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These are questions asked by nm

why LinearAlgebra:-RowDimension works on...

nm 11378 Maple 2023
parameters linearalgebra type
June 13 2023
2 3

From help it says

But in the following it works on list type. Why? Should have not given an error?

158332

> 

restart;

158332

> 

interface(warnlevel=4);
kernelopts('assertlevel'=2):

3

> 

T:=[ [1,2],[3,4],[6,6]];
whattype(T);
type(T,Matrix);
LinearAlgebra:-RowDimension(T);

[[1, 2], [3, 4], [6, 6]]

list

false

3

> 

T:=Matrix([[1,2],[3,4],[6,6]]);
whattype(T);
type(T,Matrix);
LinearAlgebra:-RowDimension(T);

T := Matrix(3, 2, {(1, 1) = 1, (1, 2) = 2, (2, 1) = 3, (2, 2) = 4, (3, 1) = 6, (3, 2) = 6})

Matrix

true

3

> 

 

Download row_dim_june_13_2023.mw

label="dontexpand" where does it come fr...

nm 11378 Maple 2023
solve sum rootof
June 10 2023
1 3

Where do you think label="dontexpand" is coming from in the following? I never seen this before. Is this a bug?

When using PDEtools:-Solve no such error shows up. Worksheet below

998948

> 

interface(version);

`Standard Worksheet Interface, Maple 2023.0, Windows 10, March 6 2023 Build ID 1689885`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1462 and is the same as the version installed in this computer, created 2023, June 10, 2:26 hours Pacific Time.`

> 

restart;

998948

> 

sol:=sum((-2*_R^2+1)/(6*_R^2+4*_R-1)*ln(y(x)/x-_R),_R = RootOf(2*_Z^3+2*_Z^2-_Z+1))-ln(x)-c[1] = 0;
solve(sol,y(x))

sum((-2*_R^2+1)*ln(y(x)/x-_R)/(6*_R^2+4*_R-1), _R = RootOf(2*_Z^3+2*_Z^2-_Z+1))-ln(x)-c[1] = 0

Error, (in solve) cannot solve expressions with sum((-2*_R^2+1)/(6*_R^2+4*_R-1)*ln(y(x)/x-_R),_R = RootOf(2*_Z^3+2*_Z^2-_Z+1,label = "dontexpand")) for y(x)

> 

PDEtools:-Solve(sol,y(x))

y(x) = exp(-c[1])+_R*x

> 

 

Download dontexpand_june_10_2023.mw

"already assigned to outputvariable" and...

nm 11378 Maple 2023
dynamicsystems
June 09 2023
1 1

How can one set their own symbols for DynamicSystems continuoustimevar?  If I try to use DynamicSystems:-SystemOptions('continuoustimevar'=x): or DynamicSystems:-SystemOptions('continuoustimevar'=y): Maple complains that these letters are already assigned. Why can not one have their own choice of which letters to use?  Is there a workaround?


 

858904

> 

interface(version);

`Standard Worksheet Interface, Maple 2023.0, Windows 10, March 6 2023 Build ID 1689885`

> 

restart;

858904

> 

DynamicSystems:-SystemOptions('continuoustimevar'=t):
> 

restart;

858904

> 

DynamicSystems:-SystemOptions('continuoustimevar'=x):

Error, (in DynamicSystems:-SystemOptions) cannot assign x to continuoustimevar, already assigned to statevariable

> 

restart;

858904

> 

DynamicSystems:-SystemOptions('continuoustimevar'=y):

Error, (in DynamicSystems:-SystemOptions) cannot assign y to continuoustimevar, already assigned to outputvariable

> 

restart;

858904

> 

DynamicSystems:-SystemOptions('continuoustimevar'=XXXXXX):
> 

 


 

Download dynamics_june_9_2023.mw

 

missing ode solution when adding singsol...

nm 11378 Maple 2023
ode singular dsolve
June 09 2023
2 0

When adding singsol=all to this ode in the first example, dsolve returns nothing. But it should have returned the general solution if it can not find singular solution. This is what it does always as can be seen from the second example given below.

Why did dsolve return nothing in the first example? Is this a bug?

319824

> 

interface(version);

`Standard Worksheet Interface, Maple 2023.0, Windows 10, March 6 2023 Build ID 1689885`

> 

restart;

319824

> 

ode:=y(x)=x*diff(y(x),x)+ a*diff(y(x),x)/(sqrt(1+diff(y(x),x)^2));
sol_1:=dsolve(ode,y(x));
sol_2:=dsolve(ode,y(x),singsol=all);

y(x) = x*(diff(y(x), x))+a*(diff(y(x), x))/(1+(diff(y(x), x))^2)^(1/2)

y(x) = x*c__1+a*c__1/(c__1^2+1)^(1/2)

"sol_2 := "

> 

ode:=diff(y(x),x)^2-(1+2*x*y(x))*diff(y(x),x)+2*x*y(x) = 0;
sol_1:=dsolve(ode,y(x));
sol_2:=dsolve(ode,y(x), singsol=all)

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

y(x) = c__1*exp(x^2), y(x) = x+c__1

y(x) = c__1*exp(x^2), y(x) = x+c__1

> 

 

Download missing_sol.mw

workaround to integrating this...

nm 11378 Maple 2023
integration
June 06 2023
3 1

I am surprised Maple could not do this integral. Any ideas how to make it do it?

restart;
integrand:=(ln(-x + sqrt(x^2 - 1))*x + sqrt(x^2 - 1))*x*sqrt(-x^2 + 1)/sqrt(x^2 - 1);
int(integrand,x)

For reference, another software gives

ClearAll[x]
integrand = (Log[-x + Sqrt[x^2 - 1]]*x + Sqrt[x^2 - 1])*x*Sqrt[-x^2 + 1]/Sqrt[x^2 - 1]
Integrate[integrand, x]

Which I verified to be correct.

Any workarounds? I tried assuming x>0 for example. Not sure what else to try now. I am sure with some pre-processing Maple can do it. 

Maple 2023

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