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MaplePrimes Questions

Showing Solutions for a complex Integral...

Asked by: heather0511 15
integration step-by-step calculus1
February 15 2022
3  7

Hi!

I am fairly new to maple and needing to use it for my project this year. I have been advised to use it to help solve the following integral:

int(2/(1-x^p)^(1/p), x=0..1)

It will give me the answer I am looking for, however I cannot get it to explain the steps to get the answer. I have tried Student Calculus1 and ShowSolution but neither of them seem to be working.

Any help would be really appreiacted!

Plot axes with fractions instead of decimal points...

Asked by: Simwar 80
plotting
February 15 2022
2  2

When plotting for exampe 1/x, can I make the x-axis show 1/10, 2/10, 3/10 and so forth instead of 0.1, 0.2, 0.3?

how to use the digital block of electrical in mapl...

Asked by: TX 110
circuit electrical-engineering
February 15 2022
2  1

i wanna build an integrated circuit by digital block of electrical in maplesim. i know the input of digital items should be a vector, but i dont know how to build a vector in maplesim. for example, how to build a simple gate circuit in maplesim? Maybe i should use the modelica to do it?

 i use maplesim 2020.

Facing issue in integration evaluations...

Asked by: Tamour_Zubair 80
integration numeric
February 15 2022
2  5

Hello Sir
Hope you are fine. I am facing issues in integration evaluations. I have attched code and pic as well. Kindly guide me. I am waiting for your kind response.
Thanks

question.mw

> 

restart; printlevel := 4; kernelopts(version)

{--> enter Terminate, args =

<-- exit Terminate (now at top level) = }
{--> enter ModuleUnload, args =
<-- exit ModuleUnload (now at top level) = }
{--> enter OnUnload, args =
<-- exit OnUnload (now at top level) = }

  

`Maple 2015.0, X86 64 WINDOWS, Feb 17 2015, Build ID 1022128`

 (1)
> 

with(LinearAlgebra):
> 

L[time] := 1:
> 

> 

ff11 := cos(1.0*k*(p+q+x+t)):
> 

NULL
> 

JJx11 := QQ*(int(int(p*ff11/`&gamma;&gamma;Exact`, p), q))/m;

175631174533.479692645444566411*(int(int(0.273299999999999999999999999999e-21*p*cos(.50*p+.50*q+.50*x+.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2), p), q))

 (2)
> 

evalf(IntegrationTools:-Expand(%));

Warning,  computation interrupted

  
> 

``
> 

``
> 

int(int(p*ff11/`&gamma;&gamma;Exact`, p = 0 .. 1), q = 0 .. 1); evalf(IntegrationTools:-Expand(%))

int(int(0.273299999999999999999999999999e-21*p*cos(.50*p+.50*q+.50*x+.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2), p = 0 .. 1), q = 0 .. 1)

  

0.273299999999999999999999999999e-21*(Int(Int(p*cos(.50*p)*cos(.50*q)*cos(.50*x)*cos(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2)-1.*p*cos(.50*p)*cos(.50*q)*sin(.50*x)*sin(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2)-1.*p*cos(.50*p)*sin(.50*q)*sin(.50*x)*cos(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2)-1.*p*cos(.50*p)*sin(.50*q)*cos(.50*x)*sin(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2)-1.*p*sin(.50*p)*sin(.50*q)*cos(.50*x)*cos(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2)+p*sin(.50*p)*sin(.50*q)*sin(.50*x)*sin(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2)-1.*p*sin(.50*p)*cos(.50*q)*sin(.50*x)*cos(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2)-1.*p*sin(.50*p)*cos(.50*q)*cos(.50*x)*sin(.50*t)/(p^2+q^2+0.746928900000000000000000000000e-43)^(1/2), p = 0. .. 1.), q = 0. .. 1.))

 (3)
> 

``

Download question.mw

error when using dslove...

Asked by: Ngu? Van Thái 10
ode syntax numeric
February 15 2022
2  1

i use dslove command to solve system of differential equations but got an error, i checked the error but i don't know where i went wrong, please help me!

error: Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

HOI.mw

How to convert a dsegment into a vector?...

Asked by: bstuan 90
vector user-error incomplete-question
February 15 2022
2  8

In Maple what is the fastest way to convert a directed line segment into a vector? Please help me. Thank you a lot.

Help With Assignment Please...

Asked by: Maxwell_MA 10
homework vectorcalculus do-my-homework-for-me
February 14 2022
1  5

I have an assignment for my class but I don't know how to get the answer without getting an error. Maple_2.mw
 

Vector Valued Functions

and

Level Sets of Scalar Valued Functions

 

This worksheet is meant to give you some tools that you can use to

explore vector valued functions and scalar valued functions of several variables.

We will use the Student[VectorCalculus]  and the plots  packages.

 

First we load the packages with a restart at the beginning.  That is

meant to make it easier to check what happens when you run your

solutions.

 

> 

restart;
with(Student:-VectorCalculus);
BasisFormat(false):
with(plots):
with(plottools):

Deivatives and integrals for vector valued functions

   

Plotting velocity and acceleration along a curve

   

Plotting functions of two variables and contours.

   

Exercises

   


 

Download Maple_2.mw

 

all possible sigma algebra in finite set...

Asked by: Zeineb 520
algebra finite global
February 14 2022
0  1

Dear all 
I have a finite set, I would like to compute all possible sigma algebra

Using the following code ( thanks to vv), for helping me to use this code:

sigma_algebra_all.mw 

 

This code give me the sigma algebra if I fix the generator of the sigma algebra, How can I find all possible sigma algebra in the global set {1,2,3}

 

Thank you

Maple doesn't plot anything...

Asked by: Pima 5
output plotting
February 14 2022
1  2

Hi,

I have a problem with maple. I used to work with maple until 2019. Now I installed Maple 2021 and I wanted to plot something, but it didn't worked anymore. I have problems to plot anything. When I try to plot something, maple only writes a very long list instead of a graphic. Here you can see, what I wrote in the worksheet:

restart;
with(LinearAlgebra):
with(plots):

plot(x^2,x=0..2);
INTERFACE_PLOT(CURVES(Matrix(200,2,{(2, 1) = HFloat(.105152100502512568e-1), (2
, 2) = HFloat(.110569642400905045e-3), (3, 1) = HFloat(.196644380904522631e-1),
(3, 2) = HFloat(.386690125413229849e-3), (4, 1) = HFloat(.299537019095477385e-1
), (4, 2) = HFloat(.897224258086043816e-3), (5, 1) = HFloat(.403111696482412116\
e-1), (5, 2) = HFloat(.162499039840928341e-2), (6, 1) = HFloat(.\
506194101507537672e-1), (6, 2) = HFloat(.256232468401023337e-2), (7, 1) =
HFloat(.601764686432160745e-1), (7, 2) = HFloat(.362120737836796758e-2), (8, 1)
= HFloat(.700722491457286406e-1), (8, 2) = HFloat(.491012010034106838e-2), (9,
1) = HFloat(.803064794974874402e-1), (9, 2) = HFloat(.644913064928037075e-2), (
10, 1) = HFloat(.905078885427135632e-1), (10, 2) = HFloat(.819167788846026160e-\
2), (11, 1) = HFloat(.101001291658291470), (11, 2) = HFloat(.102012609166432580\
e-1), (12, 1) = HFloat(.110243886834170857), (12, 2) = HFloat(.\
121537145843054698e-1), (13, 1) = HFloat(.120648859899497501), (13, 2) = HFloat
(.145561473950485756e-1), (14, 1) = HFloat(.131096556783919599), (14, 2) =
HFloat(.171863072005994551e-1), (15, 1) = HFloat(.141164848643216101), (15, 2)
= HFloat(.199275144924621096e-1), (16, 1) = HFloat(.150307822211055264), (16, 2
) = HFloat(.225924414178301988e-1), (17, 1) = HFloat(.161179702110552769), (17,
2) = HFloat(.259788963724465298e-1), (18, 1) = HFloat(.170389610452261309), (18
, 2) = HFloat(.290326193500733548e-1), (19, 1) = HFloat(.181102923316582926), (
19, 2) = HFloat(.327982688338121151e-1), (20, 1) = HFloat(.190586020502512554),
(20, 2) = HFloat(.363230312109841386e-1), (21, 1) = HFloat(.200990481105527641)
, (21, 2) = HFloat(.403971734950314618e-1), (22, 1) = HFloat(.21089798804020101\
8), (22, 2) = HFloat(.444779613594047732e-1), (23, 1) = HFloat(.221235432160804\
046), (23, 2) = HFloat(.489451164433777272e-1), (24, 1) = HFloat(.2307284328643\
21625), (24, 2) = HFloat(.532356097320257696e-1), (25, 1) = HFloat(.24096791658\
2914582), (25, 2) = HFloat(.580655368223104776e-1), (26, 1) = HFloat(.251603862\
412060286), (26, 2) = HFloat(.633045035806669570e-1), (27, 1) = HFloat(.2608624\
84522613070), (27, 2) = HFloat(.680492358313105478e-1), (28, 1) = HFloat(.27086\
2050050251268), (28, 2) = HFloat(.733662501574248171e-1), (29, 1) = HFloat(.281\
192579698492429), (29, 2) = HFloat(.790692668774930219e-1), (30, 1) = HFloat(.2\
91298987537688459), (30, 2) = HFloat(.848551001404823785e-1), (31, 1) = HFloat(
.301077456783919617), (31, 2) = HFloat(.906476349834729883e-1), (32, 1) =
HFloat(.311934779698492481), (32, 2) = HFloat(.973033067855470363e-1), (33, 1)
= HFloat(.321690567236180891), (33, 2) = HFloat(.103484821048735812), (34, 1) =
HFloat(.332106952763819130), (34, 2) = HFloat(.110295028074069587), (35, 1) =
HFloat(.341545746231155745), (35, 2) = HFloat(.116653496768597043), (36, 1) =
HFloat(.351864840603015094), (36, 2) = HFloat(.123808866052585217), (37, 1) =
HFloat(.361574304221105480), (37, 2) = HFloat(.130735977472976550), (38, 1) =
HFloat(.371723491356783953), (38, 2) = HFloat(.138178354026477046), (39, 1) =
HFloat(.381646176884422095), (39, 2) = HFloat(.145653804330495601), (40, 1) =
HFloat(.392034309045226126), (40, 2) = HFloat(.153690899468567871), (41, 1) =
HFloat(.402039314974874384), (41, 2) = HFloat(.161635610785466260), (42, 1) =
HFloat(.412270878592964851), (42, 2) = HFloat(.169967277335815153), (43, 1) =
HFloat(.422417719698492511), (43, 2) = HFloat(.178436729915274178), (44, 1) =
HFloat(.431741612864321611), (44, 2) = HFloat(.186400820278685764), (45, 1) =
HFloat(.442427846633165867), (45, 2) = HFloat(.195742399476460133), (46, 1) =
HFloat(.451985741507537675), (46, 2) = HFloat(.204291110526118674), (47, 1) =
HFloat(.462176450954773888), (47, 2) = HFloat(.213607071817150523), (48, 1) =
HFloat(.471930260201005036), (48, 2) = HFloat(.222718170493388323), (49, 1) =
HFloat(.482760611859296529), (49, 2) = HFloat(.233057808362762353), (50, 1) =
HFloat(.492138900603015073), (50, 2) = HFloat(.242200697486744360), (51, 1) =
HFloat(.502783342211055251), (51, 2) = HFloat(.252791089204919106), (52, 1) =
HFloat(.512484595175879409), (52, 2) = HFloat(.262640460292584976), (53, 1) =
HFloat(.523096241306532650), (53, 2) = HFloat(.273629677669022242), (54, 1) =
HFloat(.532252297286432086), (54, 2) = HFloat(.283292507966684481), (55, 1) =
HFloat(.542679976281407073), (55, 2) = HFloat(.294501556656788566), (56, 1) =
HFloat(.552752599396984956), (56, 2) = HFloat(.305535436140123740), (57, 1) =
HFloat(.562818642311557871), (57, 2) = HFloat(.316764824133425327), (58, 1) =
HFloat(.572847654070351764), (58, 2) = HFloat(.328154434773905379), (59, 1) =
HFloat(.582482394673366821), (59, 2) = HFloat(.339285740104419864), (60, 1) =
HFloat(.592897804422110597), (60, 2) = HFloat(.351527806488559302), (61, 1) =
HFloat(.602824445125628161), (61, 2) = HFloat(.363397311641021459), (62, 1) =
HFloat(.613271767035175941), (62, 2) = HFloat(.376102260242447139), (63, 1) =
HFloat(.622729109145728654), (63, 2) = HFloat(.387791543377432824), (64, 1) =
HFloat(.633181242613065298), (64, 2) = HFloat(.400918485997025453), (65, 1) =
HFloat(.643192565125628168), (65, 2) = HFloat(.413696675832885441), (66, 1) =
HFloat(.653179519798995023), (66, 2) = HFloat(.426643485084845731), (67, 1) =
HFloat(.663610932663316611), (67, 2) = HFloat(.440379469950276936), (68, 1) =
HFloat(.673218644723618143), (68, 2) = HFloat(.453223343603505191), (69, 1) =
HFloat(.683058256080402049), (69, 2) = HFloat(.466568581199600096), (70, 1) =
HFloat(.693922356180904587), (70, 2) = HFloat(.481528236407658183), (71, 1) =
HFloat(.703758908944723593), (71, 2) = HFloat(.495276601919067749), (72, 1) =
HFloat(.713818626633165865), (72, 2) = HFloat(.509537031728459100), (73, 1) =
HFloat(.724049100402010093), (73, 2) = HFloat(.524247099792960136), (74, 1) =
HFloat(.733452896582914682), (74, 2) = HFloat(.537953151505867755), (75, 1) =
HFloat(.743477038793969869), (75, 2) = HFloat(.552758107213850214), (76, 1) =
HFloat(.753424876582914571), (76, 2) = HFloat(.567649044653980028), (77, 1) =
HFloat(.764065970854271415), (77, 2) = HFloat(.583796807817480334), (78, 1) =
HFloat(.773456275577889429), (78, 2) = HFloat(.598234610230820030), (79, 1) =
HFloat(.784290737889447254), (79, 2) = HFloat(.615111961539173691), (80, 1) =
HFloat(.794068004824120544), (80, 2) = HFloat(.630543996285359509), (81, 1) =
HFloat(.803742099396984933), (81, 2) = HFloat(.646001362343072816), (82, 1) =
HFloat(.814144858894472301), (82, 2) = HFloat(.662831851264300220), (83, 1) =
HFloat(.824589699698492495), (83, 2) = HFloat(.679948172848850008), (84, 1) =
HFloat(.834092958291457243), (84, 2) = HFloat(.695711063071394631), (85, 1) =
HFloat(.844184996783919672), (85, 2) = HFloat(.712648308795066465), (86, 1) =
HFloat(.854033840000000044), (86, 2) = HFloat(.729373799865145722), (87, 1) =
HFloat(.864710089949748739), (87, 2) = HFloat(.747723539660902548), (88, 1) =
HFloat(.873948014472361812), (88, 2) = HFloat(.763785132000183498), (89, 1) =
HFloat(.884558106633165808), (89, 2) = HFloat(.782443044010451172), (90, 1) =
HFloat(.894532151055276392), (90, 2) = HFloat(.800187769271579863), (91, 1) =
HFloat(.904409857085427094), (91, 2) = HFloat(.817957189593282674), (92, 1) =
HFloat(.914295420904522649), (92, 2) = HFloat(.835936116686978203), (93, 1) =
HFloat(.924378070251256290), (93, 2) = HFloat(.854474816761436551), (94, 1) =
HFloat(.935065509648241200), (94, 2) = HFloat(.874347507333725016), (95, 1) =
HFloat(.944864845025125577), (95, 2) = HFloat(.892769575364354528), (96, 1) =
HFloat(.954538047336683348), (96, 2) = HFloat(.911142883813328308), (97, 1) =
HFloat(.964878541407035106), (97, 2) = HFloat(.930990599667767538), (98, 1) =
HFloat(.975196525125628155), (98, 2) = HFloat(.951008262617099920), (99, 1) =
HFloat(.984457528241206137), (99, 2) = HFloat(.969156624910785136), (100, 1) =
HFloat(.995427854271356827), (100, 2) = HFloat(.990876613059277656), (101, 1) =
HFloat(1.00460731437185924), (101, 2) = HFloat(1.00923585608943966), (102, 1) =
HFloat(1.01534372402010042), (102, 2) = HFloat(1.03092287790700587), (103, 1) =
HFloat(1.02559058693467331), (103, 2) = HFloat(1.05183605200900776), (104, 1) =
HFloat(1.03473981497487433), (104, 2) = HFloat(1.07068648469423722), (105, 1) =
HFloat(1.04502907879397000), (105, 2) = HFloat(1.09208577552497355), (106, 1) =
HFloat(1.05538654653266328), (106, 2) = HFloat(1.11384076260214138), (107, 1) =
HFloat(1.06569478703517584), (107, 2) = HFloat(1.13570537911394887), (108, 1) =
HFloat(1.07525184552763808), (108, 2) = HFloat(1.15616653131059177), (109, 1) =
HFloat(1.08514762603015091), (109, 2) = HFloat(1.17754537027887229), (110, 1) =
HFloat(1.09538185638190955), (110, 2) = HFloat(1.19986141129067825), (111, 1) =
HFloat(1.10558326542713559), (111, 2) = HFloat(1.22231435679252809), (112, 1) =
HFloat(1.11607666854271348), (112, 2) = HFloat(1.24562713006540182), (113, 1) =
HFloat(1.12531926371859292), (113, 2) = HFloat(1.26634344529615617), (114, 1) =
HFloat(1.13572423678391954), (114, 2) = HFloat(1.28986954201841653), (115, 1) =
HFloat(1.14617193366834180), (115, 2) = HFloat(1.31371010152902579), (116, 1) =
HFloat(1.15624022552763828), (116, 2) = HFloat(1.33689145912820373), (117, 1) =
HFloat(1.16538319909547727), (117, 2) = HFloat(1.35811800073400879), (118, 1) =
HFloat(1.17625507899497483), (118, 2) = HFloat(1.38357601086147453), (119, 1) =
HFloat(1.18546498733668337), (119, 2) = HFloat(1.40532723620116284), (120, 1) =
HFloat(1.19617830020100513), (120, 2) = HFloat(1.43084252587176586), (121, 1) =
HFloat(1.20566139738693479), (121, 2) = HFloat(1.45361940514901633), (122, 1) =
HFloat(1.21606585798994971), (122, 2) = HFloat(1.47881617096883256), (123, 1) =
HFloat(1.22597336492462317), (123, 2) = HFloat(1.50301069150460331), (124, 1) =
HFloat(1.23631080904522617), (124, 2) = HFloat(1.52846441656206178), (125, 1) =
HFloat(1.24580380974874383), (125, 2) = HFloat(1.55202713238448431), (126, 1) =
HFloat(1.25604329346733667), (126, 2) = HFloat(1.57764475506427404), (127, 1) =
HFloat(1.26667923929648252), (127, 2) = HFloat(1.60447629526471558), (128, 1) =
HFloat(1.27593786140703536), (128, 2) = HFloat(1.62801742617195888), (129, 1) =
HFloat(1.28593742693467328), (129, 2) = HFloat(1.65363506599136811), (130, 1) =
HFloat(1.29626795658291449), (130, 2) = HFloat(1.68031061526364467), (131, 1) =
HFloat(1.30637436442211063), (131, 2) = HFloat(1.70661398001927345), (132, 1) =
HFloat(1.31615283366834168), (132, 2) = HFloat(1.73225828157320549), (133, 1) =
HFloat(1.32701015658291466), (133, 2) = HFloat(1.76095595567421159), (134, 1) =
HFloat(1.33676594412060301), (134, 2) = HFloat(1.78694318936064711), (135, 1) =
HFloat(1.34718232964824125), (135, 2) = HFloat(1.81490022931646267), (136, 1) =
HFloat(1.35662112311557781), (136, 2) = HFloat(1.84042087168337165), (137, 1) =
HFloat(1.36694021748743699), (137, 2) = HFloat(1.86852555818460164), (138, 1) =
HFloat(1.37664968110552777), (138, 2) = HFloat(1.89516434448795135), (139, 1) =
HFloat(1.38679886824120602), (139, 2) = HFloat(1.92321110095508985), (140, 1) =
HFloat(1.39672155376884422), (140, 2) = HFloat(1.95083109876245442), (141, 1) =
HFloat(1.40710968592964836), (141, 2) = HFloat(1.97995766823703367), (142, 1) =
HFloat(1.41711469185929650), (142, 2) = HFloat(2.00821404988346908), (143, 1) =
HFloat(1.42734625547738680), (143, 2) = HFloat(2.03731733302531737), (144, 1) =
HFloat(1.43749309658291469), (144, 2) = HFloat(2.06638640272353680), (145, 1) =
HFloat(1.44681698974874351), (145, 2) = HFloat(2.09327940182561578), (146, 1) =
HFloat(1.45750322351758776), (146, 2) = HFloat(2.12431564656415928), (147, 1) =
HFloat(1.46706111839195996), (147, 2) = HFloat(2.15226832509746835), (148, 1) =
HFloat(1.47725182783919595), (148, 2) = HFloat(2.18227296285424543), (149, 1) =
HFloat(1.48700563708542721), (149, 2) = HFloat(2.21118576472383710), (150, 1) =
HFloat(1.49783598874371848), (150, 2) = HFloat(2.24351264917587256), (151, 1) =
HFloat(1.50721427748743708), (151, 2) = HFloat(2.27169487826197702), (152, 1) =
HFloat(1.51785871909547732), (152, 2) = HFloat(2.30389509113416313), (153, 1) =
HFloat(1.52755997206030147), (153, 2) = HFloat(2.33343946824086901), (154, 1) =
HFloat(1.53817161819095460), (154, 2) = HFloat(2.36597192700818004), (155, 1) =
HFloat(1.54732767417085437), (155, 2) = HFloat(2.39422293125498564), (156, 1) =
HFloat(1.55775535316582903), (156, 2) = HFloat(2.42660174031679654), (157, 1) =
HFloat(1.56782797628140713), (157, 2) = HFloat(2.45808456321065272), (158, 1) =
HFloat(1.57789401919598005), (158, 2) = HFloat(2.48974953581444369), (159, 1) =
HFloat(1.58792303095477383), (159, 2) = HFloat(2.52149955223659550), (160, 1) =
HFloat(1.59755777155778911), (160, 2) = HFloat(2.55219083346468922), (161, 1) =
HFloat(1.60797318130653277), (161, 2) = HFloat(2.58557775180105187), (162, 1) =
HFloat(1.61789982201005023), (162, 2) = HFloat(2.61759983406015229), (163, 1) =
HFloat(1.62834714391959801), (163, 2) = HFloat(2.65151442111111191), (164, 1) =
HFloat(1.63780448603015083), (164, 2) = HFloat(2.68240353446048641), (165, 1) =
HFloat(1.64825661949748747), (165, 2) = HFloat(2.71674988371728521), (166, 1) =
HFloat(1.65826794201005034), (166, 2) = HFloat(2.74985256749824769), (167, 1) =
HFloat(1.66825489668341720), (167, 2) = HFloat(2.78307440030819908), (168, 1) =
HFloat(1.67868630954773868), (168, 2) = HFloat(2.81798772586300617), (169, 1) =
HFloat(1.68829402160804021), (169, 2) = HFloat(2.85033670339744960), (170, 1) =
HFloat(1.69813363296482422), (170, 2) = HFloat(2.88365783540631249), (171, 1) =
HFloat(1.70899773306532654), (171, 2) = HFloat(2.92067325162242497), (172, 1) =
HFloat(1.71883428582914588), (172, 2) = HFloat(2.95439130214179002), (173, 1) =
HFloat(1.72889400351758793), (173, 2) = HFloat(2.98907447539907345), (174, 1) =
HFloat(1.73912447728643227), (174, 2) = HFloat(3.02455394749680639), (175, 1) =
HFloat(1.74852827346733686), (175, 2) = HFloat(3.05735112311466573), (176, 1) =
HFloat(1.75855241567839204), (176, 2) = HFloat(3.09250659868830802), (177, 1) =
HFloat(1.76850025346733686), (177, 2) = HFloat(3.12759314651403475), (178, 1) =
HFloat(1.77914134773869348), (178, 2) = HFloat(3.16534393523345470), (179, 1) =
HFloat(1.78853165246231161), (179, 2) = HFloat(3.19884547185956691), (180, 1) =
HFloat(1.79936611477386954), (180, 2) = HFloat(3.23771841499641022), (181, 1) =
HFloat(1.80914338170854272), (181, 2) = HFloat(3.27299977557982169), (182, 1) =
HFloat(1.81881747628140711), (182, 2) = HFloat(3.30809701202666684), (183, 1) =
HFloat(1.82922023577889470), (183, 2) = HFloat(3.34604667098299524), (184, 1) =
HFloat(1.83966507658291456), (184, 2) = HFloat(3.38436759399882092), (185, 1) =
HFloat(1.84916833517587942), (185, 2) = HFloat(3.41942353181713354), (186, 1) =
HFloat(1.85926037366834174), (186, 2) = HFloat(3.45684913709334163), (187, 1) =
HFloat(1.86910921688442211), (187, 2) = HFloat(3.49356926464229778), (188, 1) =
HFloat(1.87978546683417092), (188, 2) = HFloat(3.53359340132096200), (189, 1) =
HFloat(1.88902339135678377), (189, 2) = HFloat(3.56840937309308481), (190, 1) =
HFloat(1.89963348351758787), (190, 2) = HFloat(3.60860737170116597), (191, 1) =
HFloat(1.90960752793969868), (191, 2) = HFloat(3.64660091076396720), (192, 1) =
HFloat(1.91948523396984938), (192, 2) = HFloat(3.68442356342828736), (193, 1) =
HFloat(1.92937079778894471), (193, 2) = HFloat(3.72247167536074919), (194, 1) =
HFloat(1.93945344713567835), (194, 2) = HFloat(3.76147967360646573), (195, 1) =
HFloat(1.95014088653266326), (195, 2) = HFloat(3.80304947732640164), (196, 1) =
HFloat(1.95994022190954786), (196, 2) = HFloat(3.84136567345884794), (197, 1) =
HFloat(1.96961342422110564), (197, 2) = HFloat(3.87937704087198920), (198, 1) =
HFloat(1.97995391829145739), (198, 2) = HFloat(3.92021751855769507), (199, 1) =
HFloat(1.99027190201005011), (199, 2) = HFloat(3.96118224393070228), (200, 1) =
HFloat(2.), (200, 2) = HFloat(4.)},datatype = float[8],storage = rectangular,
order = Fortran_order,shape = []),COLOUR(RGB,.47058824,0.,.54901961e-1,
_ATTRIBUTE("source" = "mathdefault"))),AXESLABELS(x,""),VIEW(0. .. 2.,DEFAULT,
_ATTRIBUTE("source" = "mathdefault")))

I also opened an old worksheet with plots and pressed the "!!!" buttom, but maple didn't plotted anything, but 3 years ago, it worked with the old version of maple.  Does anybody knows what the problem is?

How to define a piecewise periodic function in mul...

Asked by: dirk1000 5
piecewise multivariate densityplot
February 14 2022
1  3

Hello,

I'm struggling with following simple problem which I however cannot seem to implement easily in Maple:

  • I have 2 different periodic functions: f1 and f2, each time in  variables x and t.
  • On the second function f2 a duty cycle with period T and fraction q should need to be applied so that:
    • during the DUTY (=ON or 1) part of this period, so from 0 -> q*T, f2__DC=f2
    • during the remainder (=OFF or 0) part of this period, so from q*T->T, f2__DC=0
    • each subsequent DUTY part starts at the same point where it ended at the previous cycle, so as if f2 was 'froozen' during the OFF part (see code for more details, but basically this means that the t parameter needs to be constantly translated depending on which duty cycle we are in).
  • In the end I want to calculate f1*f2 in a simple way using ranges for both variables x and t so that e.g. plotting can easily be done.

I've tried implicit functions and procedures but keep getting stuck whenever I introduce a second variable.  Somehow, Maple does not seem to work straightforward with non-univariate stuff.  Such an examples can also not be found in the programming guide so I'm hoping that one of you knows how to tackle this.

Any help will be much appreciated!
 

> 

restart;
with(plots):
> 

f1 := (x, t) -> A * (1 + B * sin(a*x-b*t));

proc (x, t) options operator, arrow; A*(1+B*sin(a*x-b*t)) end proc

 (1)
> 

f2 := (x, t) -> C * (1 + E * sin(c*x-d*t));

proc (x, t) options operator, arrow; C*(1+E*sin(c*x-d*t)) end proc

 (2)
> 

A:=1: B:=0.5: a:=100: b:=1:
C:=1: E:=0.5: c:=10: d:=10:
> 

densityplot(f1(x,t) * f2(x,t), x = 0..1, t = 0..10, style=patchnogrid);

 
> 

#Duty cycle (DC) applied to f2
# ON state:      n*T <= t <(n+q)*T  : f2__DC(x,t)=f2(x,t-n*(1-q)*T)
# OFF state: (n+q)*T <= t < (n+1)*T : f2__DC(x,t)=0 (so all other cases)
# (n is a positive integer, zero included, and n=floor(t/T))

T:=1:
q:=0.3; #fraction of T where DC is 1=ON
> 

#How to apply the above DC to f2(x,t) so that f2__DC is obtained and following command works:
densityplot(f1(x,t) * f2__DC(x,t), x = 0..1, t = 0..10, style=patchnogrid);
> 

 


 

Download dutycycle_.mw

Solving systems of equations with "or" logical con...

Asked by: Dmitrii_U 20
solve or
February 14 2022
1  2

Could anyone please tell me how to solve the following system of equations and inequalities numerically in Maple:

{x + y = 2 and y = 1 and x > 0} or {x^2 = 4 and x < 0 and y = 0}?

By now I have been using solve() function in similar cases, but did not manage to adopt it for the or logical connector. 

Solving the two cases separately obviously works here, but does not help in the example, for which I need this, 

Thank you in advance!

Basins of attraction...

Asked by: RM 20
newton fractal plotting
February 14 2022
4  7

Hi! I'm trying to draw the basins of attraction for Newton's method with f(z) = z^3 - 1 in three colors, just like the pictures on the links below:

https://i.stack.imgur.com/0wHfa.jpg

or

http://dept.cs.williams.edu/~heeringa/classes/cs135/s15/labs/lab3/

Can this be done? Thanks in advance,

RM

intsolve error for Abel integral equation...

Asked by: danielpf 25
abel intsolve
February 13 2022
1  2

The Abel integral equation of the form

g(x) =  Int( f(y) / (x-y)^alpha, y = 0 .. x ) assuming alpha>0, alpha<1;

is linear and has a well known explicit solution for f(x).  

It is a particular form of Volterra equation of the first kind. 

It occurs in many problems of physics with alpha = 1/2.

However intsolve gives an error message:

> eq := g(x) =  Int(f(y)/(x-y)^alpha, y = 0 .. x) assuming alpha>0, alpha<1

> intsolve(eq, f(x));
Error, (in intsolve) numeric exception: division by zero

Replacing (x-y)^alpha by sqrt(x-y) gives the same error message.

why doesn't greek char work as tensor index?...

Asked by: larry stead 45
tensor physics
February 13 2022
3  2

restart

with(Physics)

Setup(spacetime)

[spacetimeindices = greek]

 (1)

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1142 and is the same as the version installed in this computer, created 2022, February 12, 11:16 hours Pacific Time.`

 (2)

Define(t[mu])

{Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], t[mu], Physics:-LeviCivita[alpha, beta, mu, nu]}

 (3)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

 (4)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

 (5)

NULL

SumOverRepeatedIndices(t[mu]*t[`~&mu;`])

t[mu]*t[`~&mu;`]

 (6)

NULL

Download greek-index.mw

Monotone_class_generated_by_set...

Asked by: Zeineb 520
set
February 13 2022
0  5

Dear all

I have a set of three element, I want to apply each step of the definition of monotone class generated by a set to obtain the element of the monotone class generated by a given set. 

The definition and condition of monotone class is added in maple worksheet. 

I hope find some steps ( using maple) that will be applied later to other problem.

Monotone_class.mw

thanks

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