*m[7]+4*m[8]+m[11]-4*m[13]
 +m[14] = 6*sqrt(2)-6, m[28]+2*sqrt(2)*m[19]-4*sqrt(2)*m[10]-2*sqrt(2)*m[16]
 +m[15]+2*m[16]+m[18]+2*m[4]+m[6]+6*m[19]+m[21]+4*m[9]+2*m[10]+m[12]-2*m[13]
  = 6*sqrt(2)+21, m[25]+6*sqrt(2)*m[19]-2*sqrt(2)*m[20]-8*sqrt(2)*m[7]
 +4*sqrt(2)*m[8]-4*sqrt(2)*m[13]+2*sqrt(2)*m[14]+6*m[13]-4*m[14]+m[16]
 -2*m[17]+m[1]+4*m[4]+11*m[19]-6*m[20]-4*m[5]+18*m[7]-16*m[8] = 6*sqrt(2)-33,
 m[26]+6*sqrt(2)*m[19]+2*sqrt(2)*m[21]-4*sqrt(2)*m[10]-4*sqrt(2)*m[12]
 -2*sqrt(2)*m[16]-2*sqrt(2)*m[18]+m[13]-2*m[15]+3*m[16]+2*m[18]+2*m[1]
 +11*m[19]+6*m[21]+m[4]+2*m[6]+9*m[10]+2*m[12] = 6*sqrt(2)-33, m[29]
 +2*sqrt(2)*m[18]+6*sqrt(2)*m[20]-12*sqrt(2)*m[21]-2*sqrt(2)*m[3]
 -4*sqrt(2)*m[11]-2*sqrt(2)*m[15]-2*sqrt(2)*m[17]+m[14]+4*m[15]+3*m[17]
 -2*m[18]+2*m[2]+11*m[20]-22*m[21]+m[5]-4*m[6]+9*m[11] = 6*sqrt(2)-6, m[30]
 -12*sqrt(2)*m[20]+6*sqrt(2)*m[21]-2*sqrt(2)*m[2]-8*sqrt(2)*m[9]
 -2*sqrt(2)*m[14]-4*sqrt(2)*m[15]+2*sqrt(2)*m[17]+4*m[14]+6*m[15]-2*m[17]
 +m[18]+m[3]-22*m[20]+11*m[21]-4*m[5]+4*m[6]+18*m[9] = 6*sqrt(2)+21,
 -4*m[4]+2*m[5]+2*m[17]-2*m[18]-22*m[19]+6*m[20]-6*m[21]-2*m[16]-4*m[15]
 +m[31]-4*m[6]-16*m[9]+2*m[11]+4*m[13]-2*m[14]-2*sqrt(2)*m[1]+4*sqrt(2)*m[9]
 -2*sqrt(2)*m[17]-4*sqrt(2)*m[11]+2*sqrt(2)*m[15]+2*sqrt(2)*m[16]
 -12*sqrt(2)*m[19]-2*sqrt(2)*m[13]+2*sqrt(2)*m[20]-2*sqrt(2)*m[21]
 = 12*sqrt(2)-120}:
> 

S:=Optimization:-LPSolve(1,L,map(u->u=0..infinity,
                                 indets(L,And(name,Not(constant))))[])[2]:
> 

C2:=solve(eval(L,lhs~(select(type,S,name=0.0))=~0))
    union (lhs~(select(type,{S[]},name=0.0))=~0);

{m[1] = 0, m[2] = 0, m[3] = (261/7)*2^(1/2)-309/7, m[4] = 0, m[5] = 0, m[6] = 0, m[7] = 219/98-(61/49)*2^(1/2), m[8] = -22/7+(23/7)*2^(1/2), m[9] = -(51/14)*2^(1/2)+114/7, m[10] = -95/49+(342/49)*2^(1/2), m[11] = 0, m[12] = -(8/7)*2^(1/2)+109/7, m[13] = 0, m[14] = 0, m[15] = 0, m[16] = 0, m[17] = 0, m[18] = 0, m[19] = 0, m[20] = 366/7-36*2^(1/2), m[21] = 0, m[22] = 0, m[23] = 0, m[24] = 0, m[25] = 0, m[26] = 0, m[27] = 0, m[28] = 0, m[29] = 0, m[30] = 0, m[31] = 0}

> 

normal(eval(map(lhs-rhs,L),C2));

{0}

> 

 

Download LPSolve_ex2e.mw

others...

acer 32348
August 15 2020
0 0

@abdulganiy There are many more ways than this. Here are a few of them.

> 

restart;
plot(ln(1+sin(Pi*x)), x = 0 .. 1, legend = numerical,
     style = point, symbol = box, color = blue,
     symbolsize = 15, numpoints = 8, adaptive=false);

> 

restart;
f:=unapply(ln(1+sin(Pi*x)),x):
V:=Vector(8,i->0+(i-1)*(1-0)/(8-1)):
plot(<V|f~(V)>, legend = numerical, symbolsize = 15,
     style = point, symbol = box, color = blue);

> 

restart;
f:=unapply(ln(1+sin(Pi*x)),x):
N,a,b := 8,0,1:
V:=Vector(N,i->a+(i-1)*(b-a)/(N-1)):
plot(<V|f~(V)>, legend = numerical, symbolsize = 15,
     style = point, symbol = box, color = blue);

> 

restart;
f:=unapply(ln(1+sin(Pi*x)),x):
V:=<[seq(0..1,(1-0)/(8-1))]>:
plot(<V|f~(V)>, legend = numerical, symbolsize = 15,
     style = point, symbol = box, color = blue);

> 

restart;
N,a,b := 8,0,1:
f:=unapply(ln(1+sin(Pi*x)),x):
V:=<[seq(a..b,(b-a)/(N-1))]>:
plots:-pointplot(<V|f~(V)>, legend = numerical, symbolsize = 15,
                 symbol = box, color = blue);

> 

 

Download ptplot_misc.mw

 

sure...

acer 32348
August 15 2020
0 0

@nguyenhuyenag 

> 

restart;
> 

L := {m[4]+4*m[7]+m[10]+m[13]+m[16]+m[19]+m[22] = 2*sqrt(2)+7,
 m[15]+3*m[18]+11*m[21]+m[6]+9*m[12]+2*m[3]-2*sqrt(2)*m[18]+6*sqrt(2)*m[21]
 -4*sqrt(2)*m[12]+m[24] = 2*sqrt(2)+61, -4*sqrt(2)*m[14]+6*m[14]+m[17]
 +11*m[20]+m[2]+4*m[5]+18*m[8]+6*sqrt(2)*m[20]-8*sqrt(2)*m[8]+m[23]
 = 2*sqrt(2)+34, m[27]-2*sqrt(2)*m[19]+4*sqrt(2)*m[7]+2*sqrt(2)*m[13]
 -2*m[16]+m[17]-6*m[19]-4*m[4]+m[5]+m[20]-16*m[7]+4*m[8]+m[11]-4*m[13]
 +m[14] = 6*sqrt(2)-6, m[28]+2*sqrt(2)*m[19]-4*sqrt(2)*m[10]-2*sqrt(2)*m[16]
 +m[15]+2*m[16]+m[18]+2*m[4]+m[6]+6*m[19]+m[21]+4*m[9]+2*m[10]+m[12]-2*m[13]
  = 6*sqrt(2)+21, m[25]+6*sqrt(2)*m[19]-2*sqrt(2)*m[20]-8*sqrt(2)*m[7]
 +4*sqrt(2)*m[8]-4*sqrt(2)*m[13]+2*sqrt(2)*m[14]+6*m[13]-4*m[14]+m[16]
 -2*m[17]+m[1]+4*m[4]+11*m[19]-6*m[20]-4*m[5]+18*m[7]-16*m[8] = 6*sqrt(2)-33,
 m[26]+6*sqrt(2)*m[19]+2*sqrt(2)*m[21]-4*sqrt(2)*m[10]-4*sqrt(2)*m[12]
 -2*sqrt(2)*m[16]-2*sqrt(2)*m[18]+m[13]-2*m[15]+3*m[16]+2*m[18]+2*m[1]
 +11*m[19]+6*m[21]+m[4]+2*m[6]+9*m[10]+2*m[12] = 6*sqrt(2)-33, m[29]
 +2*sqrt(2)*m[18]+6*sqrt(2)*m[20]-12*sqrt(2)*m[21]-2*sqrt(2)*m[3]
 -4*sqrt(2)*m[11]-2*sqrt(2)*m[15]-2*sqrt(2)*m[17]+m[14]+4*m[15]+3*m[17]
 -2*m[18]+2*m[2]+11*m[20]-22*m[21]+m[5]-4*m[6]+9*m[11] = 6*sqrt(2)-6, m[30]
 -12*sqrt(2)*m[20]+6*sqrt(2)*m[21]-2*sqrt(2)*m[2]-8*sqrt(2)*m[9]
 -2*sqrt(2)*m[14]-4*sqrt(2)*m[15]+2*sqrt(2)*m[17]+4*m[14]+6*m[15]-2*m[17]
 +m[18]+m[3]-22*m[20]+11*m[21]-4*m[5]+4*m[6]+18*m[9] = 6*sqrt(2)+21,
 -4*m[4]+2*m[5]+2*m[17]-2*m[18]-22*m[19]+6*m[20]-6*m[21]-2*m[16]-4*m[15]
 +m[31]-4*m[6]-16*m[9]+2*m[11]+4*m[13]-2*m[14]-2*sqrt(2)*m[1]+4*sqrt(2)*m[9]
 -2*sqrt(2)*m[17]-4*sqrt(2)*m[11]+2*sqrt(2)*m[15]+2*sqrt(2)*m[16]
 -12*sqrt(2)*m[19]-2*sqrt(2)*m[13]+2*sqrt(2)*m[20]-2*sqrt(2)*m[21]
 = 12*sqrt(2)-120}:
> 

Digits:=60:
S:=Optimization:-LPSolve(1,L,map(u->u=0..infinity,
                                 indets(L,And(name,Not(constant))))[])[2]:
Digits:=15:
> 

C:=identify(S);

[m[1] = 0, m[2] = 0, m[3] = -309/7+(261/7)*2^(1/2), m[4] = 0, m[5] = 0, m[6] = 0, m[7] = 219/98-(61/49)*2^(1/2), m[8] = -22/7+(23/7)*2^(1/2), m[9] = 114/7-(51/14)*2^(1/2), m[10] = -95/49+(342/49)*2^(1/2), m[11] = 0, m[12] = 109/7-(8/7)*2^(1/2), m[13] = 0, m[14] = 0, m[15] = 0, m[16] = 0, m[17] = 0, m[18] = 0, m[19] = 0, m[20] = 366/7-36*2^(1/2), m[21] = 0, m[22] = 0, m[23] = 0, m[24] = 0, m[25] = 0, m[26] = 0, m[27] = 0, m[28] = 0, m[29] = 0, m[30] = 0, m[31] = 0]

> 

normal(eval(map(lhs-rhs,L),C));

{0}

> 

 

Download LPSolve_ex2.mw

First 160 161 162 163 164 165 166 Last Page 162 of 592