Hello,

I would like to ask, if somebody knows whether the CAD Toolbox is included in the students version and if not how much is it?

Thanks!
Fabian

Hi,

Could you please help me in solving this problem ?

• N is the number of row, about 10^4 in real applications
• P is the number of columns (about 5)
• A and B are two NxP matrices
• C is the Nx(2P) matrix defined by
  • its 2*k-1 th column is the k th column of A
  • its 2*k th column is the k th column of B

What is the fastest and less memory consumming way to construct this matrix C ?

Thanks in advance

 

I have a matirx

where ci and si represent cos(θi) and sin(θi), respectively. I need to substitute

What is the right way of using trigsubs command?

collect((sqrt(x)+y)^2, [x, y], distributed);
                                       (sqrt(x)+y)^2

I think this is wrong. Documentation says that collect supports fractional powers of the variables, so in this case collect should return x+2*sqrt(x)*y+y^2.

Why when I write (9b² - r² - a² cos(theta)²)² maple changes to (r²+ a² cos(theta)² - 9b²)² ? Would anyone know how to block this change?

Thanks!

write a maple script to find the relation on set s is

1)reflexsive

2)symmetric

3)trasitive

How do I change my input of variable current, I1, to I, without violating the imaginary unit?

S

After waiting about six hours for the worksheet to be executed, I finally lost hope and stopped it. (My CPU usage was stuck on 100% the whole time and I almost ran out of memory) Is this evaluation time normal and should I have waited longer, or is there a problem with my worksheet? (I'm uploading it here) Or is it possible that the equation cannot be solved by Maple at all?

parasitic.mw

how dsolve differential equations?

ta.mw

Hi all,

I have a system of 18 polynomial equations (and 18 variables).

The polynomials are of second degree (meaning, every polynomial has at most multiplications of two different variables or a single variable squared).

My goal is to be able to solve the polynomials by getting ALL the possible solutions.

For now, when I use the solve command, Maple is trying to solve and never returns the solutions to the equations (I stopped after 3 hours).

But when I use fsolve, Maple returns a single solution (immediately) which is sometimes the solution I expected to get but not always.

If I don't get the solution I expected to get, I call fsolve again but this time with the 'avoid' option in order not to get the same solution again. that way if I use 'fsolve' about 3 times I get the solution I expected to get in most cases. but still not always.

My question, since the equations are polynomials, is there a way to tell Maple to solve the equations in a more efficient way so that I will get ALL the possible solutions? (when I use the 'solve' command I don't tell Maple in any way that the equations are polynomials). or any other way to get all the solutions (I'm new with Maple so maybe there are other commands that I don't know about and can give me all the solutions).

btw, I need only the real solutions. I don't need the complex solutions if exist.

I wrote bellow an example of the code in Maple with the equations that I'm trying to solve (note that I use fsolve twice but only in the second time I get the solutions I expected to get).

The 'h' function in the code looks extermely long but I don't try to solve 'h' in the fsolve command. only the g1* and diff_r1* and diff_t1* functions (which are much shorter than 'h').

I will appreciate any help.

Thanks!

Here is the code:

restart;
g1_1_1:=r1__1_1^2+r1__1_2^2+r1__1_3^2-1;
g1_1_2:=r1__1_1*r1__2_1+r1__1_2*r1__2_2+r1__1_3*r1__2_3;
g1_1_3:=r1__1_1*r1__3_1+r1__1_2*r1__3_2+r1__1_3*r1__3_3;
g1_2_2:=r1__2_1^2+r1__2_2^2+r1__2_3^2-1;
g1_2_3:=r1__2_1*r1__3_1+r1__2_2*r1__3_2+r1__2_3*r1__3_3;
g1_3_3:=r1__3_1^2+r1__3_2^2+r1__3_3^2-1;
h:=(-.992492661403*r1__1_1+12.3284921161777*r1__1_2+7.57084655768457*r1__1_3+.324267866473309*t11+.0749281794197556+1.09088742857604*r1__2_1-13.5507269559957*r1__2_2-8.32141299937268*r1__2_3-.356415470609132*t12+.928796854654334*r1__3_1-11.5372789567796*r1__3_2-7.08496771958172*r1__3_3-.303457129743798*t13)^2+(-2.48532903781461*r1__2_1+30.87212696684*r1__2_2+18.958371709801*r1__2_3+.81200836636144*t12-.197547504455846+1.09088742838705*r1__1_1-13.550726959431*r1__1_2-8.32141299910563*r1__1_3-.356415470592923*t11+.48989466626242*r1__3_1-6.08534729180524*r1__3_2-3.73697206129778*r1__3_3-.160058713114523*t13)^2+(-2.6436153220831*r1__3_1+32.8383190443191*r1__3_2+20.1657974352703*r1__3_3+.863723767113888*t13+.0651743072009662+.928796854295815*r1__1_1-11.5372789582423*r1__1_2-7.08496772054044*r1__1_3-.303457129759512*t11+.48989466615819*r1__2_1-6.08534729103406*r1__2_2-3.73697206192339*r1__2_3-.160058713130091*t12)^2+(-3.0453012837136*r1__1_1+28.3453761824993*r1__1_2+20.6329645159026*r1__1_3+.803383631995274*t11+1.1433809887851+.588739190174359*r1__2_1-5.47992867285244*r1__2_2-3.98891068120136*r1__2_3-.15531580779083*t12+1.38673265028867*r1__3_1-12.9075762854695*r1__3_2-9.39559107531887*r1__3_3-.365835170130537*t13)^2+(-3.32552348095664*r1__2_1+30.9536578751004*r1__2_2+22.5315663656812*r1__2_3+.877309298336102*t12-1.987216561269+.588739190114314*r1__1_1-5.47992866961904*r1__1_2-3.98891068053918*r1__1_3-.155315807786897*t11+1.09544034380124*r1__3_1-10.1962550610257*r1__3_2-7.42198542424216*r1__3_3-.28898908845837*t13)^2+(-1.21036350562772*r1__3_1+11.2659489790199*r1__3_2+8.20062940888435*r1__3_3+.319307069650757*t13+.229170772052734+1.38673265024704*r1__1_1-12.9075762829888*r1__1_2-9.39559107412026*r1__1_3-.365835170095885*t11+1.09544034388008*r1__2_1-10.1962550650824*r1__2_2-7.4219854245274*r1__2_3-.288989088438315*t12)^2+(-5.95351974815554*r1__1_1+36.6994162407641*r1__1_2+25.4290813546269*r1__1_3+.974842575637377*t11-2.63695732507178+.0862138869060729*r1__2_1-.531450210031119*r1__2_2-.368242659171055*r1__2_3-.0141168537454004*t12+.952506399264142*r1__3_1-5.87155670816424*r1__3_2-4.06841057826005*r1__3_3-.155965518005519*t13)^2+(-6.05878205069695*r1__2_1+37.3482870296174*r1__2_2+25.8786849115508*r1__2_3+.992078459354551*t12-1.33152058265882+.0862138869007144*r1__1_1-.531450210081823*r1__1_2-.368242659219069*r1__1_3-.0141168537421636*t11+.534490070726969*r1__3_1-3.29476921378019*r1__3_2-2.28295060211721*r1__3_3-.087518593905657*t13)^2+(-.202018537282116*r1__3_1+1.24530743607334*r1__3_2+.862875410606218*r1__3_3+.0330789650607677*t13+.545863834860738+.952506399246256*r1__1_1-5.87155670833708*r1__1_2-4.06841057735347*r1__1_3-.155965517969505*t11+.534490070750153*r1__2_1-3.29476921356283*r1__2_2-2.28295060131082*r1__2_3-.0875185939055155*t12)^2+(-6.07959771459677*r1__1_1+30.9674242426801*r1__1_2+22.3705097998352*r1__1_3+.857873368534317*t11-1.76471733145788+1.65075563468967*r1__2_1-8.40839352379239*r1__2_2-6.07412642093546*r1__2_3-.232933059628316*t12+1.84351225448619*r1__3_1-9.39023086096381*r1__3_2-6.78339437706986*r1__3_3-.260132354459928*t13)^2+(-4.38138073503315*r1__2_1+22.3172786035824*r1__2_2+16.1217444412232*r1__2_3+.618243184218713*t12-.923385301124302+1.65075563490521*r1__1_1-8.40839352323243*r1__1_2-6.07412642020582*r1__1_3-.232933059620808*t11+3.02135458680454*r1__3_1-15.3897632163199*r1__3_2-11.1173872944915*r1__3_3-.426334069877298*t13)^2+(-3.71266987086301*r1__3_1+18.9110905602843*r1__3_2+13.6611535221535*r1__3_3+.523883447195053*t13+1.79101248019951+1.84351225469879*r1__1_1-9.39023085830571*r1__1_2-6.78339437737683*r1__1_3-.260132354453603*t11+3.02135458675847*r1__2_1-15.3897632129884*r1__2_2-11.1173872963301*r1__2_3-.426334069880672*t12)^2+(-3.90011435645636*r1__1_1+33.4181858543797*r1__1_2+19.9362529914774*r1__1_3+.790634768245585*t11-3.40601893140435+1.48764430833506*r1__2_1-12.7469016125627*r1__2_2-7.60440607186657*r1__2_3-.301576621987651*t12+1.34716650703029*r1__3_1-11.5432155550731*r1__3_2-6.88632430891628*r1__3_3-.273098832924476*t13)^2+(-2.79003782913976*r1__2_1+23.9064791937414*r1__2_2+14.261863864387*r1__2_3+.565599033947199*t12+2.94191879923881+1.48764430859128*r1__1_1-12.7469016146313*r1__1_2-7.6044060696602*r1__1_3-.301576621995954*t11+1.94050330636006*r1__3_1-16.6272304379243*r1__3_2-9.91928987276943*r1__3_3-.393380614413616*t13)^2+(-3.17562785143546*r1__3_1+27.2104128357136*r1__3_2+16.2328881834776*r1__3_3+.643766197822571*t13-.637542053291817+1.34716650724399*r1__1_1-11.5432155571023*r1__1_2-6.88632430841617*r1__1_3-.273098832949826*t11+1.94050330633365*r1__2_1-16.627230438149*r1__2_2-9.91928987492707*r1__2_3-.3933806144393*t12)^2+(-2.01324057094153*r1__1_1+40.4637240018238*r1__1_2+19.1624249532275*r1__1_3+.995107416713897*t11+1.84529512341763+.0539908034671229*r1__2_1-1.08515047907221*r1__2_2-.513895226737029*r1__2_3-.0266866512328603*t12+.130433143363034*r1__3_1-2.62154994723571*r1__3_2-1.24148865078056*r1__3_3-.0644706798567015*t13)^2+(-1.72864549456945*r1__2_1+34.7437038570169*r1__2_2+16.453592301917*r1__2_3+.854437357037078*t12+1.26622268071142+.0539908034660728*r1__1_1-1.08515047910239*r1__1_2-.513895226549678*r1__1_3-.026686651233501*t11+.711449065385413*r1__3_1-14.2992740321447*r1__3_2-6.77171397936849*r1__3_3-.351656057242671*t13)^2+(-.304391827618365*r1__3_1+6.11791114030412*r1__3_2+2.89726208101195*r1__3_3+.150455226223174*t13-.664170181540941+.130433143328345*r1__1_1-2.62154994715954*r1__1_2-1.24148865060744*r1__1_3-.0644706798534696*t11+.711449065210039*r1__2_1-14.2992740313315*r1__2_2-6.77171398089296*r1__2_3-.3516560572166*t12)^2+(-.554028798262323*r1__1_1+16.4352774899688*r1__1_2+12.212735424138*r1__1_3+.451248010725026*t11+1.80668680530669+.561213036138882*r1__2_1-16.6483980707805*r1__2_2-12.3711011963105*r1__2_3-.457099462951262*t12+.241478758779813*r1__3_1-7.16347312712678*r1__3_2-5.32303772144054*r1__3_3-.19668076798868*t13)^2+(-.760290795908938*r1__2_1+22.5540445569422*r1__2_2+16.7594723669968*r1__2_3+.619245263577858*t12-.547959274703874+.561213036185506*r1__1_1-16.6483980712546*r1__1_2-12.3711011949445*r1__1_3-.457099462966984*t11+.201146990103896*r1__3_1-5.96703024933782*r1__3_2-4.43398426133857*r1__3_3-.163831157208818*t13)^2+(-1.14122053061752*r1__3_1+33.854334200315*r1__3_2+25.1564980835807*r1__3_3+.929506725704928*t13-3.76727778582615+.241478758813686*r1__1_1-7.16347312565607*r1__1_2-5.32303772203581*r1__1_3-.196680768005511*t11+.201146990115401*r1__2_1-5.96703024794285*r1__2_2-4.43398426232404*r1__2_3-.163831157217202*t12)^2+(-4.02477735374144*r1__1_1+27.7950101802505*r1__1_2+21.425586834354*r1__1_3+.78027956702849*t11+.221994737480659+1.24285496385638*r1__2_1-8.5831248120031*r1__2_2-6.61624099843662*r1__2_3-.24095105086973*t12+1.73688577463857*r1__3_1-11.9948890468077*r1__3_2-9.24617530570086*r1__3_3-.336728310946364*t13)^2+(-3.7951756300308*r1__2_1+26.2093865067395*r1__2_2+20.2033200543809*r1__2_3+.735766910103154*t12-.764444377219279+1.2428549639263*r1__1_1-8.58312481092265*r1__1_2-6.61624100152625*r1__1_3-.240951050879308*t11+1.90471339873406*r1__3_1-13.1539023563811*r1__3_2-10.1395925103233*r1__3_3-.369264884863308*t13)^2+(-2.49629140831476*r1__3_1+17.2393250571566*r1__3_2+13.2888116882479*r1__3_3+.483953522844612*t13+.402154769245324+1.73688577506273*r1__1_1-11.9948890436773*r1__1_2-9.24617530885054*r1__1_3-.336728310949967*t11+1.90471339909204*r1__2_1-13.153902354604*r1__2_2-10.1395925090424*r1__2_3-.36926488485258*t12)^2+(r1__1_1^2+r1__1_2^2+r1__1_3^2-1)*b1__1_1+(r1__1_1*r1__2_1+r1__1_2*r1__2_2+r1__1_3*r1__2_3)*b1__1_2+(r1__2_1^2+r1__2_2^2+r1__2_3^2-1)*b1__2_2+(r1__1_1*r1__3_1+r1__1_2*r1__3_2+r1__1_3*r1__3_3)*b1__1_3+(r1__2_1*r1__3_1+r1__2_2*r1__3_2+r1__2_3*r1__3_3)*b1__2_3+(r1__3_1^2+r1__3_2^2+r1__3_3^2-1)*b1__3_3;
diff_t11:=diff(h,t11);
diff_t12:=diff(h,t12);
diff_t13:=diff(h,t13);
diff_r1__1_1:=diff(h,r1__1_1);
diff_r1__2_1:=diff(h,r1__2_1);
diff_r1__3_1:=diff(h,r1__3_1);
diff_r1__1_2:=diff(h,r1__1_2);
diff_r1__2_2:=diff(h,r1__2_2);
diff_r1__3_2:=diff(h,r1__3_2);
diff_r1__1_3:=diff(h,r1__1_3);
diff_r1__2_3:=diff(h,r1__2_3);
diff_r1__3_3:=diff(h,r1__3_3);
with(Groebner):
with(RealDomain):
sols:=fsolve({g1_1_1,g1_1_2,g1_1_3,g1_2_2,g1_2_3,g1_3_3,diff_t11,diff_t12,diff_t13,diff_r1__1_1,diff_r1__1_2,diff_r1__1_3,diff_r1__2_1,diff_r1__2_2,diff_r1__2_3,diff_r1__3_1,diff_r1__3_2,diff_r1__3_3},{ t11, t12, t13, r1__1_1, r1__1_2, r1__1_3, r1__2_1, r1__2_2, r1__2_3, r1__3_1, r1__3_2, r1__3_3, b1__1_1, b1__1_2, b1__1_3, b1__2_2, b1__2_3, b1__3_3} );
with(Groebner):
with(RealDomain):
sols:=fsolve({g1_1_1,g1_1_2,g1_1_3,g1_2_2,g1_2_3,g1_3_3,diff_t11,diff_t12,diff_t13,diff_r1__1_1,diff_r1__1_2,diff_r1__1_3,diff_r1__2_1,diff_r1__2_2,diff_r1__2_3,diff_r1__3_1,diff_r1__3_2,diff_r1__3_3},{ t11=0.184015, t12=0.087459, t13=0.308915, r1__1_1=0.230878, r1__1_2=0.909187, r1__1_3=0.936884, r1__2_1=0.031879, r1__2_2=0.593647, r1__2_3=0.043818, r1__3_1=0.424903, r1__3_2=0.521581, r1__3_3=0.840339, b1__1_1=0.625030, b1__1_2=0.255205, b1__1_3=0.904691, b1__2_2=0.767301, b1__2_3=0.562666, b1__3_3=0.897154}, avoid={{b1__1_1 = -32.51343311, b1__1_2 = 43.92451284, b1__1_3 = 22.91611840, b1__2_2 = -6.848329887, b1__2_3 = 16.30411571, b1__3_3 = -13.09739229, r1__1_1 = .5873876993, r1__1_2 = -.8092603402, r1__1_3 = -.8566942425e-2, r1__2_1 = .2869971672e-1, r1__2_2 = .1024997381e-1, r1__2_3 = .9995355243, r1__3_1 = -.8087966474, r1__3_2 = -.5873607408, r1__3_3 = .2924625105e-1, t11 = 36.59195193, t12 = -22.18329766, t13 = 22.31332161}} );

I am beginning to study Special Relativity and Classical Field Theory - The Theoretical Minimum by Leonard Susskind and Art Friedman.

The book's notation for a 4-Vector is X superscript mu. Its components are X superscripts 0, 1, 2 and 3 which, in sequence, refer to t(ime), x, y and z.

Proper time, tau, is defined using these vector components in that sequence.

The book's notation for 4-Velocity is U superscript mu with components U superscripts 0 thru 3. U superscript zero is defined to be the derivative of X superscript zero with respect to tau i.e. dt/dtau and the remaining U components follow this pattern.

As a beginner in this area, which Maple packages/commands would most easily and clearly implement this notation in a Maple worksheet? 

Consider the following anticommutators:

with(Physics):
Simplify(AntiCommutator(Dgamma[1],Dgamma[1])),
Simplify(AntiCommutator(Dgamma[1],Dgamma[2]));

Being basic Clifford algebra, I wonder why Physics does not know that the second one should simplify to zero.

PS: Just to be sure, I have updated to Maple 2017.3 today.

restart;

eq1 := a[n+2]+4*a[n+1]+10*a[n]-5*n-1;

applyrule(a[n::anything] = n*p+q+b[n], eq1);

eq2 := a(n+2)+4*a(n+1)+10*a(n)-5*n-1;

applyrule(a(n::anything) = b(n)+n*p+q, eq2);

eq3 := a(n+2)+4*a(n+1)+10*a(n) = 5*n+1;

applyrule(a(n::anything) = b(n)+n*p+q, eq3)

So my question is: Why does the first one not work? the second one works as expected, but the third one again does not?!

CodeGeneration returns round brackets when converting a matrix to numpy. According to Python syntax it should return square brackets. I am using Maple 18, so maybe this issue has been solved in more recent releases.

MWE

----------------
>restart:
>with(CodeGeneration):
>QLoc:=proc()
local Q:
Q:= Matrix(2,2):
Q(1,1) := 1E5:
Q(2,2) := 1E4:
Q(1,2) := 1E3:
Q(2,1) := 1E3:
return Q:
end proc:
 

>Python(QLoc);

import numpy

def QLoc ():
    Q = numpy.mat([[0,0],[0,0]])
    Q(1, 1) = 0.1e6
    Q(2, 2) = 0.1e5
    Q(1, 2) = 0.1e4
    Q(2, 1) = 0.1e4
    return(Q)

------------

Hey all Maple experts, Kris here!

I could really use some help/clarfication on what is going on with alias, diff, and pointers for vectors.

A short description of what I want to do:
I have 4 equations with 4 variables. The first two equations and variables (1 and 2) are called private, and the last two (3 and 4) are called common. I want to establish an implicit dependence of common on private, namely that the private variables 1 and 2 depend on 3 and 4. Then I want to derivate the private equations with respect to the common variables.

Thus, I create pointers that point to the correct private or common equation or variables with the loop.
for i from 1 to 2 do
iP[i]:=i:
iC[i]:=i+2;
od:
So that for example, a set of four equations named "phi" phi[1..4] where phi[iP[1]] is the first private equation, and phi[iC[1]] is the first common equation. Hopefully so far I have been clear. I create an alias, and continue to derivate these equations. However, I notice that Maple does not recognize the functions in the diff command if the "pointer" notation is used. I will paste the entire code for you all to look at and maybe you can see where things get "weird". Namely if I write phi[1], is not the same as phi[iP[1]], even though iP[1]:=1 (Both are integers). 

p.s. I have used implicitdiff. It is way too slow and memory inefficient for many equations (hundreds to thousands). So that is why I am trying to find a work-around.

restart:
Digits:=15:
with(LinearAlgebra):

for i from 1 to 2 do
iP[i]:=i:
iC[i]:=i+2;
od:

alias(seq(x[iP[i]]=x[iP[i]](seq(x[iC[j]],j=1..2)),i=1..2)):
alias(seq(seq(dPdC[i,iC[k]]=diff(x[iP[i]](seq(x[iC[j]],j=1..2)),x[iC[k]]),k=1..2),i=1..2));

# Define all (PRIVATE + COMMON) phi expressions.
# 1 and 2 are the PRIVATE equations.
# 3 and 4 are the COMMON equations.
phix[1]:= x[3]**2+x[4]**2:
phix[2]:= x[1]   +x[4]:
phix[3]:= x[1]   +x[3]+x[1]:
phix[4]:= x[1]   +x[3]+x[1]:

for i from 1 to 2   do
f[i]:=x[iP[i]]-phix[iP[i]]:
od:

f[1];

x[1]-phix[1];

print(iP[1],iC[1]);

print(x[iP[1]]-phix[iP[1]],x[iC[1]]);

TEST1:=diff(x[1]-phix[1],x[3]);

TEST2:=diff(f[1],x[3]);

TEST3:=diff(f[1],x[iC[1]]);

TEST4:=diff(x[iP[1]]-phix[iP[1]],x[iC[1]]);

The result is 
      
                     -x[3]^2  - x[4]^2  + x[1]
                      x[1] - x[3]^2  - x[4]^2 
                              1, 3
     
                  -x[3]^2 - x[4]^2  + x[1], x[3]
                      dPdC[1, 3] - 2 x[3]
                            -2 x[3]
                            -2 x[3]
                            -2 x[3]
Where dPdC includes the implicit derivatives, which is the answer I want, but then I am forced to write by hand what the elements are. If I put the expression in a loop with the pointers, then I get the other "TEST" answers, and as you can see, the implicit dependence from alias has been ignored.