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ok...

acer 32490
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 32490
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 32490
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 32490
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 32490
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 32490
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 32490
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 32490
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 32490
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...

acer 32490
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...

acer 32490
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  //

welcome...

acer 32490
August 11 2020
0 0

@DoingMath2018 You are welcome.

I'm not sure whether there is an example of this in the documentation. I know that Robert Israel has an old note on it here.

I will submit a bug report, suggesting a clarifying example under the plotting Help pages.

f9, f10...

acer 32490
August 11 2020
0 0

@pik1432 I am not sure how you obtained your versions of f9 and f10, but below I have adjusted them. Then I obtain solutions using both the new and the old equations (and check against both for residuals).

I also show how procedures may be constructed from the equations, which each locally raise Digits for their own calculations, which I mentioned earlier.

I also compute an apparant second solution. (One of the solutions is picky about the supplied ranges.)

I don't know precisely why solve is not finding the solution for this reformulation, but I'm not sure that it matters so much as fsolve can be used.

> 

restart;
> 

TrainLoad := -10*10^6*(cos(convert(40*degrees, radians))+I*sin(convert(40*degrees, radians)));
#evalf(TrainLoad, 7);

-10000000*cos((2/9)*Pi)-(10000000*I)*sin((2/9)*Pi)

> 

f10 := imV[t]*(reIx[c1] - reIx[c2]) + reV[t]*(imIx[c1] - imIx[c2]) - 10000000*sin((2*Pi)/9) = 0;

imV[t]*(reIx[c1]-reIx[c2])+reV[t]*(imIx[c1]-imIx[c2])-10000000*sin((2/9)*Pi) = 0

> 

expand(f10);

imV[t]*reIx[c1]-imV[t]*reIx[c2]+reV[t]*imIx[c1]-reV[t]*imIx[c2]-10000000*sin((2/9)*Pi) = 0

> 

f9 := -10000000*cos((2*Pi)/9) + reV[t]*(reIx[c1] - reIx[c2]) - imV[t]*(imIx[c1] - imIx[c2]) = 0;

-10000000*cos((2/9)*Pi)+reV[t]*(reIx[c1]-reIx[c2])-imV[t]*(imIx[c1]-imIx[c2]) = 0

> 

f5 := 1.36*reIx[c2] - 4.44*imIx[c2] + reV[at2] - reV[t] = 0;

1.36*reIx[c2]-4.44*imIx[c2]+reV[at2]-reV[t] = 0

> 

f6 := 4.44*reIx[c2] + 1.36*imIx[c2] + imV[at2] - imV[t] = 0;

4.44*reIx[c2]+1.36*imIx[c2]+imV[at2]-imV[t] = 0

> 

f2 := 0.1515*reIx[c1] + 0.03*imIx[c1] - 0.1515*reIx[c2] - 0.03*imIx[c2] + 2*imV[at1] = 0;

.1515*reIx[c1]+0.3e-1*imIx[c1]-.1515*reIx[c2]-0.3e-1*imIx[c2]+2*imV[at1] = 0

> 

f1 := -55000 + 0.03*reIx[c1] - 0.1515*imIx[c1] - 0.03*reIx[c2] + 0.1515*imIx[c2] + 2*reV[at1] = 0;

-55000+0.3e-1*reIx[c1]-.1515*imIx[c1]-0.3e-1*reIx[c2]+.1515*imIx[c2]+2*reV[at1] = 0

> 

f8 := -2.64*reIx[c1] - 1.12*imIx[c1] - 12.00*reIx[c2] - 3.92*imIx[c2] + imV[at2] - imV[at1] = 0;

-2.64*reIx[c1]-1.12*imIx[c1]-12.00*reIx[c2]-3.92*imIx[c2]+imV[at2]-imV[at1] = 0

> 

f7 := -1.12*reIx[c1] + 2.64*imIx[c1] - 3.92*reIx[c2] + 12.00*imIx[c2] + reV[at2] - reV[at1] = 0;

-1.12*reIx[c1]+2.64*imIx[c1]-3.92*reIx[c2]+12.00*imIx[c2]+reV[at2]-reV[at1] = 0

> 

f3 := 1.6*reIx[c1] - 6.24*imIx[c1] + 1.12*reIx[c2] - 2.64*imIx[c2] + reV[t] - reV[at1] = 0;

1.6*reIx[c1]-6.24*imIx[c1]+1.12*reIx[c2]-2.64*imIx[c2]+reV[t]-reV[at1] = 0

> 

f4 := 6.24*reIx[c1] + 1.6*imIx[c1] + 2.64*reIx[c2] + 1.12*imIx[c2] + imV[t] - imV[at1] = 0;

6.24*reIx[c1]+1.6*imIx[c1]+2.64*reIx[c2]+1.12*imIx[c2]+imV[t]-imV[at1] = 0

> 

vars := {reIx[c1], imIx[c1], reIx[c2], imIx[c2], reV[at1], imV[at1], reV[at2], imV[at2], reV[t], imV[t]};

{imIx[c1], imIx[c2], imV[at1], imV[at2], imV[t], reIx[c1], reIx[c2], reV[at1], reV[at2], reV[t]}

> 

# Digits seems to need to be at least 18 in order
# to find a second solution (and also gives a better first solution).
Digits := 20;

20

> 

# Even correcting defn of f9 and f10 (and expanding them) doesn't
# seem to help `solve`. But `fsolve` can still be used, see below.

sol1:=solve(({f1, f2, f3, f4, f5, f6, f7, f8, f9, f10}), vars);

Warning, solutions may have been lost

> 

f1n2 := (0.03 + I*0.1515)*Ix[c1] - (0.03 + I*0.1515)*Ix[c2] + 2 * V[at1] - 55*10^3 = 0:
f3n4 := (1.6 + I*6.24)*Ix[c1] + (1.12 + I*2.64)*Ix[c2] + V[t] - V[at1] = 0:
f5n6 := (1.36 + I*4.44)*Ix[c2] + V[at2] - V[t] = 0:
f7n8 := (-1.12 - I*2.64)*Ix[c1] + (-3.92 - I*12.00)*Ix[c2] + V[at2] - V[at1] = 0:
f9n10 := V[t] * (Ix[c1] - Ix[c2]) + TrainLoad = 0:
> 

oldvars := {Ix[c1], Ix[c2], V[at1], V[at2], V[t]};
K:=map(var->var=cat(re,var)+I*cat(im,var),oldvars):
evalc(eval(map(eq->[Re(eq),Im(eq)][],{f1n2, f3n4, f5n6, f7n8, f9n10}),K)):
sol2:=eval(K,simplify(fnormal(fsolve(%,complex)),zero));

{Ix[c1], Ix[c2], V[at1], V[at2], V[t]}

{Ix[c1] = 181.28189005805791743+162.01046250921478591*I, Ix[c2] = -81.655484607695036328-76.947655535280817396*I, V[at1] = 27514.157016821884248-23.501877901598220297*I, V[at2] = 27892.767479423787347-644.96659512864599818*I, V[t] = 28123.363610933968927-1112.1657583147938711*I}

> 

evalf[100](eval((lhs-rhs)~({f1n2, f3n4, f5n6, f7n8, f9n10}), sol2)):
max(abs~(evalf[5](%)));

0.21823907687671335089e-12

> 

S[1]:=fsolve([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10],vars,complex);

{imIx[c1] = 162.01046250921478591, imIx[c2] = -76.947655535280817396, imV[at1] = -23.501877901598220297, imV[at2] = -644.96659512864599818, imV[t] = -1112.1657583147938711, reIx[c1] = 181.28189005805791743, reIx[c2] = -81.655484607695036328, reV[at1] = 27514.157016821884248, reV[at2] = 27892.767479423787347, reV[t] = 28123.363610933968927}

> 

evalf[100](eval((lhs-rhs)~({f1, f2, f3, f4, f5, f6, f7, f8, f9, f10}), S[1])):
max(evalf[5](abs~(%)));

0.21757e-12

> 

eval(K,simplify(fnormal(S[1]),zero)):
evalf[100](eval((lhs-rhs)~({f1n2, f3n4, f5n6, f7n8, f9n10}), %)):
max(evalf[5](abs~(%)));

0.21824e-12

> 

S[2]:=fsolve([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10],vars,complex,avoid={S[1]});
evalf[100](eval((lhs-rhs)~({f1, f2, f3, f4, f5, f6, f7, f8, f9, f10}), S[2])):
max(evalf[5](abs~(%)));

{imIx[c1] = -5281.4918969451713544, imIx[c2] = 2424.8308425628567005, imV[at1] = 4.9812524290496869171, imV[at2] = 56.665451734948995089, imV[t] = 1112.1657583147938711, reIx[c1] = 955.22971037032619932-0.46908608509430945230e-33*I, reIx[c2] = -505.01568452829735058+0.21662280789933333333e-33*I, reV[at1] = 26894.342371558787522, reV[at2] = 10829.706661003599220, reV[t] = -623.36361093396892656}

0.22944e-12

> 

# no result (takes long)
#S[3]:=fsolve([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10],vars,complex,avoid={S[1],S[2]}):
#if op(0,eval(S[3],1))=fsolve then print("no additional solution found"); end if;
> 

#
# For fun, use the abs of the lhs-rhs of the new equations.
#
SS[1]:=fsolve(abs~((lhs-rhs)~([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10])));
evalf[100](eval((lhs-rhs)~({f1, f2, f3, f4, f5, f6, f7, f8, f9, f10}), SS[1])):
max(evalf[5](abs~(%)));
SS[2]:=fsolve(abs~((lhs-rhs)~([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10])),vars,avoid={SS[1]});
evalf[100](eval((lhs-rhs)~({f1, f2, f3, f4, f5, f6, f7, f8, f9, f10}), SS[2])):
max(evalf[5](abs~(%)));

{imIx[c1] = 162.01046250921478591, imIx[c2] = -76.947655535280817396, imV[at1] = -23.501877901598220297, imV[at2] = -644.96659512864599818, imV[t] = -1112.1657583147938711, reIx[c1] = 181.28189005805791743, reIx[c2] = -81.655484607695036328, reV[at1] = 27514.157016821884248, reV[at2] = 27892.767479423787347, reV[t] = 28123.363610933968927}

0.21757e-12

{imIx[c1] = -5281.4918969451713544, imIx[c2] = 2424.8308425628567005, imV[at1] = 4.9812524290496869171, imV[at2] = 56.665451734948995089, imV[t] = 1112.1657583147938711, reIx[c1] = 955.22971037032619932, reIx[c2] = -505.01568452829735058, reV[at1] = 26894.342371558787522, reV[at2] = 10829.706661003599220, reV[t] = -623.36361093396892656}

0.22944e-12

> 

# no result
SS[3]:=fsolve(abs~((lhs-rhs)~([f1, f2, f3, f4, f5, f6, f7, f8, f9, f10])),vars,avoid={SS[1],SS[2]}):
if op(0,eval(SS[3],1))=fsolve then print("no additional solution found"); end if;

"no additional solution found"

> 

# Now let's attempt making procedures which (only locally) increase Digits.
#
# Since the procedure raise Digits for the functional evaluations we can
# keep top-level Digits lower (which is used by fsolve for its accuracy
# requirement.

Digits:=10;

10

> 

oldnames:=nprintf~("%a",oldvars);

{`Ix[c1]`, `Ix[c2]`, `V[at1]`, `V[at2]`, `V[t]`}

> 

funcs:=[seq(subs(__dummy=eval((lhs-rhs)(__eq),Equate([oldvars[]],[oldnames[]])),
            proc(`Ix[c1]`,`Ix[c2]`,`V[at1]`,`V[at2]`,`V[t]`)
              Digits:=2*Digits;
              __dummy;
            end proc),
            __eq={f1n2, f3n4, f5n6, f7n8, f9n10})]:
> 

#infolevel[fsolve]:=0;
_EnvTry:=hard:
> 

FS[1]:=fsolve(funcs,[180+I*160..182+I*164, -82-77*I..-80-76*I, 27510-24*I..27520-22*I,
                     27890-650*I..27900-640*I, 28120-1120*I..28130-1110*I],complex):
Equate([oldvars[]], FS[1]);
evalf[100](eval((lhs-rhs)~({f1n2, f3n4, f5n6, f7n8, f9n10}), %)):
max(evalf[5](abs~(%)));

[Ix[c1] = 181.28189005805930+162.01046250921644*I, Ix[c2] = -81.655484607695652-76.947655535281597*I, V[at1] = 27514.157016821884-23.501877901598408*I, V[at2] = 27892.767479423792-644.96659512865114*I, V[t] = 28123.363610933976-1112.1657583148028*I]

0.90855e-7

> 

FS[2]:=fsolve(funcs,complex,avoid={FS[1]});

[955.22971037032620-5281.4918969451714*I, -505.01568452829735+2424.8308425628567*I, 26894.342371558788+4.9812524290496869*I, 10829.706661003599+56.665451734948996*I, -623.36361093396893+1112.1657583147939*I]

> 

# no result (takes long)
#FS[3]:=fsolve(funcs,[(-infinity-infinity*I..infinity+infinity*I)$5],complex,avoid={FS[1],FS[2]}):
#if op(0,eval(FS[3],1))=fsolve then print("no additional solution found"); end if;
> 

#
# This has 20 decimal digits in the result, but is more accurate than the
# than the S[1],SS[1] and S[2],SS[2] results obtained above at Digits=20.

Digits := 20:
AFS[1]:=fsolve(funcs,[180+I*160..182+I*164, -82-77*I..-80-76*I, 27510-24*I..27520-22*I,
              27890-650*I..27900-640*I, 28120-1120*I..28130-1110*I],complex):
Equate([oldvars[]], AFS[1]);
evalf[100](eval((lhs-rhs)~({f1n2, f3n4, f5n6, f7n8, f9n10}), %)):
max(evalf[5](abs~(%)));

AFS[2] := fsolve(funcs,complex,avoid={AFS[1]}):
Equate([oldvars[]], AFS[2]);
evalf[100](eval((lhs-rhs)~({f1n2, f3n4, f5n6, f7n8, f9n10}), %)):
max(evalf[5](abs~(%)));

[Ix[c1] = 181.281890058057917433399027+162.010462509214785906005715*I, Ix[c2] = -81.6554846076950363278550316-76.9476555352808173964757651*I, V[at1] = 27514.1570168218842476437442-23.5018779015982202969522171*I, V[at2] = 27892.7674794237873467298134-644.966595128645998186497765*I, V[t] = 28123.3636109339689265642830-1112.16575831479387114138115*I]

0.13186e-19

[Ix[c1] = 955.229710370326199319138724-5281.49189694517135435254499*I, Ix[c2] = -505.015684528297350584549199+2424.83084256285670047471394*I, V[at1] = 26894.3423715587875215982798+4.98125242904968691720452388*I, V[at2] = 10829.7066610035992203384338+56.6654517349489950911686282*I, V[t] = -623.363610933968926564282995+1112.16575831479387114138115*I]

0.22890e-19

> 

 

Download Q_ac_20200811_ac.mw

worksheet...

acer 32490
August 11 2020
0 0

Upload and attach your worksheet using the green up-arrow in the Mapleprimes editor.

rand...

acer 32490
August 10 2020
0 0

@Scot Gould He has Maple 18, in which version your call to rand is not supported.

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