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acer

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20 years, 331 days
Ontario, Canada

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blank portions...

acer 33400
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 33400
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  That was released thirteeen years ago, and is now 13 major releases out of date.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 33400
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 33400
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 33400
August 18 2020
0 0

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

more programmatic...

acer 33400
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 33400
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 33400
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 33400
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 33400
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

sigh...

acer 33400
August 14 2020
0 0

@Carl Love That is very unfortunate programming of the Java GUI.

(I spend so much time in the commandline interface that I reflexively think of its sane behaviour as "the normal manner".)

I will submit a bug report.

verboseproc...

acer 33400
August 14 2020
0 0

@Carl Love I agree with what you've written, except that I don't see it respecting interface(verboseproc) in the usual manner.

another way...

acer 33400
August 13 2020
0 0

@pik1432 FYI, two solutions for the new system can also be found (quickly) as follows:

RootFinding:-Isolate(evalf[100]((lhs-rhs)~([f1,f2,f3,f4,f5,f6,f7,f8,f9,f10])),
                     [vars[]],maxroots=3,digits=20);

Q_ac_20200811_ac2.mw

details...

acer 33400
August 12 2020
0 0

You could start by providing us with details of what you did to obtain this.

You can upload and attach a Worksheet to a Comment or Question here. Use the green up-arrow in the Mapleprimes editor.

G...

acer 33400
August 12 2020
0 0

@Reshu Gupta 

G:=x -> -1.50000000000*x - 0.0170454545454*(x^4 + 17.6721666667*x^2
 - 5.11042142857)*x - 0.0197950153310*exp(-4.47213595500*x)
 + 0.0197950153310*exp(4.47213595500*x)
 + 6.62030572935*10^(-13)*(-92400.*x^4 - 82645.0724484*x^3 + 526680.*x^2
  + 241736.836912*x + 27027.)*exp(-4.47213595500*x + 4.47213595500)
  + 6.62030572935*10^(-13)*(92400.*x^4 - 82645.0724484*x^3 - 526680.*x^2
  + 241736.836912*x - 27027.)*exp(4.47213595500*x + 4.47213595500):
V:=Vector([seq(G(x),x=[seq(-1..1,0.1)])]):
P1:=plot(<<[seq(-1..1,0.1)]>|V>,style=point):
P2:=plot(G,-1..1):
plots:-display(P1,P2);
ExcelTools:-Export(V, "foo.xls");
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