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Physics:-Setup(assumingusesAssume = true): causes ...

Asked by: nm 11483
timelimit physics
49 minutes ago
0  0

I found very strange behaviour of Maple 2025.1 on Linux.

Same exact code.  Calling timelimit(sol,ode) twice on two different solutions. If I do not add 

         Physics:-Setup(assumingusesAssume = true)

At the start, then both timelimits finish OK. But once  Physics:-Setup(assumingusesAssume = true) is added at the start, the second timelimit hangs.

I waited 2 hrs and nothing happens. Maple just freezes. Can't even stop the server from worksheet by clicking on the red button at lower left corner. 

This is using latest Physics.  Does anyone know why this happens? It seems due to some memory cache issue?

Make sure to save all your work before trying this just in case you have to kill Maple application.

The strange thing, unable to stop the server by clicking on red button or clicking on RESTART KERNEL icon at top, or even clicking on the debuger icon at lower left corner. Only way was to kill Maple itself from Linux command line.

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1878 and is the same as the version installed in this computer, created 2025, September 28, 11:35 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

restart;

Example 1. Not using Physics:-Setup(assumingusesAssume = true): gives NO hang

 
> 

sol_1:=y(x) = 1/2*(3*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*
sec(_Z)^2-8*3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^2
+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-\
8*3^(1/2))^(2/3))+12*_C2*3^(1/2)+12*3^(1/2)*x+36*I*_C2+36*I*x+6*_Z))^3*3^(1/2)+
9*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8*
3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*
sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^
(2/3))+12*_C2*3^(1/2)+12*3^(1/2)*x+36*I*_C2+36*I*x+6*_Z))^2+3*3^(1/2)*tan(
RootOf(2*3^(1/2)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(1/3)+2)-3^(1/2
)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(2/3)-2*(3*3^(1/2)*tan(_Z)*sec
(_Z)^2-8+9*sec(_Z)^2)^(1/3)+4)+36*I*_C2+36*I*x+12*_C2*3^(1/2)+12*3^(1/2)*x+6*_Z
))+1)^(1/3)*(I*3^(1/2)-1):
ode:=diff(y(x),x)-y(x)^3 = 8:
timelimit(30,odetest(sol_1,ode));

Error, (in simplify/ln/relations) time expired

> 

 

> 

sol_2:=y(x) = -1/2*(3*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)
*sec(_Z)^2-8*3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^
2+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2
-8*3^(1/2))^(2/3))+12*_C3*3^(1/2)+12*3^(1/2)*x-36*I*_C3-36*I*x+6*_Z))^3*3^(1/2)
+9*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8
*3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*
sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^
(2/3))+12*_C3*3^(1/2)+12*3^(1/2)*x-36*I*_C3-36*I*x+6*_Z))^2+3*3^(1/2)*tan(
RootOf(2*3^(1/2)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(1/3)+2)-3^(1/2
)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(2/3)-2*(3*3^(1/2)*tan(_Z)*sec
(_Z)^2-8+9*sec(_Z)^2)^(1/3)+4)-36*I*_C3-36*I*x+12*_C3*3^(1/2)+12*3^(1/2)*x+6*_Z
))+1)^(1/3)*(1+I*3^(1/2)):
timelimit(30,odetest(sol_2,ode));

Error, (in collect) time expired

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Example 2. using Physics:-Setup(assumingusesAssume = true): second timelimit always hangs

 
> 

restart;

> 

Physics:-Setup(assumingusesAssume = true):

> 

sol_1:=y(x) = 1/2*(3*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*
sec(_Z)^2-8*3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^2
+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-\
8*3^(1/2))^(2/3))+12*_C2*3^(1/2)+12*3^(1/2)*x+36*I*_C2+36*I*x+6*_Z))^3*3^(1/2)+
9*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8*
3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*
sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^
(2/3))+12*_C2*3^(1/2)+12*3^(1/2)*x+36*I*_C2+36*I*x+6*_Z))^2+3*3^(1/2)*tan(
RootOf(2*3^(1/2)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(1/3)+2)-3^(1/2
)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(2/3)-2*(3*3^(1/2)*tan(_Z)*sec
(_Z)^2-8+9*sec(_Z)^2)^(1/3)+4)+36*I*_C2+36*I*x+12*_C2*3^(1/2)+12*3^(1/2)*x+6*_Z
))+1)^(1/3)*(I*3^(1/2)-1):
ode:=diff(y(x),x)-y(x)^3 = 8:
timelimit(30,odetest(sol_1,ode));

Error, (in expand) time expired

> 

 

> 

 

> 

#this below will now hang

> 

sol_2:=y(x) = -1/2*(3*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)
*sec(_Z)^2-8*3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^
2+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2
-8*3^(1/2))^(2/3))+12*_C3*3^(1/2)+12*3^(1/2)*x-36*I*_C3-36*I*x+6*_Z))^3*3^(1/2)
+9*tan(RootOf(2*3^(1/2)*ln(2*3^(1/6)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8
*3^(1/2))^(1/3))-3^(1/2)*ln(4*3^(1/3)-2*3^(1/6)*(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*
sec(_Z)^2-8*3^(1/2))^(1/3)+(9*tan(_Z)*sec(_Z)^2+9*3^(1/2)*sec(_Z)^2-8*3^(1/2))^
(2/3))+12*_C3*3^(1/2)+12*3^(1/2)*x-36*I*_C3-36*I*x+6*_Z))^2+3*3^(1/2)*tan(
RootOf(2*3^(1/2)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(1/3)+2)-3^(1/2
)*ln((3*3^(1/2)*tan(_Z)*sec(_Z)^2-8+9*sec(_Z)^2)^(2/3)-2*(3*3^(1/2)*tan(_Z)*sec
(_Z)^2-8+9*sec(_Z)^2)^(1/3)+4)-36*I*_C3-36*I*x+12*_C3*3^(1/2)+12*3^(1/2)*x+6*_Z
))+1)^(1/3)*(1+I*3^(1/2)):
timelimit(30,odetest(sol_2,ode));

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Download hangs_timelimit_with_physics_maple_2025_1_oct_2_2025.mw

 

 

Trying to get the absolute difference between two ...

Asked by: JoyDivisionMan 50
probability-function statistics
1 hour ago
0  0

I have a random variable called Y1, which looks like the following: Y1 = 2*sqrt(1 - x^2)/Pi, on the (-1 < x < 1) interval. This "semicircle" integrates to 1, like other random variables. Random variable Y2 is the same as Y1 above. I want to find the random variable Z, which is equal to the absolute difference of two random variables Y1 and Y2. In other words, I want to find Z = |Y1 - Y2|. Via simulation, I know that |Y1 - Y2| takes on a logrithmic form, but I need to get a mathematical solution of this.

why dsolve gives Error, (in dsolve) this is a bug ...

Asked by: nm 11483
ode dsolve differential-equations
9 hours ago
1  0

Never seen such a message before

Here is MWE, Trace shows it comes from (SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-AttemptFactorization,2)

 

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1878 and is the same as the version installed in this computer, created 2025, September 28, 11:35 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

ode:=diff(y(x),x$2)+3*y(x)+D(y)(3)=0;
IC:=y(1)+4*y(2)+y(4)=0;

diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0

y(1)+4*y(2)+y(4) = 0

> 

dsolve(ode)

x+(1/3)*3^(1/2)*(tan(3^(1/2)*x)-arctan(tan(3^(1/2)*x)))-((1/3)*(D(y(x)))(3)*(1+tan(3^(1/2)*x)^2)^(1/2)+(1+tan(3^(1/2)*x)^2)^(1/2)*y(x))*c__1-c__2 = 0

> 

dsolve([ode,IC])

Error, (in dsolve) this is a bug

> 

tracelast

 dsolve called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], arbitraryconstants = subscripted, atomizenames = true, build = false, numeric = false, type = none
 #(dsolve,80): error

 \`dsolve/IC\` called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = particular and general
 #(\`dsolve/IC\`,53): return procname(_passed,':-usesolutions' =  "general and particular")

 \`dsolve/IC\` called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = general and particular
 #(\`dsolve/IC\`,57): ans := procname(_passed,':-usesolutions = "general"');

 \`dsolve/IC\` called with arguments: [diff(diff(y(x), x), x)+3*y(x)+(D(y))(3) = 0, y(1)+4*y(2)+y(4) = 0], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = general
 #(\`dsolve/IC\`,277): zz := map(op,{\`dsolve/IC/_C\`({ANS[i]},funcs,x,ics)});

 \`dsolve/IC/_C\` called with arguments: {y(x) = -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2)*x)^2)^(1/2)-3^(1/2)*tan(3^(1/2)*x)+3^(1/2)*arctan(tan(3^(1/2)*x))+3*_C[2]-3*x)/((1+tan(3^(1/2)*x)^2)^(1/2)*_C[1])}, {y(x)}, x, [y(1) = _C1, y(2) = _C2, y(4) = -_C1-4*_C2]
 #(\`dsolve/IC/_C\`,1): ans := \`dsolve/IC/_C/do\`(solns,depvars,t,inits,'evaluated_ans', "default",':-giveup = giveup');

 \`dsolve/IC/_C/do\` called with arguments: {y(x) = -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2)*x)^2)^(1/2)-3^(1/2)*tan(3^(1/2)*x)+3^(1/2)*arctan(tan(3^(1/2)*x))+3*_C[2]-3*x)/((1+tan(3^(1/2)*x)^2)^(1/2)*_C[1])}, {y(x)}, x, [y(1) = _C1, y(2) = _C2, y(4) = -_C1-4*_C2], evaluated_ans, default, giveup = giveup, usecansolve = false
 #(\`dsolve/IC/_C/do\`,103): csol := [\`ODEtools/Solve/EnvDropMultiplicity\`(eqns,consts)];

 \`ODEtools/Solve/EnvDropMultiplicity\` called with arguments: {-(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_C[2]-3)/((1+tan(3^(1/2))^2)^(1/2)*_C[1]) = _C1, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_C[2]-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_C[1]) = _C2, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_C[2]-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_C[1]) = -_C1-4*_C2}, {_C1, _C2, _C[1], _C[2]}, keepalreadysolveduntouched = false, removelabel = false
 #(\`ODEtools/Solve/EnvDropMultiplicity\`,29): sol := :-solve(ee,X,_rest)

 solve called with arguments: {-(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_C[2]-3)/((1+tan(3^(1/2))^2)^(1/2)*_C[1]) = _C1, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_C[2]-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_C[1]) = _C2, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_C[2]-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_C[1]) = -_C1-4*_C2}, {_C1, _C2, _C[1], _C[2]}, AllSolutions = FAIL, ConditionalSolutions = FAIL, DropMultiplicity = FAIL, Explicit = FAIL, MaxSols = FAIL, SolveOverReals = FAIL, SymbolicSolutions = true, TryHard = FAIL, UseAssumptions = false, domain = default, parameters = {}, parametric = false, split = false, useunits = FAIL
 #(solve,133): _MaxSols := oldmaxsols

 Engine:-Main called with arguments: {-(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_C[2]-3)/((1+tan(3^(1/2))^2)^(1/2)*_C[1]) = _C1, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_C[2]-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_C[1]) = _C2, -(1/3)*(_C[1]*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_C[2]-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_C[1]) = -_C1-4*_C2}, {}, {_C1, _C2, _C[1], _C[2]}
 #(SolveTools:-Engine:-Main,37): sol := [SolveTools:-PolynomialSystem(eqns,vars,ineqs,':- maxsols' = \`if\`(type([_MaxSols],[{integer, infinity}]) and 0 < _MaxSols,_MaxSols,100))]

 PolynomialSystem:-ModuleApply called with arguments: {-(1/3)*(_X000003*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_X000004-3)/((1+tan(3^(1/2))^2)^(1/2)*_X000003) = _X000001, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_X000004-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_X000003) = _X000002, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_X000004-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_X000003) = -_X000001-4*_X000002}, {_X000001, _X000002, _X000003, _X000004}, {}, FAIL, backsubstitute = true, domain = absolute, engine = default, explicit = false, maxsols = 100, preprocess = true, preservelabels = false, tryhard = true
 #(SolveTools:-PolynomialSystem:-ModuleApply,15): sol := SolveTools:-PolynomialSystem:-Main(SolveTools:-Utilities:-New( equations,notz,SolveTools:-Utilities:-Intersect(vars,indets(equations ))),':-backsub' = reallybacksub,':-domain' = domain,':-maxsols' =  realmaxsols,':-engine' = engine,':-preprocess' = preprocess,':- tryhard' = tryhard);

 PolynomialSystem:-Main called with arguments: [{-(1/3)*(_X000003*(D(_Z))(3)*(1+tan(3^(1/2))^2)^(1/2)-3^(1/2)*tan(3^(1/2))+3^(1/2)*(3^(1/2)-Pi)+3*_X000004-3)/((1+tan(3^(1/2))^2)^(1/2)*_X000003)-_X000001, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(2*3^(1/2))^2)^(1/2)-3^(1/2)*tan(2*3^(1/2))+3^(1/2)*(2*3^(1/2)-Pi)+3*_X000004-6)/((1+tan(2*3^(1/2))^2)^(1/2)*_X000003)-_X000002, -(1/3)*(_X000003*(D(_Z))(3)*(1+tan(4*3^(1/2))^2)^(1/2)-3^(1/2)*tan(4*3^(1/2))+3^(1/2)*(4*3^(1/2)-2*Pi)+3*_X000004-12)/((1+tan(4*3^(1/2))^2)^(1/2)*_X000003)+_X000001+4*_X000002}, {3*(1+tan(3^(1/2))^2)^(1/2)*_X000003 <> 0, 3*(1+tan(2*3^(1/2))^2)^(1/2)*_X000003 <> 0, 3*(1+tan(4*3^(1/2))^2)^(1/2)*_X000003 <> 0}, {_X000001, _X000002, _X000003, _X000004}, {}, true, false, 1, {_X000001, _X000002, _X000003, _X000004}], backsub = true, domain = absolute, engine = default, maxsols = 100, preprocess = true, tryhard = true
 #(SolveTools:-PolynomialSystem:-Main,86): sol := [SolveTools:-PolynomialSystemSolvers:- PseudoResultant(SolveTools:-Utilities:- GetEquations(sys),SolveTools:-Utilities:- GetVariables(sys),SolveTools:-Utilities:- GetInequations(sys),':-maxsols' = maxsols,':- tryhard' = tryhard)];

 PseudoResultant:-ModuleApply called with arguments: {(_X000003*(D(_Z))(3)*(-2*cos(3^(1/2))+1+sec(3^(1/2)))+3*_X000001*_X000003*(-2*cos(3^(1/2))+sec(3^(1/2)))+3*_X000002*_X000003+3^(1/2)*tan(3^(1/2)))/cos(2*3^(1/2)), -(sec(4*3^(1/2))+sec(3^(1/2)))*_X000003*(D(_Z))(3)+3*(sec(4*3^(1/2))-sec(3^(1/2)))*_X000001*_X000003+12*_X000002*sec(4*3^(1/2))*_X000003+3^(1/2)*Pi+3^(1/2)*tan(4*3^(1/2))-3^(1/2)*tan(3^(1/2))}, {_X000001, _X000002, _X000003}, {_X000003 <> 0}, backsub = true, maxsols = 100, tryhard = true
 #(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-ModuleApply,25): SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-ApplySubstitution ({},[],numer(tm1),notzero union map(xx -> denom(xx) <> 0,tm1), unknowns);

 ApplySubstitution called with arguments: {}, [], {_X000003*(D(_Z))(3)*sec(3^(1/2))+3*_X000001*sec(3^(1/2))*_X000003-2*_X000003*(D(_Z))(3)*cos(3^(1/2))-6*_X000001*_X000003*cos(3^(1/2))+3^(1/2)*tan(3^(1/2))+_X000003*(D(_Z))(3)+3*_X000002*_X000003, -_X000003*(D(_Z))(3)*sec(4*3^(1/2))+3*_X000001*sec(4*3^(1/2))*_X000003+12*_X000002*sec(4*3^(1/2))*_X000003+3^(1/2)*Pi+3^(1/2)*tan(4*3^(1/2))-_X000003*(D(_Z))(3)*sec(3^(1/2))-3*_X000001*sec(3^(1/2))*_X000003-3^(1/2)*tan(3^(1/2))}, {1 <> 0, _X000003 <> 0, cos(2*3^(1/2)) <> 0}, {_X000001, _X000002, _X000003}
 #(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-ApplySubstitution,48): eqns := map(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:- AttemptFactorization,eqns,not0,unknowns);

 AttemptFactorization called with arguments: _X000003*(D(_Z))(3)*sec(3^(1/2))+3*_X000001*sec(3^(1/2))*_X000003-2*_X000003*(D(_Z))(3)*cos(3^(1/2))-6*_X000001*_X000003*cos(3^(1/2))+3^(1/2)*tan(3^(1/2))+_X000003*(D(_Z))(3)+3*_X000002*_X000003, {_X000003 <> 0, cos(2*3^(1/2)) <> 0}, {_X000001, _X000002, _X000003}
 #(SolveTools:-PolynomialSystemSolvers:-PseudoResultant:-AttemptFactorization,2): error \`this is a bug\`

Error, (in dsolve) this is a bug

 locals defined as: e = e

> 

 


 

Download dsolve_error_this_is_bug_2025_1_oct_2_2025.mw

Note that changing the IC to IC:=y(1)+4*y(2)=0; makes it work with no error.

It is only when adding y(4) does the error shows up.

update Bug report emailed to Maplesoft.

 

 

Installation Maple and Mathematica...

Asked by: Hajra Abid 5
mathematica
15 hours ago
0  0

Hi! how I install Maple 2025 and Mathematica in my laptop?
Provide me Complete Set-up.

system with specified initial conditions...

Asked by: Muhsintahsin 15
ode homework dsolve
September 30 2025
0  1

How can we determine the solution of the  system

Udot1 := -beta*V;
Vdot1 := beta*U;
Pdot1 := Q;
Qdot1 := 0;

and with initial conditions 

 U(0) := U[0];
V(0) := V[0];
P(0) := P[0];
Q(0) := Q[0];

Ode1.mw

What do you think about this suggestion?...

Asked by: sand15 1052
policy
September 30 2025
2  6

I feel that it is increasingly common for answers to generate no reaction from their authors.

Perhaps the author simply voted up... but in that case, would it be possible to indicate this (something like "XXX voted up")? 

This would avoid wasting time responding to the same author in the future, as it doesn't seem to care about commenting the answer.

Assignment of ScientificConstants names in a loop...

Asked by: lemelinm 1545
assignment scientificconstants
September 29 2025
1  7

I want to load some specific constants at the beginning of my document. I load the ScientificConstants package first. Then I use a list of names of the constants I need. But the assignation in the loop does not work. Only the value and the units appear in the list, but they are not assigned to the letter. See the document included for more details.   Using_the_constants_.mw

Thank you in advance for your help

Mario

indeterminates of an expression containing undefin...

Asked by: djc 576
undefined indets indeterminates
September 29 2025
1  3


I would like to find the indeterminates of the following expression:

K:=2*x+I*y/Pi+Catalan*5-g(infinity)+f(undefined);

# I expect to get x an y.

indets(K,And(name,Not(constant)));
# answer: {x, y, undefined} I surprised at undefined.

indets(K,'name &under evalf');
#answer {x, y} it is correct.

μ₁ and μ₂ conditions in constrained optimization...

Asked by: Andiguys 85
optimization lagrange-multipliers duplicate-question
September 29 2025
0  10

I am optimizing an objective function subject to two constraints. I have obtained the solution, but I am unsure how to determine the conditions for the Lagrange multipliers μ1​ and μ2​. For example, using the KKT conditions, if μ1>0 then the solution is X, and if μ2>0 then the solution is Y. Could you guide me on how to find μ1 and μ2 along with their corresponding conditions?

> 

restart
> 

with(Optimization); with(plots); with(LinearAlgebra)
> 

_local(Pi)

Pi

 (1)
 
> 

`&pi;_m` := proc (i1) options operator, arrow; (w-i1)*(1/2+(1/2)*(i1-i2)/tau)*(1-(Pn-Pr)/(1-delta))-C0-(1/2)*Cr*(1/2+(1/2)*(i1-i2)/tau)^2*(1-(Pn-Pr)/(1-delta))^2+Ce*rho0*(1-(Pn-Pr)/(1-delta)) end proc
> 

C1 := (2*rho0-1)*tau+i2 <= i1

(2*rho0-1)*tau+i2 <= i1

 (2)
> 

C2 := i1 <= tau+i2

i1 <= tau+i2

 (3)
> 

NULL
> 

NULL
> 

``
> 

NULL
> 

# No equality constraints
#
# Inequality constraints must be of the form f[i](i1) <= 0
#
# Thus
#
# (1) For C1
#     so
      f[1] := (i1) -> (2*rho0 - 1)*tau + i2-i1:
      
#
# (2) C2
#     so
      f[2] := (i1) -> i1-(tau + i2):
      
#
> 

# Lagrangian (we want to maximize `&pi;_m` so to minimize -`&pi;_m`

L := -`&pi;_m`(i1) + add(f[i](i1)*mu[i], i=1..2):
> 

dLdi1 := collect(diff(L, i1), [i1]):
> 

KKT_conditions := [
                    seq(mu[i] >= 0, i=1..2),         # Dual feasibility conditions
                    dLdi1 = 0,                       # Stationarity condition
                    seq(``(f[i](i1)) <= 0, i=1..2),  # Primal feasibility conditions
                    add(mu[i]*f[i](i1) = 0, i=1..2)  # Complementary slackness
                  ]:

print~(KKT_conditions);

0 <= mu[1]

  

0 <= mu[2]

  

((1-(Pn-Pr)/(1-delta))/tau+(1/4)*Cr*(1-(Pn-Pr)/(1-delta))^2/tau^2)*i1+(1/2-(1/2)*i2/tau)*(1-(Pn-Pr)/(1-delta))-(1/2)*w*(1-(Pn-Pr)/(1-delta))/tau+(1/2)*Cr*(1/2-(1/2)*i2/tau)*(1-(Pn-Pr)/(1-delta))^2/tau-mu[1]+mu[2] = 0

  

``((2*rho0-1)*tau+i2-i1) <= 0

  

``(i1-tau-i2) <= 0

  

((2*rho0-1)*tau+i2-i1)*mu[1]+(i1-tau-i2)*mu[2] = 0

  

[]

 (4)


Analysis of dLdp1

> 

with(LargeExpressions):

DLDi1 := collect(dLdi1, i1, Veil[K]);

(1/4)*K[1]*i1-(1/4)*K[2]

 (5)
> 

# Thus dLdi1 = 0 verifies

isolate((5), i1)
 

i1 = K[2]/K[1]

 (6)
> 

# Where K1 and K2 are

i := 'i':
KS := [ seq(K[i] = Unveil[K](K[i]), i=1..LastUsed[K] ) ];

[K[1] = (-1+delta+Pn-Pr)*(Cr*Pn-Cr*Pr+Cr*delta+4*delta*tau-Cr-4*tau)/(tau^2*(-1+delta)^2), K[2] = (4*delta^2*tau^2*mu[1]-4*delta^2*tau^2*mu[2]+Cr*Pn^2*i2-Cr*Pn^2*tau-2*Cr*Pn*Pr*i2+2*Cr*Pn*Pr*tau+2*Cr*Pn*delta*i2-2*Cr*Pn*delta*tau+Cr*Pr^2*i2-Cr*Pr^2*tau-2*Cr*Pr*delta*i2+2*Cr*Pr*delta*tau+Cr*delta^2*i2-Cr*delta^2*tau+2*Pn*delta*i2*tau-2*Pn*delta*tau^2+2*Pn*delta*tau*w-2*Pr*delta*i2*tau+2*Pr*delta*tau^2-2*Pr*delta*tau*w+2*delta^2*i2*tau-2*delta^2*tau^2+2*delta^2*tau*w-8*delta*tau^2*mu[1]+8*delta*tau^2*mu[2]-2*Cr*Pn*i2+2*Cr*Pn*tau+2*Cr*Pr*i2-2*Cr*Pr*tau-2*Cr*delta*i2+2*Cr*delta*tau-2*Pn*i2*tau+2*Pn*tau^2-2*Pn*tau*w+2*Pr*i2*tau-2*Pr*tau^2+2*Pr*tau*w-4*delta*i2*tau+4*delta*tau^2-4*delta*tau*w+4*tau^2*mu[1]-4*tau^2*mu[2]+Cr*i2-Cr*tau+2*i2*tau-2*tau^2+2*tau*w)/(tau^2*(-1+delta)^2)]

 (7)


Analysis of the two constraints

> 

beta

beta

 (8)
> 

Cs := { seq(beta[i] = subs(i1=0, f[i](i1)), i=1..2) };

{beta[1] = (2*rho0-1)*tau+i2, beta[2] = -tau-i2}

 (9)
> 

 

> 

# two constraints problem

Cmin_value := min(rhs~(Cs));  # the "true" constraints
Cmax_value := max(rhs~(Cs)):

Cmin_name  := min(lhs~(Cs));  # the "abstract" constraints
Cmax_name  := max(lhs~(Cs)):

Cmin_name  := LowerBound;  # and an even more abstract form
Cmax_name  := UpperBound:

Complementary_Slackness := mu[1]*(Cmin_name-i1) , mu[2]*(i1-Cmax_name);

L2     := -`&pi;_m`(i1) + add(Complementary_Slackness):
dL2di1 := diff(L2, i1):
dL2di1 := map(simplify, %, size);
 

min(-tau-i2, (2*rho0-1)*tau+i2)

  

min(beta[1], beta[2])

  

LowerBound

  

mu[1]*(LowerBound-i1), mu[2]*(i1-UpperBound)

  

(1/2)*(tau+i1-i2)*(-1+delta+Pn-Pr)/(tau*(-1+delta))+(1/2)*(-w+i1)*(-1+delta+Pn-Pr)/(tau*(-1+delta))+(1/4)*Cr*(tau+i1-i2)*(-1+delta+Pn-Pr)^2/(tau^2*(-1+delta)^2)-mu[1]+mu[2]

 (10)
> 

type(dL2di1, linear([i1, seq(mu[i], i=1..2)]));

SC_CS_sols := solve(
  {
    dL2di1 = 0,
    op([Complementary_Slackness] =~ 0)
  }
  ,
  {i1, seq(mu[i], i=1..2)}
):

true

  

Main: Entering solver with 3 equations in 3 variables
Main: attempting to solve as a linear system
Main: attempting to solve as a polynomial system
Main: Polynomial solver successful. Exiting solver returning 1 solution

  
> 

# How many solutions did we get?

numelems([SC_CS_sols]);

# And those solutions are charecterized by

map(s -> if eval(lambda[1], s) = 0 then
           if eval(lambda[2], s) = 0 then
             "i1 belongs to interval (LowerBound, UpperBound)"
           else
             "i1 is equal to the UpperBound"
           end if
         else
           "i1 is equal to the LowerBound"
         end if
         , [SC_CS_sols]);

# So we get as expected the three possible situations.

3

  

["i1 is equal to the LowerBound", "i1 is equal to the LowerBound", "i1 is equal to the LowerBound"]

 (11)
> 

Cmin_value

min(-tau-i2, (2*rho0-1)*tau+i2)

 (12)
 

 

Download I_1_Optimum_condition.mw

why i can't get same parameter ? ...

Asked by: salim-barzani 1645
ode special-function differential-equations
September 28 2025
1  3

in here  for jacobieliptic i got two lambda[0] same as paper did but in second one is different and is true make my ode be zero, but is so different from paper 

test-Dr.D.mw

Normal form and limit cycle?...

Asked by: Muhsintahsin 15
ode homework limit
September 28 2025
3  2

In this maple file i try to find normal form and limit cycle of this jerk system but l don't know find like a paper did?

av.mw

DrawGraph and export as 300 dpi png...

Asked by: vs140580 500
graphtheory export drawgraph
September 28 2025
1  3

DrawGraph(Graph({[{1, 2}, 0.7462761011], [{2, 3}, 0.8190708767], [{2, 4}, 0.6810933318], [{4, 5}, 0.7451261104], [{4, 23}, 0.6746390886], [{5, 6}, 0.7231256359], [{6, 7}, 0.6775594149], [{6, 10}, 0.7019893588], [{7, 8}, 0.6618796622], [{7, 9}, 0.6623496808], [{8, 9}, 0.6688297164], [{10, 11}, 0.7092623872], [{10, 22}, 0.7112560850], [{11, 12}, 0.7098970677], [{12, 13}, 0.7108845941], [{12, 19}, 0.7092202631], [{13, 14}, 0.6734297238], [{13, 18}, 0.6767541419], [{14, 15}, 0.6466191140], [{15, 16}, 0.6773709292], [{16, 17}, 0.6780410682], [{17, 18}, 0.6468993314], [{19, 20}, 0.7444847640], [{19, 21}, 0.7192676187], [{21, 22}, 0.7167453581], [{22, 23}, 0.6726943362], [{23, 24}, 0.8156746068]}), layout = spring)

DrawGraph and save that as 300 dpi png increase edge length so that the edge weight show up How do the edge are small sized and weights overlap and and are not neatly seen in the middle of edge without overlap kind help with a code to correct this

Comparing two identical Matrices or Vectors...

Asked by: Geoff 40
matrix
September 28 2025
1  5

Why can't Maple compare two identical matrices or vectors?

Incorrect calculation of limits...

Asked by: mthkvv 180
ellipticpi limit
September 27 2025
1  3

Hi there.

There is an issue with following limits in Maple 2025:

Maple returned an incorrect zero answers. Plotting functions we see that non-zero limits do exist:

Thank you.

limits.mw

simplify((D@@2)(y)(Pi) = 0) fail when adding Physi...

Asked by: nm 11483
simplify diff physics
September 27 2025
3  3

Another very serious bug in Maple.

I have code that simplifies intitial conditions passed.

I found that simplify((D@@2)(y)(Pi) = 0) gives error 

Error, (in unknown) invalid input: diff received Pi, which is not valid for its 2nd argument

but Pi is constant. It works for any other values other than Pi.

This only happens when adding Physics:-Setup(assumingusesAssume = true):

Any idea why this happens?

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1877 and is the same as the version installed in this computer, created 2025, July 11, 19:24 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

simplify((D@@2)(y)(Pi) = 0)

((D@@2)(y))(Pi) = 0

> 

Physics:-Setup(assumingusesAssume = true):
> 

simplify((D@@2)(y)(Pi) = 0)

Error, (in unknown) invalid input: diff received Pi, which is not valid for its 2nd argument

 

 

Download simplify_fail_when_adding_physics_sept_27_2025.mw

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