Advanced Search

nm

12238 Reputation

20 Badges

13 years, 257 days
Contact nm

MaplePrimes Activity


These are questions asked by nm

strange latex result. Why an extra 1 sho...

nm 12238 Maple 2019
latex
August 29 2019
2 3

We all know that Maple's Latex is not the best of Maple to say the least.

But this one is really strange. Maple prints a `1` for no apparant reason in the latex which makes it ugly. 

I wonder if Maplesoft still maintains its Latex conversion code at all?  So one can at least hope may be one day all of this will get fixed? Year after year, and Maple's Latex still not changed.  

If Mapesoft do not intend to make any changes in its Latex conversion software at all, it will be good if an official statement is made in this regards so that at least customers know.

> 

sol:=dsolve((x-a)*(x-b)*diff(y(x),x)+k*(y(x)-a)*(y(x)-b) = 0,y(x)):
sol:=subs(_C1=C[1],sol);

y(x) = ((x-b)^(-k)*(x-a)^k*a*exp(a*k*C[1]-b*k*C[1])-(x-b)^(-k)*(x-a)^k*b*exp(a*k*C[1]-b*k*C[1])+b*((-x+b)/(-x+a))^(-k)*exp(a*k*C[1]-b*k*C[1])-b)/(-1+((-x+b)/(-x+a))^(-k)*exp(a*k*C[1]-b*k*C[1]))

> 

latex(sol)

y \left( x \right) ={1 \left(  \left( x-b \right) ^{-k} \left( x-a
 \right) ^{k}a{{\rm e}^{akC_{{1}}-bkC_{{1}}}}- \left( x-b \right) ^{-k
} \left( x-a \right) ^{k}b{{\rm e}^{akC_{{1}}-bkC_{{1}}}}+b \left( {
\frac {-x+b}{-x+a}} \right) ^{-k}{{\rm e}^{akC_{{1}}-bkC_{{1}}}}-b

 \right)  \left( -1+ \left( {\frac {-x+b}{-x+a}} \right) ^{-k}{{\rm e}
^{akC_{{1}}-bkC_{{1}}}} \right) ^{-1}}

> 

 

 

Download why_1_in_latex.mw

 

why odetest fail to verify solution when...

nm 12238 Maple 2019
differential-equations odetest
August 29 2019
2 5

Why odetest sometimes fail to give 0  from odetest when simply using C[1] instead of _C1 as constant of integration?

I do not remember now if I asked about this before now. But for me as a user, this does not look right. I like to use C[1] instead of _C1 as the constant of integration as it looks better in Latex. I had no idea it will make a difference to odetest what the constant of integration symbol used is.

Is this a known issue? Do you consider this a bug? Maple 2019.1 on windows 10.

> 

restart;
> 

ode:= x^2*diff(y(x),x)+x*y(x)+sqrt(y(x)) = 0;

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

> 

sol_1:=sqrt(y(x))=1/x+_C1/sqrt(x);
odetest(sol_1,ode)

y(x)^(1/2) = 1/x+_C1/x^(1/2)

0

> 

sol_2:=subs(_C1=C[1],sol_1);
odetest(sol_2,ode); #why this now fails??

y(x)^(1/2) = 1/x+C[1]/x^(1/2)

-y(x)^(1/2)-y(x)^(1/2)*x^(1/2)*C[1]+x*y(x)

> 

sol_3:=subs(C[1]=_C1,sol_2);
odetest(sol_3,ode)

y(x)^(1/2) = 1/x+_C1/x^(1/2)

0

 

Download why_odetest_fail.mw

A=B but Maple does not want to simplify ...

nm 12238 Maple 2019
simplify
August 29 2019
3 1

A=B  but not able to simplify arctanh(A)-arctanh(B)  to be zero.  Why? Is there a workaround? Using Maple 2019.1

> 

restart;
> 

A:=((y*sqrt(3) + 3)*sqrt(3))/(6*sqrt(y^2 + 1));
B:=(y + sqrt(3))/(2*sqrt(y^2 + 1));
simplify(A-B)

(1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2)

(1/2)*(y+3^(1/2))/(y^2+1)^(1/2)

0

> 

simplify(arctanh(A)-arctanh(B))

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

> 

simplify(arctanh(A)-arctanh(B),trig)

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

> 

simplify(arctanh(A)-arctanh(B)) assuming positive

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

> 

simplify(arctanh(A)-arctanh(B),trig) assuming positive

arctanh((1/6)*(y*3^(1/2)+3)*3^(1/2)/(y^2+1)^(1/2))-arctanh((1/2)*(y+3^(1/2))/(y^2+1)^(1/2))

> 

plot(arctanh(A),y=-Pi..Pi)

> 

plot(arctanh(B),y=-Pi..Pi)

> 

 

 

Download will_not_simplify.mw

Compare to Mathematica:

why rewriting the ODE changes it classif...

nm 12238 Maple 2019
differential-equations odeadvisor
August 27 2019
1 2

This for me seems strange. A first oder ODE of degree one of form   A+B*y'=0. Asking Maple for its classification, it gives exact AND rational.  After rewriting it in the form y'=f(x,y) , now Maple says it is rational only. It no longer recognize it as exact.

How could this be possible? It is the same ODE, just rewrittng differently.  Maple 2019.1 on windows.

> 

restart;
> 

Typesetting:-Settings(typesetprime=true):
> 

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

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

[_exact, _rational]

> 

dsolve(ode)

y(x) = x/tan(RootOf(-_Z+x*tan(_Z)+_C1))

> 

new_ode:=convert(ode,D); #so I can solve for y'
RHS:=solve(new_ode,D(y)(x));

2*x/y(x)-y(x)/(x^2+y(x)^2)+(-x^2/y(x)^2+x/(x^2+y(x)^2))*(D(y))(x) = 0

(2*x^3+2*x*y(x)^2-y(x)^2)*y(x)/(x*(x^3+x*y(x)^2-y(x)^2))

> 

new_ode:=diff(y(x),x)=RHS;
DEtools:-odeadvisor(new_ode);

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

[_rational]

> 

dsolve(new_ode)

_C1-arctanh((-2/(x^4*(1/y(x)^2+(x-1)/x^3)))^(1/2)*x/((-2*x+2)/(x^3*(1/y(x)^2+(x-1)/x^3))+2)^(1/2))+((-2*x+2)/(x^3*(1/y(x)^2+(x-1)/x^3))+2)^(1/2)/(-2/(x^4*(1/y(x)^2+(x-1)/x^3)))^(1/2) = 0

> 

 


 

Download why_type_changed.mw

how to correctly find leading sign on ex...

nm 12238 Maple 2019
sign
August 24 2019
3 8

8/24/19. Updated question the bottom

I need to find if expression has  a "-" in front of it or not.  This is for formatting purposes for something I am doing, that is all. 

I was using the command sign() for this, and it seems to work OK, but sometimes a Maple error is generated or not leading term sign is returned.

The sign function computes the sign of the leading coefficient of expr.

Is there a better and more robust way to do this other than using sign() or Am I using sign wrong?

> 

restart;
> 

expr:=-sin(x)/ln(y)+1;
op(expr);

-sin(x)/ln(y)+1

-sin(x)/ln(y), 1

> 

#why this gives 1 as sign for the above?
sign(expr);

1

> 

#workaround?
sign(op(1,expr))

-1

> 

expr:=sin(x)/ln(y)+1;
sign(expr);

sin(x)/ln(y)+1

1

> 

expr:=-x;
sign(expr);

-x

-1

> 

expr:=-LambertW(exp(p))+1;
sign(expr)

-LambertW(exp(p))+1

-1

> 

expr:=-LambertW(exp(p))/(1+LambertW(exp(p)))+1;
sign(expr)

-LambertW(exp(p))/(1+LambertW(exp(p)))+1

Error, invalid argument for sign, lcoeff or tcoeff

> 

#it seems the following is a work around for the above case
#but why it is needed just here?
sign(op(1,expr))

-1

> 

 

 

Download q1.mw

UPDATE

Thanks to comment below about using frontend. I never used this before except for now. It seems a very useful command and I think I will be using it a lot more from now on.

Just to clarify again what I want. I am just looking to see if there is a leading negative sign in front of an expression. I am not looking to find if the expression itself can be postive or negative when evaluated or anything more subtle or deep than that.

I simply want to check if there is literally a "-" in front of the maple expression. That is all.

Only issue left, is why Maple still gives Error, invalid argument for sign, lcoeff or tcoeff for the last example below? Here is the updated worksheet.

> 

restart;
> 

expr:=-sin(x)/ln(y)+1;
frontend(sign,[expr]);

-sin(x)/ln(y)+1

-1

> 

expr:=sin(x)/ln(y)+1;
frontend(sign,[expr]);

sin(x)/ln(y)+1

1

> 

expr:=-x;
frontend(sign,[expr]);

-x

-1

> 

expr:=-LambertW(exp(p))+1;
frontend(print,[expr]);
frontend(sign,[expr]);

-LambertW(exp(p))+1

-O+1

-1

> 

expr:=-LambertW(exp(p))/(1+LambertW(exp(p)))+1 ;
frontend(print,[expr]);
frontend(sign,[expr]);

-LambertW(exp(p))/(1+LambertW(exp(p)))+1

-O/(1+O)+1

Error, invalid argument for sign, lcoeff or tcoeff

> 

 

 

Download q1_2.mw

First 152 153 154 155 156 157 158 Last Page 154 of 217