I have encountered bug in factors/fsolve while working with 19-th degree polynomial: 

restart;

Digits:=150:
T:=-6.22380759047872668130713536877030256364968636070065651396334810246948704517800844289400608484048587112392332204805530128070851889819985512874202683743*10^11*x^15+1.30320674544020861155773378297484119553167774488351680864188235543008368581731239587845304516984389100205019741111280194189829856859808540642557769603*10^10*x^6-4.66269056752439302342961934783764679009596024511170531603537327397832302302620600217387943312388922053304167698527169182278585860427802821480352854136*10^11*x^9-2.23704996926446119043671514798254764988240075983626880645807120500701523185370168392321824617257975062292105400290171941856646211919772527234308968846*10^9*x^5+1.70227750800986164284793608409450414651109713000703213281475661248797845709368255736580952492853671050778821135335145407044800619189451776936359075686*10^12*x^12+2.75132914316444017343930750158891109941047127103886960894939389127711887329536485172215512793127850186551483171384960841607262449527761786758828223621*10^8*x^4-34932.1305741980482332724462824276603543110574918698909627427160477228536038554704823433224807581628905769847550345090785500099182662763447500819501675*x+1.14859089243616386902401277001127426741536679789632050800564282457083136981495352758127041512610195469873039580049988570650313838832989727748112868586*10^12*x^14-6.60479740997269404871863401649844958253760499264982628400515571200965556608668632440745621931354881132921476624343305820884923453724427367494415551238*10^10*x^17-5.62833694496139881587566825658979473046292640751330993837612787833792702707901920475562429114656627532669843830531312111426766840057855202536781521123*10^10*x^7-1.41317084251894030640575308228417182186337397538022537825365672333611503622567981167488384741420461775617951229535582868905095341476313150469092017698*10^12*x^11-8.21268191019727949807038061270674769712976810595535494085869238004490345847174711476348954310804852930678468602300916137608391140935636924900016951244*10^8*x^19+397.252699937115297695173788383107213691513398731729934944369484808586994493337920006396692649274392699364304534062337678482629861430643165733668575822+2.45061767631130714142188028061597642324588736935628490184983950396964320020866945354270367821778753632385377702112725604392839751008695021580743844404*10^11*x^16+1.08699947236093139248842860047684411564605736115175003178583710408973712475471303403438454553797809672473740940054172927497665894877177132800140413775*10^10*x^18+1.84485142971549353599220669614768264648023215439682851036030548807708252959822522849421648368214446092969270608024147362000126035954415744321702508798*10^11*x^8-2.30461084758765666852675422975553976835398815305842562217293737088819307979848024374022174488508670823626363788957243202121075401744096241597591787541*10^7*x^3+9.17691101238967627829517731270700894639677345422963842539705370480050031196020089039807157125184117990094461042715726886282973724309183151499484709563*10^11*x^10-1.59505142070054081045558935086478494555622632474984266672719416019069437321867830698450310020630535513817946854845186492455277659549284062382504657541*10^12*x^13+1.21399269842294123787022397507857250840398420627023248941081275489711499859955449395398103964932227544163416388726749227644470585060488880538430515276*10^6*x^2:

infolevel[fsolve]:=3:
fsolve(T,fulldigits); # <-- completes without issues

factors(T);           # <-- freezes with log:
fsolve: ill-conditioned polynom of degree 19, with 0(0) given roots
fsolve: 1th root found in 9 iters at 165 Digits
fsolve: 2th root found in 11 iters at 164 Digits
fsolve: 3th root found in 11 iters at 165 Digits
fsolve: 4th root found in 10 iters at 174 Digits
fsolve: 5th root found in 10 iters at 167 Digits
fsolve: 6th root found in 11 iters at 168 Digits
fsolve: 7th root found in 11 iters at 174 Digits
fsolve: 8th root found in 11 iters at 170 Digits
fsolve: 9th root found in 11 iters at 181 Digits
fsolve: 10th root found in 11 iters at 172 Digits
fsolve: 11th root found in 12 iters at 175 Digits
fsolve: 12th root found in 11 iters at 182 Digits
fsolve: 14th root found in 14 iters at 177 Digits
fsolve: 15th root found in 10 iters at 176 Digits
fsolve: 16th root found in 11 iters at 173 Digits
Warning,  computation interrupted

The most interesting thing is that standalone 'fsolve' finishes fine, but 'factors' freezes in 'fsolve:-polyill' on the same polynomial.

My system is: Windows 7 x64, Maple 2017.0.

Would appreciate any help on how to avoid the issue with 'factors'.

ode1a := diff(y1(tt), tt) = 1.342398800*10^5*y1(tt)+89591.20000*y2(tt)+44647.44000*y3(tt);
ode2a := diff(y2(tt), tt) = 89591.20000*y1(tt)+89803.24000*y2(tt)+44901.60000*y3(tt);
ode3a := diff(y3(tt), tt) = 44647.44000*y1(tt)+44901.60000*y2(tt)+44859.24000*y3(tt);

would like to find the origin eigenstate before it collapse to eigenvalues

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i find help file , and can not find some relationship between this application and inputs of ricci related function

which functions in maple can help to find origin of eigenstate

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Hi all!

I am using the solve command for solving 200 equations (linear in 200 unknowns) symbolically. The solve command computes efficiently for 50 equations, after which the efficiency decreases (RAM memory and computation issues).

Is there some other better way available to solve a system of algebraic equations symbolically?

thanks

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i would be very thankfull if someone help me in thisway please :)

g3 := tanh(x+1);
a:=eval(diff(g3,x$n)/n!, x=0) assuming n>=0:
tanhx := sum(a*x^n, n=0..infinity):
tanhx2 := subs(x^n=subs(_C1=0, subs(t=n!, g2))*x^n, tanhx):
diff(tanhx2, x) - tanhx2;
 

would like to find a operator to make it equalt to itself , a new differential operator for new transcendental function tanhx2

I wonder - would it be possible to automate the following way of adding a legend to plots? If so - how?

plot([f(x), g(x), 7], legend = ['f(x)' = f(x), 'g(x)' = g(x), y = 7]);

In my opinion such a legend makes the plot much more readable - but most students (and others) will usually be too lazy to type this out, hence the wish for it be to automated.

Any help will be much appreciated.

In Maple 17, the following expression needs to be integrated with respect to q3, p3 and q. Here, mu is a real, positive scalar. 

a := 1/(sqrt(mu^2+(px-p3x-q3x)^2)*sqrt(mu^2+(-p3x+qx-q3x)^2)*sqrt(mu^2+q3x^2)*(sqrt(mu^2+(-p3x+qx-q3x)^2)+sqrt(mu^2+q3x^2)))

However, the integration will not work with the "int" command (e.g. wrt q3). The indefinite integration will work if the integral is evaluated using the steps: highlight expression -> right click -> Integrate -> wrt q3 command.

The output of the integral (using the above method) is very long, it's impossible to manipulate the answer (on my i5, 8GB machine running Maple 17) because it is very tough to copy such a long output. Also, there is no way to specify that mu is a positive scalar. 

Is there a better way to perform the integration, e.g. between 0 and lambda, -1 through 1, or -infinity to +infinity?  

Assume I had a 2D line

how to put and draw this line into a new geometric world defined by patch?

I have gotten an expression:

eq21 := collect(eq20, [exp(-sqrt(s)*x/sqrt(Dp)), exp(sqrt(s)*(-lh+x)/sqrt(Dp)), exp((-2*lh+x)*sqrt(s)/sqrt(Dp)), exp((lh-x)*sqrt(s+thetac)/sqrt(Dc))], simplify);

q(x, s) = exp(-sqrt(s)*x/sqrt(Dp))*_F1(s)+sqrt(Dp)*(-Dp*sqrt(s+thetac)*alpha1*pinf*s^2-2*Dp*sqrt(s+thetac)*alpha1*pinf*s*thetac-Dp*sqrt(s+thetac)*alpha1*pinf*thetac^2+A2*Dp*sqrt(s+thetac)*alpha1*s+A2*Dp*sqrt(s+thetac)*alpha1*thetac+Dc*sqrt(s+thetac)*alpha1*pinf*s^2+Dc*sqrt(s+thetac)*alpha1*pinf*s*thetac+A1*Dc*alpha1*s^2+A1*Dc*alpha1*s*thetac+A1*sqrt(Dc)*sqrt(s+thetac)*s^2+A1*sqrt(Dc)*sqrt(s+thetac)*s*thetac-A2*Dc*sqrt(s+thetac)*alpha1*s)*exp(sqrt(s)*(-lh+x)/sqrt(Dp))/((s+thetac)^(3/2)*(-sqrt(Dp)*alpha1+sqrt(s))*s*(Dc*s-Dp*s-Dp*thetac))+(sqrt(Dp)*alpha1+sqrt(s))*_F1(s)*exp((-2*lh+x)*sqrt(s)/sqrt(Dp))/(-sqrt(Dp)*alpha1+sqrt(s))+Dc*A1*exp((lh-x)*sqrt(s+thetac)/sqrt(Dc))/((Dc*s-Dp*s-Dp*thetac)*sqrt(s+thetac))-(-pinf*s-pinf*thetac+A2)/((s+thetac)*s)

I need to further simplify the coefficient of

exp(sqrt(s)*(-lh+x)/sqrt(Dp))

Would you like to give some tips?

Thanks.

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how to find back a patch in maple from Pi+GaussCurvature*Area(triangle) = Pi

restart:
with(LinearAlgebra):
EFG := proc(X)
local Xu, Xv, E, F, G;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
E := DotProduct(Xu, Xu, conjugate=false);
F := DotProduct(Xu, Xv, conjugate=false);
G := DotProduct(Xv, Xv, conjugate=false);
simplify([E,F,G]);
end proc;

UN := proc(X)
local Xu,Xv,Z,s;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Z := CrossProduct(Xu,Xv);
s := VectorNorm(Z, Euclidean, conjugate=false);
simplify(<Z[1]/s|Z[2]/s|Z[3]/s>,sqrt,trig,symbolic);
end:

lmn := proc(X)
local Xu,Xv,Xuu,Xuv,Xvv,U,l,m,n;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Xuu := <diff(Xu[1],u), diff(Xu[2],u), diff(Xu[3],u)>;
Xuv := <diff(Xu[1],v), diff(Xu[2],v), diff(Xu[3],v)>;
Xvv := <diff(Xv[1],v), diff(Xv[2],v), diff(Xv[3],v)>;
U := UN(X);
l := DotProduct(U, Xuu, conjugate=false);
m := DotProduct(U, Xuv, conjugate=false);
n := DotProduct(U, Xvv, conjugate=false);
simplify([l,m,n],sqrt,trig,symbolic);
end proc:

GK := proc(X)
local E,F,G,l,m,n,S,T;
S := EFG(X);
T := lmn(X);
E := S[1];
F := S[2];
G := S[3];
l := T[1];
m := T[2];
n := T[3];
simplify((l*n-m^2)/(E*G-F^2),sqrt,trig,symbolic);
end proc:

sph := <f(u,v)|g(u,v)|h(u,v)>;
cur := GK(sph);
X := sph;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Z := CrossProduct(Xu,Xv);
AreaTriangle := int(int(Z[1]^2+Z[2]^2+Z[3]^2,v=-Pi/2..Pi/2),u=0..2*Pi);
dsolve(Pi+cur*AreaTriangle = Pi, [f(u,v),g(u,v),h(u,v)]);
 

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While Maple is perfectly happy to use non-latin letters such as the Scandinavian letters æ, ø and å it seems that MapleCloud can't handle that. Specifically, strings containing such letters is displayed in garbled form (the non-latin letters are shows as squares), and symbolic names containing such characters seems not to be recognized. The latter problem in particular makes MapleCloud quite useless to me.

I have attached a simple workbook demonstrating the problems to this message.

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