MaplePrimes Questions

I want to export plots as PNG but found in the past that when using commands to automate the process (and explicitly controlling for image quality) some symbolic notation on the axes or in the plots themselves are translated to 1D.

Anyway, regardless of the reason just provided, I have a preference for exporting plots as PNG manually rather than automatically in some of my scripts. How to do this while ensuring the best quality? By default, manual exports into PNG have quite bad quality. 

I was wondering why Maple do not give this simpler solution to this ode. It solves it as exact. But if solved as separable, the solution is much simpler.

I solved this by hand and Maple verifies my solution. You can see the separable solution is much simpler. Any tricks to make Maple gives the simpler solution?

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

ode:=diff(y(x),x)^4+f(x)*(y(x)-a)^3*(y(x)-b)^3*(y(x)-c)^2 = 0;

(diff(y(x), x))^4+f(x)*(y(x)-a)^3*(y(x)-b)^3*(y(x)-c)^2 = 0

infolevel[dsolve]:=5;
sol:=dsolve(ode);
odetest(sol,ode);

5

Methods for first order ODEs:

-> Solving 1st order ODE of high degree, 1st attempt

trying 1st order WeierstrassP solution for high degree ODE

trying 1st order WeierstrassPPrime solution for high degree ODE

trying 1st order JacobiSN solution for high degree ODE

trying 1st order ODE linearizable_by_differentiation

trying differential order: 1; missing variables

trying simple symmetries for implicit equations

--- Trying classification methods ---

trying homogeneous types:

trying exact

<- exact successful

Intat(1/((_a-c)^(1/2)*(_a-b)^(3/4)*(_a-a)^(3/4)), _a = y(x))+Intat(-(-f(_a)*(-y(x)+c)^2*(-y(x)+b)^3*(-y(x)+a)^3)^(1/4)/((y(x)-c)^(1/2)*(y(x)-b)^(3/4)*(y(x)-a)^(3/4)), _a = x)+c__1 = 0

0

mysol:=Intat(1/( (_a-c)^(2/3)*(_a-b)*(_a-a))^(3/4),_a = y(x))=Intat( (-f(_a))^(1/4),_a=x)+_C1;
odetest(mysol,ode)

Intat(1/((_a-c)^(2/3)*(_a-b)*(_a-a))^(3/4), _a = y(x)) = Intat((-f(_a))^(1/4), _a = x)+c__1

0


 

Download why_not_this_simpler_solution.mw

Hand solution

Maple 2024

Hi

A padel group organises doubles tournaments with the following structure: 16 players participate in four rounds, with each round consisting of four doubles matches. Players switch partners after each round.

So what I require is some code to generate the first round matches, the second round, the third, the nth .....

note the worksheet I bastardised from Tom Leslie's work. 

2_man_teams_doubles.mw

it took me hrs to find this as my solution was failing verification and I did not know why.

What logic do you think Maple used to simplify this:

expr:=sqrt(1 + sin(x))/x;
simplify(expr)

To this

How could the above be simpler than

?

Compare to Mathematica

And this is what I expected. I am now scared to use simplify in Maple as I do not know what I will get back.

Is there a way to tell Maple not to do such strange "simplification"? I am doing this in code, and the code does not know what the expression is.

To see an example of the side effect of this, here is one, where if solution to an ode is simplified first, it no longer verifies by odetest without adding extra assumptions:


 

155324

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

restart;

155324

ode:=diff(y(x),x)=(cos(x)-2*x*y(x)^2)/(2*x^2*y(x));
sol:=dsolve([ode,y(Pi)=1/Pi]);
odetest(sol,ode);

diff(y(x), x) = (1/2)*(cos(x)-2*x*y(x)^2)/(x^2*y(x))

y(x) = (sin(x)+1)^(1/2)/x

0

odetest(simplify(sol),ode);

(1/4)*cos(x)*2^(1/2)*csgn(cos((1/2)*x)+sin((1/2)*x))^2*csgn(1, (1/2)*2^(1/2)*(cos((1/2)*x)+sin((1/2)*x)))/x

One does not expect that simplified solution no longer verfiies the ode.

Sure, I can do

          odetest(simplify(sol),ode) assuming real;

and now it gives 0. But the point is that the first one did not need assumptions.

Download simplify_with_odetest.mw

Maple 2024 on windows 10.

I am trying to tidy up cases where a proc returns multiple values. Have being trying Tabulate. I can get it to work when called after the results are returned. I would the procedure to do this but  keep acces to the name(s) assigned to the returned values.

A,B,C:= proc(...)  .....  return a, b, c    end proc. 

So basically display a tabulated of a, b, c.
 

restart

 

QQFProj := proc(q12::algebraic, q23::algebraic, q34::algebraic, q14::algebraic,{columns:=[QQFproj,Q13proj,Q24proj]},prnt::boolean:=true)
description "Projective quadruple quad formula and intermediate 13 and 24 quads. Useful for cyclic quadrilaterals";
local qqf,q13,q24, sub1,sub2,sub3, R;
#uses  DT = DocumentTools;
sub1:= (q12 + q23 + q34 + q14)^2 - 2*(q12^2 + q23^2 + q34^2 + q14^2) ;
sub2:=-4*(q12*q23*q34+q12*q23*q14+q12*q34*q14+q23*q34*q14)+8*q12*q23*q34*q14;
sub3:=64*q12*q23*q34*q14*(1-q12)*(1-q23)*(1-q34)*(1-q14);
qqf:=(sub1+sub2)^2=sub3;
q13:=((q12-q23)^2-(q34-q14)^2)/(2*(q12+q23-q34-q14-2*q12*q23+2*q34*q14));#check this
q24:=((q23-q34)^2-(q12-q14)^2)/(2*(q23+q34-q12-q14-2*q23*q34+2*q12*q14));#check this
#if prnt then
#return [columns,[qqf,q13,q24]];


if prnt then
print(cat(" ",columns[1],"    ",columns[2],"     ",columns[3])) ;
end if;
return qqf ,q13,q24


 end proc:

q12:=1/2:q23:=9/10:q34:=25/26:q41:=9/130: #Cyclic quadrilateral
 AA:=QQFProj(q12,q23,q34,q41,true);


AA[1];
AA[2];
AA[3]

" QQFproj    Q13proj     Q24proj"

 

9801/2856100 = 9801/2856100, 4/5, 16/65

 

9801/2856100 = 9801/2856100

 

4/5

 

16/65

(1)

# Can the below be built into the proc to nicely didplay the results but maintain access to the results as shown when prnt=true.

columns:=[QQFproj,Q13proj,Q24proj]:
BB:=QQFProj(q12,q23,q34,q41,false):
DocumentTools:-Tabulate([columns,[BB]],width=55):#could do with a variable width depending on length of output epression.

BB[1];
BB[2];
BB[3]

9801/2856100 = 9801/2856100

 

4/5

 

16/65

(2)

dspformat:=(BB,columns)->DocumentTools:-Tabulate([columns,[BB]],width=75);

proc (BB, columns) options operator, arrow; DocumentTools:-Tabulate([columns, [BB]], width = 75) end proc

(3)

CC:=dspformat(BB,columns):#layout not as expected

CC[1] ; #  just gives  letters from Tabulate

"T"

(4)

 


 

Download 2024-03-18_Q_Format_Returned_Results_into_a_Table..mw

Hi,

I calculate the standard deviation using Maple, which differs from the standard deviation obtained by the calculator (TI). Can you provide an explanation for this difference?

Thanks

StDevQ.mw

I am trying to get Maple to simplify the following trigonometric expressions (for "generic" parameters) as much as possible

sineExpr(3) := (
   sin(a[2] - b[1])*sin(a[3] - b[1]))/(
   sin(b[2] - b[1])*sin(b[3] - b[1]))*sin(a[1] - b[1]) + (
   sin(a[3] - b[2])*sin(a[1] - b[2]))/(
   sin(b[3] - b[2])*sin(b[1] - b[2]))*sin(a[2] - b[2]) + (
   sin(a[1] - b[3])*sin(a[2] - b[3]))/(
   sin(b[1] - b[3])*sin(b[2] - b[3]))*sin(a[3] - b[3]);
 = 
   (('RealDomain:-sin'(a[2]-b[1])*'RealDomain:-sin'(a[3]-b[1]))/('RealDomain:-sin'(b[2]-b[1])*'RealDomain:-sin'(b[3]-b[1])))&*'RealDomain:-sin'(a[1]-b[1])+(('RealDomain:-sin'(a[3]-b[2])*'RealDomain:-sin'(a[1]-b[2]))/('RealDomain:-sin'(b[3]-b[2])*'RealDomain:-sin'(b[1]-b[2])))&*'RealDomain:-sin'(a[2]-b[2])+(('RealDomain:-sin'(a[1]-b[3])*'RealDomain:-sin'(a[2]-b[3]))/('RealDomain:-sin'(b[1]-b[3])*'RealDomain:-sin'(b[2]-b[3])))&*'RealDomain:-sin'(a[3]-b[3])


sineExpr(4) := (
   sin(a[2] - b[1])*sin(a[3] - b[1])*sin(a[4] - b[1]))/(
   sin(b[2] - b[1])*sin(b[3] - b[1])*sin(b[4] - b[1]))*
   sin(a[1] - b[1]) + (
   sin(a[3] - b[2])*sin(a[4] - b[2])*sin(a[1] - b[2]))/(
   sin(b[3] - b[2])*sin(b[4] - b[2])*sin(b[1] - b[2]))*
   sin(a[2] - b[2]) + (
   sin(a[4] - b[3])*sin(a[1] - b[3])*sin(a[2] - b[3]))/(
   sin(b[4] - b[3])*sin(b[1] - b[3])*sin(b[2] - b[3]))*
   sin(a[3] - b[3]) + (
   sin(a[1] - b[4])*sin(a[2] - b[4])*sin(a[3] - b[4]))/(
   sin(b[1] - b[4])*sin(b[2] - b[4])*sin(b[3] - b[4]))*
   sin(a[4] - b[4]);
 = 
(('RealDomain:-sin'(a[2]-b[1])*'RealDomain:-sin'(a[3]-b[1])*'RealDomain:-sin'(a[4]-b[1]))/('RealDomain:-sin'(b[2]-b[1])*'RealDomain:-sin'(b[3]-b[1])*'RealDomain:-sin'(b[4]-b[1])))&*'RealDomain:-sin'(a[1]-b[1])+(('RealDomain:-sin'(a[3]-b[2])*'RealDomain:-sin'(a[4]-b[2])*'RealDomain:-sin'(a[1]-b[2]))/('RealDomain:-sin'(b[3]-b[2])*'RealDomain:-sin'(b[4]-b[2])*'RealDomain:-sin'(b[1]-b[2])))&*'RealDomain:-sin'(a[2]-b[2])+(('RealDomain:-sin'(a[4]-b[3])*'RealDomain:-sin'(a[1]-b[3])*'RealDomain:-sin'(a[2]-b[3]))/('RealDomain:-sin'(b[4]-b[3])*'RealDomain:-sin'(b[1]-b[3])*'RealDomain:-sin'(b[2]-b[3])))&*'RealDomain:-sin'(a[3]-b[3])+(('RealDomain:-sin'(a[1]-b[4])*'RealDomain:-sin'(a[2]-b[4])*'RealDomain:-sin'(a[3]-b[4]))/('RealDomain:-sin'(b[1]-b[4])*'RealDomain:-sin'(b[2]-b[4])*'RealDomain:-sin'(b[3]-b[4])))&*'RealDomain:-sin'(a[4]-b[4])

So far, all of my attempts have failed: 
 

restart:

kernelopts('version');

Physics:-Version();

`Maple 2024.0, X86 64 WINDOWS, Mar 01 2024, Build ID 1794891`

 

`The "Physics Updates" version in the MapleCloud is 1701 and is the same as the version installed in this computer, created 2024, March 17, 17:24 hours Pacific Time.`

(1)

sineExpr := proc (m::posint) options operator, arrow; add(mul(ifelse(j <> t, (':-sin')(a[j]-b[t])/(':-sin')(b[j]-b[t]), (':-sin')(a[t]-b[t])), j = 1 .. m), t = 1 .. m) end proc

Warning, (in sineExpr) `t` is implicitly declared local

 

Warning, (in sineExpr) `j` is implicitly declared local

 

Warning, (in sineExpr) `t` is implicitly declared local

 

Warning, (in sineExpr) `j` is implicitly declared local

 

combine(simplify(normal(sineExpr(1), expanded), trig), trig);

sin(a[1]-b[1])

(2)

combine(simplify(normal(sineExpr(2), expanded), trig), trig); # which can be transformed into sin((a[1]+a[2])-(b[1]+b[2])) only in certain legacy versions!

-(1/2)*(cos(-2*b[2]+a[1]+a[2])-cos(-2*b[1]+a[1]+a[2]))/sin(b[1]-b[2])

(3)

combine(simplify(normal(sineExpr(3), expanded), trig), trig);

(1/2)*(cos(-b[1]-3*b[2]+b[3]+a[2]+a[3]+a[1])-cos(b[1]-3*b[2]-b[3]+a[2]+a[3]+a[1])-cos(-b[1]-3*b[3]+a[2]+a[3]+a[1]+b[2])+cos(b[1]-3*b[3]-b[2]+a[2]+a[3]+a[1])+cos(-3*b[1]+a[2]+a[3]+a[1]+b[2]-b[3])-cos(-3*b[1]+a[2]+a[3]+a[1]-b[2]+b[3]))/(sin(-2*b[2]+2*b[1])-sin(-2*b[3]+2*b[1])+sin(2*b[2]-2*b[3]))

(4)

CodeTools:-Usage(combine(simplify(normal(sineExpr(4), expanded), trig), trig));

memory used=244.67MiB, alloc change=0 bytes, cpu time=6.17s, real time=5.49s, gc time=1000.00ms

 

(1/2)*(sin(-2*a[3]+4*a[4]+2*a[2]-b[3]-b[4]-b[2]-b[1])-sin(4*a[2]-2*a[4]-b[3]-b[4]-b[2]-b[1]+2*a[1])+sin(-2*a[2]-b[3]-b[4]-b[2]-b[1]+4*a[4]+2*a[1])+sin(-2*a[2]+b[3]+b[4]+b[2]+b[1]-4*a[4]+2*a[1])+sin(-b[3]-b[4]-b[2]-b[1]+4*a[1]-2*a[3]+2*a[4])-sin(4*a[3]-2*a[4]+2*a[2]-b[3]-b[4]-b[2]-b[1])-sin(-4*a[3]-2*a[4]+2*a[2]+b[3]+b[4]+b[2]+b[1])+sin(-2*a[3]-4*a[4]+2*a[2]+b[3]+b[4]+b[2]+b[1])-sin(-2*a[3]+2*a[4]+4*a[2]-b[3]-b[4]-b[2]-b[1])+sin(-4*a[3]+b[3]+b[4]+b[2]+b[1]-2*a[4]+2*a[1])-sin(4*a[4]-2*a[3]-b[3]-b[4]-b[2]-b[1]+2*a[1])-sin(-2*a[2]-b[3]-b[4]-b[2]-b[1]+4*a[3]+2*a[1])-sin(-2*a[2]+b[3]+b[4]+b[2]+b[1]-4*a[3]+2*a[1])+sin(2*a[3]-2*a[4]+4*a[2]-b[3]-b[4]-b[2]-b[1])-sin(-4*a[2]-2*a[4]+b[3]+b[4]+b[2]+b[1]+2*a[1])+sin(4*a[3]-b[3]-b[4]-b[2]-b[1]-2*a[4]+2*a[1])-sin(-b[3]-b[4]-b[2]-b[1]+4*a[1]+2*a[3]-2*a[4])-sin(-b[3]-b[4]-b[2]-b[1]+4*a[1]+2*a[4]-2*a[2])+sin(-b[3]-b[4]-b[2]-b[1]+4*a[1]-2*a[4]+2*a[2])+sin(-b[3]-b[4]-b[2]-b[1]+4*a[1]+2*a[3]-2*a[2])-sin(-b[3]-b[4]-b[2]-b[1]+4*a[1]-2*a[3]+2*a[2])-sin(-4*a[4]-2*a[3]+b[3]+b[4]+b[2]+b[1]+2*a[1])+sin(4*a[2]-2*a[3]-b[3]-b[4]-b[2]-b[1]+2*a[1])+sin(-4*a[2]-2*a[3]+b[3]+b[4]+b[2]+b[1]+2*a[1]))/(cos(a[1]-a[2]-3*a[3]+3*a[4])-cos(a[1]-a[2]+3*a[3]-3*a[4])+cos(-3*a[2]-a[3]+a[4]+3*a[1])-cos(-3*a[2]+a[3]-a[4]+3*a[1])-cos(a[1]+3*a[2]-3*a[3]-a[4])+cos(a[3]-3*a[4]-a[2]+3*a[1])-cos(-a[3]-3*a[4]+a[2]+3*a[1])+cos(-3*a[3]-a[4]+a[2]+3*a[1])-cos(-3*a[3]+a[4]-a[2]+3*a[1])+cos(a[1]-3*a[2]+3*a[3]-a[4])-cos(a[1]-3*a[2]-a[3]+3*a[4])+cos(a[1]+3*a[2]-a[3]-3*a[4]))

(5)

CodeTools:-Usage(combine(simplify(normal(sineExpr(5), expanded), trig), trig)): # rather lengthy

memory used=4.23GiB, alloc change=-32.00MiB, cpu time=2.66m, real time=2.29m, gc time=29.98s

 

Can sineExpr(3), sineExpr(4), and sineExpr(5) be reduced to sin(a[1]+a[2]+a[3]-b[1]-b[2]-b[3]), sin(a[1]+a[2]+a[3]+a[4]-b[1]-b[2]-b[3]-b[4]), and sin(a[1]+a[2]+a[3]+a[4]+a[5]-b[1]-b[2]-b[3]-b[4]-b[5]) respectively by Maple itself (that is, with as little user-intervention as possible) if one is not aware of such reductions in advance?


 

Download sinIdentity.mw

Note that because zero testing is frequently considerably easier, combine always succeeds in showing that the difference between the simplest possible and the original version is zero. 

combine(sin((a[1]+a[2]+a[3])-(b[1]+b[2]+b[3]))-sineExpr(3));
 = 
                               0

combine(sin((a[1]+a[2]+a[3]+a[4])-(b[1]+b[2]+b[3]+b[4]))-sineExpr(4));
 = 
                               0

However, I wonder if Maple can thoroughly simplify them without knowing those known “simplest possible” form beforehand
I also tried some other functions like rationalize, radnormal, and `convert/trig`, yet Maple appears to have not been capable of completely simplifying even the sub-simplest case 𝑚=2. Is there any workaround? 

Of note, it can be demonstrated inductively that m∈ℕ 

 

where none of the denominators is 0. Nevertheless, as mentioned above, is it possible to transform  and  (as well as , if possible) into potentially more elegant forms (Ideally,  is rewritten into ,  is rewritten into , and  is rewritten into .) without any such a priori knowledge
In Mma, these may be done using TrigReduce directly (cf. ); unfortunately, I cannot found a Maple equivalent to such functionality. 

Good everyone,

I am solving a pde problem and I wanted to get the table values for u(0,0.1) but it's just returning the pds. Attach below is the maple worksheet for the code. 

Anyone with suggestions, please. 

Test.mw

When I calculate the edge values of a matrix the result is lengthy expression that could be simplified if evaluated numerically, Why is that not done? 

 I am writing help pages for a package. The inital Overview should be at the top of the listing like in other Maple help directories. 

How to I do this? Mine is listing purely alphabetically.
 

NULL

with(HelpTools)

[Database, TableOfContents, Worksheet]

(1)

currentdir()

"D:\User Account Ronan\Documents\MAPLE\Rational Trigonometry"

(2)

 

NULL

NULL

HelpTools[Database][Create]("C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help")

"C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help"

(3)

HelpTools[Database][Add]("C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help")

["C:\Program Files\Maple 2024\lib\maple.help", "C:\Program Files\Maple 2024\lib\maple_ja.help", "C:\Users\Ronan\maple\toolbox\CodeBuilder\lib\CodeBuilder.help", "C:\Users\Ronan\maple\toolbox\DirectSearch\lib\DirectSearch.help", "C:\Users\Ronan\maple\toolbox\OEIS\lib\OEIS.help", "C:\Users\Ronan\maple\toolbox\UTF8\lib\UTF8.help"]

(4)

HelpTools[Database][GetActive]()

["C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", "C:\Program Files\Maple 2024\lib\maple.help", "C:\Program Files\Maple 2024\lib\maple_ja.help", "C:\Users\Ronan\maple\toolbox\CodeBuilder\lib\CodeBuilder.help", "C:\Users\Ronan\maple\toolbox\DirectSearch\lib\DirectSearch.help", "C:\Users\Ronan\maple\toolbox\OEIS\lib\OEIS.help", "C:\Users\Ronan\maple\toolbox\UTF8\lib\UTF8.help", "C:\Users\Ronan\maple\toolbox\personal\lib\RationalTrigonometry.help"]

(5)

NULL

makehelp("RationalTrigonometry", "Rational Trigonometry Overiew Help.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", aliases = ["RatTrig", "Rat Trig", "RT", "R T"], browser = ["Rational Trigonometry", " Overview"])

["C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", "C:\Program Files\Maple 2024\lib\maple.help", "C:\Program Files\Maple 2024\lib\maple_ja.help", "C:\Users\Ronan\maple\toolbox\CodeBuilder\lib\CodeBuilder.help", "C:\Users\Ronan\maple\toolbox\DirectSearch\lib\DirectSearch.help", "C:\Users\Ronan\maple\toolbox\OEIS\lib\OEIS.help", "C:\Users\Ronan\maple\toolbox\UTF8\lib\UTF8.help", "C:\Users\Ronan\maple\toolbox\personal\lib\RationalTrigonometry.help"]

(6)

makehelp("RationalTrigonometry,Quadrance", "Help Quadrance.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", browser = ["Rational Trigonometry", "Quadrance"])

makehelp("RationalTrigonometry,Cross Law", "Help Cross Law.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", browser = ["Rational Trigonometry", "CrossLaw"])

makehelp("RationalTrigonometry,Spread", "Help Spread.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", aliases = ["RT Spread", "R T Spread"], browser = ["Rational Trigonometry", "Spread"])

makehelp("RationalTrigonometry,Spread Law", "Help Spread Law.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", aliases = ["RT Spread Law", "Spread Law Quadrea"], browser = ["Rational Trigonometry", "Spread Law"])

makehelp("RationalTrigonometry,TQF", "Help Triple Quad Formula.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", aliases = ["Triple Quad Formula", "TQF"], browser = ["Rational Trigonometry", "Triple Quad Formula"])

makehelp("RationalTrigonometry,TSF", "Help Triple Spread Formula.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", aliases = ["Triple Spread Formula", "TSF"], browser = ["Rational Trigonometry", "Triple Spread Formula"])

makehelp("RationalTrigonometry,QQF", "Help Quadruple Quad Formula.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", aliases = ["Quadruple Quad Formula", "QQF"], browser = ["Rational Trigonometry", "Quadruple Quad Formula"])

makehelp("RationalTrigonometry,QSF", "Help Quadruple Spread Formula.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", aliases = ["Quadruple Spread Formula", "QSF"], browser = ["Rational Trigonometry", "Quadruple Spread Formula"])

makehelp("RationalTrigonometry,Quadrea", "Help Quadrea Triangle.mw", "C:/Users/Ronan/Maple/toolbox/personal/lib/RationalTrigonometry.help", browser = ["Rational Trigonometry", "Quadrea"])

NULL

NULL

NULL       

NULL


 

Download Help_Edit_to_Database_2023.mw

Dear all 

I have an ideal, and code its definition  and I compute the height  but no result return. There is an error. 

height_ideal.mw

Thank you for you help

Hello

I am looking for an efficient code to divide a given integer n by another integer d as many times as possible.

For example:

For n=294912 and d=8 the answer shoud be 9, because 294912/8^5=9.

Thank you for your help.

THis ode looks complicated

ode := (2*x^(5/2) - 3*y(x)^(5/3))/(2*x^(5/2)*y(x)^(2/3)) + ((-2*x^(5/2) + 3*y(x)^(5/3))*diff(y(x), x))/(3*x^(3/2)*y(x)^(5/3)) = 0;

But is actually a simple first order linear ode:

RHS:=solve(ode,diff(y(x),x));
new_ode:=diff(y(x),x)=RHS;

Whose solution is 

But Maple gives this very complicated answer as shown below. When asking it to solve as linear ode, it now gives the much simpler solution.  

Maple complicated solutions are all verified OK. But the question is, why did it not give this simple solution?

Attached worksheet.  All on Maple 2024


 

204152

restart;

204152

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1700. The version installed in this computer is 1693 created 2024, March 7, 17:27 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

ode := (2*x^(5/2) - 3*y(x)^(5/3))/(2*x^(5/2)*y(x)^(2/3)) + ((-2*x^(5/2) + 3*y(x)^(5/3))*diff(y(x), x))/(3*x^(3/2)*y(x)^(5/3)) = 0;

(1/2)*(2*x^(5/2)-3*y(x)^(5/3))/(x^(5/2)*y(x)^(2/3))+(1/3)*(-2*x^(5/2)+3*y(x)^(5/3))*(diff(y(x), x))/(x^(3/2)*y(x)^(5/3)) = 0

DEtools:-odeadvisor(ode);

[[_1st_order, _with_linear_symmetries], _exact, _rational]

#why such complicated solutions?
sol:=[dsolve(ode)];

[y(x) = (1/3)*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*(-(1/4)*5^(1/2)-1/4-((1/4)*I)*2^(1/2)*(5-5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*(-(1/4)*5^(1/2)-1/4+((1/4)*I)*2^(1/2)*(5-5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*((1/4)*5^(1/2)-1/4-((1/4)*I)*2^(1/2)*(5+5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), y(x) = (1/3)*((1/4)*5^(1/2)-1/4+((1/4)*I)*2^(1/2)*(5+5^(1/2))^(1/2))^3*2^(3/5)*3^(2/5)*(x^(5/2))^(3/5), x/y(x)^(2/3)+y(x)/x^(3/2)+c__1 = 0]

#all solution are correct
map(X->odetest(X,ode),sol);

[0, 0, 0, 0, 0, 0]

RHS:=solve(ode,diff(y(x),x));
new_ode:=diff(y(x),x)=RHS;

(3/2)*y(x)/x

diff(y(x), x) = (3/2)*y(x)/x

dsolve(new_ode);

y(x) = c__1*x^(3/2)

#force it to solve it as first order linear ode
dsolve(ode,y(x),[`linear`])

y(x) = c__1*x^(3/2)


 

Download why_missed_simple_solution_march_17_2024.mw

I am wondering why Maple simplifies (x^(1/3))^3 to x ,  but not (x^3)^(1/3) .
I even tried the surd function. I believe the surd function is for real number arguments, so it should simplify to x.

restart:

f:=x->x^3:
g:=x->x^(1/3):

f(g(x));
g(f(x));

x

 

(x^3)^(1/3)

(1)

simplify((x^3)^(1/3))

(x^3)^(1/3)

(2)

simplify(x^(1/3))^3

x

(3)

simplify(surd(x^3,3))

surd(x^3, 3)

(4)

simplify(surd(x,3)^3)

surd(x, 3)^3

(5)

 

Download inverse1.mw

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