acer

legend...

Answered: acer 32333

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...

Answered: acer 32333

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...

Answered: acer 32333

August 18 2020

0 0

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

more programmatic...

Answered: acer 32333

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^2psi)/(2sin(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^2sin(-beta + alpha)((1 - h^2/H^2)gamma + h^2psi/H^2)/(2sin(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);

>	# 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))

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

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

>

Download manipulation.mw

ok...

Answered: acer 32333

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...

Answered: acer 32333

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));

>

Download LPSolve_ex2e.mw

others...

Answered: acer 32333

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(Pix)),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(Pix)),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...

Answered: acer 32333

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);

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

>

Download LPSolve_ex2.mw

sigh...

Answered: acer 32333

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...

Answered: acer 32333

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...

Answered: acer 32333

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...

Answered: acer 32333

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...

Answered: acer 32333

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");

printlevel...

Answered: acer 32333

August 12 2020

0 0

@nm Debugging your example is easier at first, since one can trace or stopat the signum command, starting with argument 1/sin(x).

That leads to Re(x) under the assumption. But Re is a kernel builtin, so showstat and stopat appear to be a dead end. However, some kernel builtins will also call back out to Library commands. By setting printlevel:=999: you can tell how the kernel calls back into the Library, for this example, and continue on with Library-side debugging techniques.

It gets a little awkward, as you have to also dispel the chaff after setting printlevel:=1: again. But it's workable.

So, I traced signum to find that Re(x) assuming x::{} returned 0. Then I used higher printlevel to see (fortunately) where the kernel happened to call back into the Library.

for fun...

Answered: acer 32333

August 12 2020

0 0

Your original question was about why the (accidental) use of assuming {} produced the division by zero error, since you had already corrected your syntax for using `assuming` in prefix form.

But for fun, a few other ways to get the more compact tan form result,

restart;

u1 := -ln(csc(x)-cot(x));

                   u1 := -ln(csc(x) - cot(x))

subs(X=x/2,convert(simplify(convert(subs(x=2*X,u1),tan)),tan));

                            /   /1  \\
                         -ln|tan|- x||
                            \   \2  //

[sin(x)=trigsubs(sin(x),trigidentity="Double Angle")[1]]:
convert(simplify(subs(%,simplify(u1))),tan);


                            /   /1  \\
                         -ln|tan|- x||
                            \   \2  //

[csc(x)=trigsubs(csc(x),trigidentity="Double Angle")[1],
 cot(x)=trigsubs(cot(x),trigidentity="Double Angle")[1]]:
convert(simplify(subs(%,u1)),tan);

                            /   /1  \\
                         -ln|tan|- x||
                            \   \2  //

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more programmatic...

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others...

sure...

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verboseproc...

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G...

printlevel...

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