gaurav_rs

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These are questions asked by gaurav_rs

Dear Users,

I have difficulty in finding numerical integration of a function f(r,t) which is a function of position r and time t. Function f(r,t) consists 100 terms (for example : BesselJ(0, 151.5793716314014*r)+BesselJ(0, 151.5793716314014*r)*r^2+......100 terms). For a particular time t=t1, f(r,t1) is calculated and then integrated as follows:

I am using evalf(Int(f(r,t1),r=0..1)

Maple takes a lot of time  to evaluate it as it is integrating it in one shot!  Is there a way to

a) pick the terms individually and integrate it

b) then sum these individual terms up together

c) How reliable is evalf(int(f(r,t1),r=0..1)) is? Is evalf (Int()..)  the best way to evaluate integration?

thanks.

Dear users,

I have an issue with finding real part of a complex variable function. In calculating the real part I see two arguments and the plot is not smooth. How to get real part correct. The worksheet is attached.
 

``

 

 

##Toya complex variable method

``

restart;

stress_c:=-(1+1/nu_c)*k*p2*zeta_c/2;

-(1/2)*(1+1/nu_c)*k*p2*zeta_c

(1.1)

p2:=(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)/k*a*(N_infty-T_infty)*exp(2*I*phi_c+2*lambda*(alpha-Pi))*((a*(cos(alpha)-2*lambda*sin(alpha)))/z-a^2/z^2)

(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)*a*(N_infty-T_infty)*exp((2*I)*phi_c+2*lambda*(alpha-Pi))*(a*(cos(alpha)-2*lambda*sin(alpha))/z-a^2/z^2)/k

(1.2)

``

z := exp(I*theta)

exp(I*theta)

(1.3)

``

k := beta_c/(1+nu_c)

beta_c/(1+nu_c)

(1.4)

nu_c := (kappa2*mu+mu2)/(kappa*mu2+mu)

(kappa2*mu+mu2)/(kappa*mu2+mu)

(1.5)

d_1c := (N_infty+T_infty)*(1/2)

(1/2)*N_infty+(1/2)*T_infty

(1.6)

lambda := -evalf(ln(nu_c)/(2*Pi))

-.1591549430*ln((kappa2*mu+mu2)/(kappa*mu2+mu))

(1.7)

``

beta_c := mu*(1+kappa2)/(kappa*mu2+mu)

mu*(1+kappa2)/(kappa*mu2+mu)

(1.8)

zeta_c := ((z-a*exp(I*alpha))/(z-a*exp(-I*alpha)))^(I*lambda)/((z-a*exp(I*alpha))^.5*(z-a*exp(-I*alpha))^.5)

((exp(I*theta)-a*exp(I*alpha))/(exp(I*theta)-a*exp(-I*alpha)))^(-(.1591549430*I)*ln((kappa2*mu+mu2)/(kappa*mu2+mu)))/((exp(I*theta)-a*exp(I*alpha))^.5*(exp(I*theta)-a*exp(-I*alpha))^.5)

(1.9)

``

c0_c := G_c+I*H_c

G_c+I*H_c

(1.10)

G_c:=(0.5*(T_infty+N_infty)*(1-(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha)))-0.5*(1-k)*(1+4*lambda^2)*(N_infty-T_infty)*(sin(alpha))^2*cos(2*phi_c))/(2-k-k*(cos(alpha)+2*lambda*sin(alpha))*exp(evalf(2*lambda*(Pi-alpha))));

(.5*(N_infty+T_infty)*(1-(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha)))-.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*cos(2*phi_c))/(2-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu)))-mu*(1+kappa2)*(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-1.*alpha))/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))

(1.11)

H_c:=0.5*(1-k)*(1+4*lambda^2)*(-T_infty+N_infty)*(sin(alpha))^2*sin(2*phi_c)/(k*(1+(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha))));

.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*sin(2*phi_c)*(kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))/(mu*(1+kappa2)*(1+(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha))))

(1.12)

##Input

alpha:=evalf(Pi/6)

.5235987758

(1.13)

phi_c:=alpha;

.5235987758

(1.14)

N_infty:=0;

0

(1.15)

T_infty:=1;

1

(1.16)

a:=1;nu2:=22/100;kappa2:=3-4*nu2;nu:=35/100;kappa:=3-4*nu;mu:=239/100;mu2:=442/10;

1

 

11/50

 

53/25

 

7/20

 

8/5

 

239/100

 

221/5

(1.17)

``

stress_c

-(9321/123167)*(((.5586916801-.5*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775))+0.5946710490e-2*ln(123167/182775)^2)/(22817/11767-(717/11767)*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-(1.668336947*I)*(.1013211835*ln(123167/182775)^2+1)/(1+(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-11767/1434)*(exp(I*theta)-.8660254037+.1591549431*ln(123167/182775))-(11050/717)*exp(1.047197552*I+.8333333328*ln(123167/182775))*((.8660254037+.1591549431*ln(123167/182775))/exp(I*theta)-1/(exp(I*theta))^2))*((exp(I*theta)+(-.8660254037-.5000000002*I))/(exp(I*theta)+(-.8660254037+.5000000002*I)))^(-(.1591549430*I)*ln(123167/182775))/((exp(I*theta)+(-.8660254037-.5000000002*I))^.5*(exp(I*theta)+(-.8660254037+.5000000002*I))^.5)

(1.18)

assume((1/6)*Pi < theta, theta < 2*Pi-(1/6)*Pi)

simplify(evalc(Re(stress_c)))

-0.8815855810e-10*((((1.000000000*cos(theta)^7+(0.5294827753e-2+.5671599115*sin(theta))*cos(theta)^6-4.533186669*cos(theta)^5+(-11.80630620+4.886343937*sin(theta))*cos(theta)^4+3.402782742*cos(theta)^3+(9213180122.+0.9866808100e-1*sin(theta))*cos(theta)^2+(-0.1055437876e11+0.1595769608e11*sin(theta))*cos(theta)-5794103792.*sin(theta)+1760041721.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(0.6523625301e-2+1.134319823*sin(theta))*cos(theta)^6+4.644568297*cos(theta)^5+(-0.2905669688e-1+10.20004207*sin(theta))*cos(theta)^4-0.1774243515e-1*cos(theta)^3+(0.1595769609e11-9.082306669*sin(theta))*cos(theta)^2+(-7023191163.-9213180109.*sin(theta))*cos(theta)-3154310102.*sin(theta)-7408031461.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.644568284*cos(theta)^5+(11.37920491*sin(theta)-0.2640575516e-1)*cos(theta)^4-0.1774243890e-1*cos(theta)^3+(-11.39571957*sin(theta)+0.1595769607e11)*cos(theta)^2+(-9213180108.*sin(theta)-7023191160.)*cos(theta)-7408031458.-3154310086.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7+(-.5671599115*sin(theta)-0.5294826902e-2)*cos(theta)^6+4.531921682*cos(theta)^5+(-4.886343941*sin(theta)+11.76153292)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807692e-1*sin(theta)-9213180122.)*cos(theta)^2+(-0.1595769609e11*sin(theta)+0.1055437877e11)*cos(theta)-1760041726.+5794103798.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*cos(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.))+(((-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.626658979*cos(theta)^5+(-0.2905667760e-1+10.24488508*sin(theta))*cos(theta)^4-.1341529536*cos(theta)^3+(0.1595769608e11-9.127079936*sin(theta))*cos(theta)^2+(-7023191161.-9213180109.*sin(theta))*cos(theta)-3154310089.*sin(theta)-7408031435.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.134319823*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.531921682*cos(theta)^5+(11.80860365-4.107288978*sin(theta))*cos(theta)^4-3.402959469*cos(theta)^3+(-9213180123.+0.1774243833e-1*sin(theta))*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)+5794103807.*sin(theta)-1760041748.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.537223485*cos(theta)^5+(-4.886343950*sin(theta)+11.80860366)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807250e-1*sin(theta)-9213180123.)*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)-1760041739.+5794103821.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(.5600908440*cos(theta)^7+(-1.134319823*sin(theta)-0.4756356038e-2)*cos(theta)^6-4.644554360*cos(theta)^5+(-10.21771474*sin(theta)+0.2905668928e-1)*cos(theta)^4+0.1774243685e-1*cos(theta)^3+(9.082306650*sin(theta)-0.1595769608e11)*cos(theta)^2+(9213180109.*sin(theta)+7023191165.)*cos(theta)+7408031453.+3154310085.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*sin(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.)))/((-sin(theta)+2.-1.732050807*cos(theta))^(1/4)*(sin(theta)+2.-1.732050807*cos(theta))^(1/4))

(1.19)

plot(%, theta = (1/6)*Pi .. 2*Pi-(1/6)*Pi)

 


 

Download Toya_complexPlot2.mw

Hi All!

Is there a way to

1) sechedule the job

2) make it parallel

for computing Ax=B where A is a matrix (n*n) and B is a vector (n).

thanks.


 

restart;

Digits:=50;

A11:= 1.0000000000000000000000000000000000000000000000000*10^(-7)*(-2.5371361080198636732473763516755733087783841018170*10^8515*y^52-2.5682916864364461018876089817027829349729972598145*10^8511*y^118-8.4747208167823896652789620415242113024646500383584*10^8475*y^156-7.0973392025624720825652840212522978368268373080519*10^8514*y^110-8.8052634112991425064821529334897431676429996585193*10^8504*y^31-1.6472736182931730318373390809274526418048821840783*10^8515*y^109-3.4915488631639337623561469549167018169698449760097*10^8516*y^105-1.8648897040502425673332564918257100737272347061207*10^8504*y^30-1.7350350044631380327296789440528743348277795652204*10^8506*y^33-2.4402743405185212194691411556528521403537441901346*10^8516*y^55-4.0714341045744099661015191696314839899399825641016*10^8491*y^15-1.2448510727169172443541597142261710648571818634985*10^8490*y^146-2.2769347278615925887334921880003704106200930647502*10^8518*y^98-4.1875154960616508784147371031658177346824585674863*10^8493*y^17-6.8908510205423224604237562530919308400658046098227*10^8518*y^65-8.0705757255759766519585958706737861776653196868557*10^8515*y^107-2.1234522662689238596130937707990549717374387500852*10^8494*y^142-4.6757486544282170861175940883663855408524031383409*10^8513*y^113-5.6256767384686469294547974274654974293947541346854*10^8487*y^148-2.3667794156402717849832357737043058826502430856228*10^8501*y^134-1.1955708738478973602304171305150038469305944735032*10^8513*y^46-1.2229433916279605188228472869508020737406276934003*10^8482*y^7-1.0359942900497464263463322634590397630995748789812*10^8519*y^66-7.3577937250552680213618842893731191171017237168564*10^8502*y^28-1.6780317940142468912677977158676729074792728705946*10^8520*y^79-1.0188879426769871779634856274674561388204588547021*10^8499*y^23-8.3834163867972974773322872823619870147258375964774*10^8498*y^137-8.7167696030066179229415400068223274105756753084368*10^8473*y^157-2.5423845331789200034600726713334929841949530920620*10^8479*y^154-3.8400819852144312141390565045108971739848198770878*10^8494*y^18-1.5967261576416053607752429820872991323335743262311*10^8520*y^78-1.0175740692585689531634424955890114976014444308933*10^8518*y^61-2.4285179995148629407580354176987125130661349445523*10^8501*y^26-9.9591230938294084010283929867041070209088721794711*10^8519*y^74-1.5124785750379412355186078281009850256857725039212*10^8509*y^38-1.3696257334801547432715188212364024825978277580525*10^8518*y^99-2.5043379550164697208863253414438885954940319418237*10^8510*y^120-2.6305035680296659521217994891132781709179981823953*10^8519*y^92-6.4633168857441661801397078657885868645527618896321*10^8512*y^115-5.4017137062835482229400862860704710101104939466346*10^8477*y^155-1.3319332479266630416544055381399156457205375789742*10^8520*y^76-1.1229179453936158801565711524134745656617998399217*10^8515*y^51-2.1072238939760510496168542795319210517882197759574*10^8509*y^122-7.4202951194571591382703904653143254672490997668970*10^8483*y^151-3.8070289285557325159584243346313284671324915495170*10^8500*y^135-1.1039925581103150720522042406500486542915736245074*10^8520*y^86-5.6617914522620010790945778522914661973615369528464*10^8510*y^41-1.6087035160973756036538832079523009248794530721987*10^8491*y^145-1.4850201031906675776350324581492012684281688447293*10^8498*y^22-1.5146247410262645573925305579471723277055334370925*10^8519*y^67-4.7211130001373051878950913154719403710636491284680*10^8480*y^6-1.6530002518788994941149248059829590520008440377562*10^8520*y^82-1.7047076469980128563965847960657802574607166189462*10^8516*y^106-2.1535689236782065779546222373046347806024179149085*10^8519*y^68-1.7663207202025704123021189232952843065338109601207*10^8511*y^42-2.0054000346149665950873656769091881277646008431218*10^8514*y^49-8.7980985658203695061909911148317791080293037920173*10^8518*y^95-6.6382089342334567702605185897161035295052107532885*10^8499*y^24-5.2423518701418206080645845528109724107178201134724*10^8519*y^71-2.5005223984780390224009659120569911266411465016141*10^8517*y^102-2.9166995984685295180483355964884005809318120438676*10^8507*y^35-5.5605332423183301781370124657024028252864513225132*10^8515*y^53-4.2088985508608984037637955818873668034650441141989*10^8508*y^37-1.5359069780830356990250444855818636390995287737421*10^8487*y^11-4.8195822055982315209243519558327594854332125953476*10^8514*y^50-7.4019159776239374282920917712985331824056305640757*10^8509*y^121-1.1824401371065279253129270148658783843985808299790*10^8516*y^54-5.7699445263820038176602320228433347310150065071114*10^8518*y^96-4.8887240826161304314145695217669095642625562448079*10^8516*y^56-9.3168096457369483705678128915607768202734995258500*10^8519*y^87-7.6483335053880959242217872221711779939205126053655*10^8519*y^88-2.8022165140012359383220386299165583012323933610511*10^8518*y^63-8.7913174849933209946633264469576789417889752795771*10^8488*y^147-6.1070602577931150981002852101247677893073469678402*10^8519*y^89-6.6735204940436023143379559279002699661221027971978*10^8519*y^72-3.70386075781506254277680215375929321413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factor(A11);

Warning,  computation interrupted

 

 

50

(1)

 

 

``


 

Download factor_puz.mw

Dear Maple users,

I am struck with a polynomial. Is there a way to factor it ?

work sheet is attached.

 

regards,

 

Dear Users,

Recently, I started using Maple2017. In Maple 18, I have used the following commands for import/export and it worked fine.

 

Digits := 50;

Rhs:= ImportVector("/home/15_degree_3izto1_fixed/Vec.txt", source = delimited);

MatA:=ImportMatrix("/home/15_degree_3izto1_fixed/Mat.txt", source = delimited) ;

Note : Vec.txt contains float with 50 digits, and Mat.txt contains algebraic equation eg. 123456716798271394816*y+173974937*10^(-16)

 

While maple 18 used to import all the informations with 50 digits of accuracy, Maple2017 only import float[8] ?It only imports first 20 digits and so on..? What has changed in 2017?

Thanks and regards,

 

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