I am learning how to use select with my own types defined, to find parts of expression. This is instead of using patmach.

For example, given   3+x^2*sin(x) and then I want to find any POLYNIMAL*sin function, if present. So I did the following

restart;
expr_1:=3+x^2*sin(x):
mytype_1 := `&*`( polynom(And(algebraic, satisfies(u -> not has(u, I))),x),specfunc('sin')):
select( z->type(z,mytype_1),expr_1);

Which works. Maple returned 

The problem is that if I change the order of multiplication, and also at same time change the polynomial by adding one more term, it no longer works!

I have no idea why. It seems Maple rememebrs something.  Here is a screen shot, followed by plain text code.

code

restart;
expr_1:=3+(1+x)*sin(x):
mytype_1 := `&*`( polynom(And(algebraic, satisfies(u -> not has(u, I))),x),specfunc('sin')):
select( z->type(z,mytype_1),expr_1);
expr_1:=3+sin(x)*(1+x):
select( z->type(z,mytype_1),expr_1);

#change polynomial but keep same order, it works
expr_2:=3+(1+x+x^2)*sin(x):
select( z->type(z,mytype_1),expr_2);

#change order BUT keep same polynomial, it works
expr_3:=3+sin(x)*(1+x+x^2):
select(z->type(z, mytype_1),expr_3);

#keep same order as above, but change polynomial, now it does not works
expr_4:=3+sin(x)*(1+x+x^2+x^4):
select(z->type(z, mytype_1),expr_4);

#keep same order as first one  but change polynomial, it does not work
expr_5:=3+(1+x+x^2+x^4)*sin(x):
select(z->type(z, mytype_1),expr_5);

#keep same order as first one but change polynomial back to what it was, now it works
expr_6:=3+(1+x)*sin(x):
select(z->type(z, mytype_1),expr_6);

What Am I doing wrong?

Maple 2021.1

Maple 2021.1/Windows 10.

When entering 2d expressions into the bottom line of a worksheet, i.e. at the bottom of the window, I can't see the underscores used to indicate bracketing.

A workaround is to use ^J to get another input prompt at the bottom of the window.

Is there some way to get a bigger margin at the bottom of the window?

Cheers,

Steve.

Hi,

In Maple 2020, the following line works fine:

Statistics:-HeatMap(Matrix(128,(i,j)->modp(binomial(i,j),2)),color=["White","Black"]);

With Maple 2021, I get

Interestingly, the exported PNG is better with Maple 2021 (not blurry as in Maple 2020). However, there is an alignment problem with the axes. And it appears in Maple, before exporting. Bug?

(Maple 2020/2021 on Windows 10)

I need to check if an expression is polynomial in x but with coefficients that are either symbolic, or do not include the complex numebr I.

The problem is that maple considers integers and reals complex also.   

type(1,complex) gives true. so I can't use

restart;
type(1+2*x,polynom(Not(complex),x))

Since this gives false. 

I could instead list all the types to be accepted using Or, like this

restart;
type(1+2*x,polynom(Or(float,realcons,rational,integer),x))

But I might overlook something if I have to enumerate every type accepted. It is easier to just exclude complex numbers. 

What is the correct way to tell Maple to check if expression is polynomial in x where coefficients do not have the complex I in them? It it ok if the coefficient are any other numeric value, or a known Maple constant, or a parameter (symbol). I just want to exclude complex numbers.

I know I could do this

restart;
the_poly:=1+2*x;
if not has(the_poly,I) then
   type(the_poly,polynom(anything,x))
else
   print("not allowed");
fi;

But I wanted to learn how to make a type which excludes complex numbers.

Maple 2021.1

Given an expressions such as 

expr:=sin(x)+cos(x)*exp(x)+x*tan(x)*f(x)+x+y;

I want to use indets to find only the mathematical functions in it, and also symbol but only x symbol in this above. I can do the following to find the mathematical functions and symbols, but I do not know how to tell it to find type symbol which happend to be x. Since x is not a type.

expr:=sin(x)+cos(x)*exp(x)+x*tan(x)*f(x)+x+y;
type_1:={function,typefunc(mathfunc)};
type_2:=symbol;
lis:=indets(expr,  Or( And(type_1),  type_2 ))

Which gives

But I really wanted this output

I know I can post process the outout using has or remove, to remove symbol y. But is it possible to do that using indets? something similar to specfunc but specsymbol ? I looked at the help page for Definition of a Structured Type in Maple but do not see anything there so far.

I tried

expr:=sin(x)+cos(x)*exp(x)+x*tan(x)*f(x)+x+y;
type_1:={function,typefunc(mathfunc)};
type_2:={symbol,identical(x)};
lis:=indets(expr,  Or( And(type_1),  And(type_2) ))

but it gives same output.

I need to calculate dozens of piecewise-defined  (but elementary) definite integrals of the following kind. Maple returns them unevaluated. Is there a trick to force evaluation? 

restart;
u := piecewise(0 <= x and 0 <= y and y <= x, x-1, 0 <= x and 0 <= y and x <= y, x, 0);
v := piecewise(0 <= x and 0 <= y and y <= x, x-1, y <= 0 and 0 <= x and -x <= y, x-1, 0);
plot3d(u*v, x=-1..1, y=-1..1);
# integrating over (0,1)x(0,1) works
int(u*v, x=0..1, y=0..1);
# but integrating over (-1,1)x(-1,1) returns unevaluated.
# How to force evaluation on (-1,1)x(-1,1)?
int(u*v, x=-1..1, y=-1..1);

integration-problem.mw

given one equation where both sides are polynomials in one variable x, like this

eq:=c1*(x^2+x)+c2*(2+2*x)+c3=-4*x^2+2*x+6;

And we want to solve for the coefficients on the LHS, which are c1,c2,c3.  By hand, this is solved by expanding both sides, and then comparing the coefficient of each power of x. This generates 3 equations (in this example) and then these are solved for c1,c2,c3.

Is there a way to automatically do this in Maple without the user having to do the first manual step of generating the equations needed to solve for c1,c2,c3?

eq1:=c1=-4;eq2:=c1+2*c2=2;eq3:=2*c2+c3=6;
PDEtools:-Solve([eq1,eq2,eq3],[c1,c2,c3])

gives

              {c1 = -4, c2 = 3, c3 = 0}

But It will be nice if there is a command in Maple which will do it starting from the first equation. Ofcourse one has to tell Maple what to solve for. PDEtools:-Solve(eq,[c1,c2,c3]); or solve(eq,[c1,c2,c3]) does not work, because Maple does not know it needs to expand and compare coefficients as we do by hand.

It is not hard to write code to generate these equations, but I am asking if there is already a command in Maple which somehow does it automatically. I looked at SolveTools, but did not spot something yet there.

edit

Ok, I think this is easy to do. I found a command

eq:=c1*(x^2+x)+c2*(2+2*x)+c3=-4*x^2+2*x+6;
eqs:=PolynomialTools:-CoefficientList((lhs-rhs)(eq),x);
PDEtools:-Solve(eqs,[c1,c2,c3])

{c1 = -4, c2 = 3, c3 = 0}

There is code at Maple app center  here  called "A Simple Expression Parser" which generates the actual tree structure of an expression. I tested it a little and it seems to work correctly on what I tried so far.

My question if some Graph expert could take the output of the above and generate an actual tree graph from it, to make it easier to see, similar to Mathematica TreeForm command which would make it much more useful.

I will show 2 examples, and the code from the above application and what the final graph should look like,. The code is (formatted a little to make it easier to read)

#code from https://www.maplesoft.com/applications/view.aspx?SID=4808
Op := proc(x) 
    if 1 < nops(x) and not type(x, function) then 
       [whattype(x), op(x)]; 
    elif type(x, function) then 
       [op(0, x), op(x)]; 
    else 
        x; 
    fi; 
end proc;

Parse := proc(expr) 
   local tmp, i; 
   tmp := Op(expr); 
   for i from 2 to nops(tmp) do 
       if 1 < nops(tmp[i]) or type(tmp[i], function) then 
          tmp := subsop(i = Parse(tmp[i]), tmp); 
       end if; 
   od; 
   RETURN(tmp); 
end proc;

ps. I do not think using name Parse above is good idea, since I see it is an inert form of Maple build in command.

Now, lets look at this

first example 

expr:=sin(x)+x*y + 1/x;
Parse(expr)

The above says the tree is rooted at `+` with three branches. The first is sin(x), the second is a tree rooted at `*` with two leafs x,y, and the third branch is roots at `^` with two leafs x,-1. Physically it looks like this

Second example

expr := sin(x)*(x + y) + 1/x;
Parse(expr)

Which physically will look like

So it is possible in theory to make a TreeForm command in Maple, using this Parse() command. May be using Graph package in Maple? by reading the output from the Parse() command, and generating nodes and arcs along the way.

How hard will such a task be? I never used the Maple 's Graph package.  

Could may be  someone may be give this an attempt? I never understood why Maple do not have a build in similar command to TreeForm. It is very useful to understanding expressions.

I have

f:=a^6*o + a^5*i + a^4*u + a^3*q + a^2*t + a

and

f1:=7*a^6*p + 6*a^5*o + 5*a^4*i + 4*a^3*u + 3*a^2*q + 2*a*t + 1

I want to divide two functions f/f1 to produce a result.

a^2*t+ a^3*(-2*t^2 + 2*q)+ a^4*(4*t^3 - 7*t*q + 3*u)(-8*t^4 + 20*t^2*q - 6*q^3 - 10*t*u + 4*i)*a^5+a^6*(16*t^5 - 52*t^3*q + 33*t*q^3 + 28*t^2*u - 13*i*t - 17*u*q + 5*o)+O(a^7)

I have tried collect and asympt, the result is not satisfactory.

Hi guys ,

I have the equation dt=(L/r)*(1 - a^3/r^3)^(-1/2) dr which want to integrate on both side and then solve in terms of r.(L and a are constants). I know the answer (r=a (cosh(3t/2*L)^2/3),but it seems maple can not produce it!

Mathematical almost compute it corectly! altough i think  tanh-1, should be cosh^-1(x/a)^3/2

I would appreciate if someone can help me

Thanks so muchproblem.mw

Why does Maple write

restart;
eq:=x-infinity=0;

as 

Update 3 years later

FYI, The above bug is still present in Maple 2024

Download wrong_display_of_math_maple_2024_june_28_2024.mw

I've send a bug report to Maplesoft also.

Any one has smart way to help verify this Maple solution to this ODE? I can't figure it out

restart;
ode:=diff(y(x),x)-y(x) = x*y(x)^(1/2):
ic:= y(0)=4:
maple_sol:=dsolve([ode,ic],'implicit'):
the_diff_1:=odetest( (lhs-rhs)(maple_sol)=0,[ode,ic]);


maple_sol:=dsolve([ode,ic],'explicit'):
the_diff_2:=odetest( (lhs-rhs)(maple_sol)=0,[ode,ic]);

Tried few simplifications but not everything. I am assuming Maple solution is correct.

Maple 2021.1

Background

This 'quirk' of Maple behaviour cropped up when I was considering solutions for the question posted here

https://www.mapleprimes.com/questions/232433-Extract-From-Record

where the OP had "poorly structured" data which meant it was a bit "awkward" to access required fields. A number of more-or-less satisfactory solution were proposed, and the OP seems happy

The Issue

One possible way to solve the original problem would be to restructure the data as a DataFrame. The "natural" way to do this would be to use numeric row indexes.. Note that these row indexes are not contiguous, and are in no particular order. However using this approach means that accessing fields from the dataframe is not consistent.

Sometimes the supplied row label is interpreted as a 'label', sometimes it is interpreted as the "row number". It appears that the latter interpretation is preferentially used

I can't make up my mind whether to call this a "bug" or not, but I can see the inconsistent interpretation resulting in chaos.

Before submitting an SCR I'd like to know if anyone else sees this as a bug

Consider the code

  restart;
  prettyprint=1:
#
# data
#
  S := [`206` = Record(mu = 508.001018040,  sigma = 125.002863204708),
          `4` = Record(mu = 1008.001018040, sigma = 167.707232430134),
          `2` = Record(mu = 1208.001018040, sigma = 141.512246146314),
          `5` = Record(mu = 808.001018040,  sigma = 117.156800098735)
       ]:
#
# Construct the above as a dataframe - note row labels are numbers!
#
  DF:= DataFrame( Matrix([seq( [rhs(j):-mu, rhs(j):-sigma], j in S)]),
                  rows= [seq( parse( lhs(j) ), j in S)],
                  columns=[mu, sigma]
              );
  DF[206, mu];
  DF[2, mu];  ## Errr No!
  DF[5, sigma];
               [           mu             sigma      ]
               [                                     ]
               [206  508.001018040   125.002863204708]
               [                                     ]
         DF := [ 4   1008.001018040  167.707232430134]
               [                                     ]
               [ 2   1208.001018040  141.512246146314]
               [                                     ]
               [ 5   808.001018040   117.156800098735]

                         508.001018040

                         1008.001018040

                        117.156800098735

Note that DF[2, mu] outputs the entry from the second row - not the one from the row labelled with the number 2

I imagina a similar issue would occur with numeric column indexes, although I haven't tried this
     

restart:
with(plots):
kernelopts(version);
 

How do I setup solve to find only the real and imaginary part of Zeta to be both positive and the real part of Zeta to be the smallest positive value? For example: real part = 1.348412872 and imaginary part = 0.04230725448.

Acceleration ratio (db) and phase (deg). Convert ratio to linear and phase to radian. 
dat := <14.52407334|-162.1310124>:
A := 10^(dat[1]/20.):
phi := dat[2]*Pi/180.:
R:= 0.3036:
Characteristic equation Eqn 5
f := (Zeta,A,phi) -> cos(Zeta) - R * Zeta * sin(Zeta) - exp(-phi * I)/A:

soln := [solve(f(Zeta,A,phi), Zeta)]:
 

Tests.mw

Textbook gives this nice short implicit solution for this ode

As

But Maple does not give an implicit solution

restart;
ode:=diff(y(x),x) = 2*(2*y(x)-x)/(x+y(x));
ic:=y(0)=2;
sol:=dsolve([ode,ic],'implicit')

Removing implicit gives very complicated solution as it tries to solve for y(x).

book_sol:=(x-y(x))^2-1/2*(y(x)-2*x)^3=0;
odetest(book_sol,[ode,ic])

Any suggestion or a trick or a different approach to make Maple generate the same solution given in the textbook?

ps. manually, it is possible to obtain the same solution as book as follows

restart;
ode:=diff(y(x),x) = 2*(2*y(x)-x)/(x+y(x));
ic:=y(0)=2;
sol:=dsolve(ode,'implicit');
sol:=simplify(exp(lhs(sol))=exp(rhs(sol)));
the_constant:=solve(sol,_C1);
the_constant:=eval(the_constant,[y(x)=2,x=0]);
sol:=eval(sol,_C1=the_constant);
odetest((lhs-rhs)(sol)=0,[ode,ic])

edit june 14,2021

I found a direct way to get an implicit solution which is close enough to book solution. It is by using Lie symmetry method

restart;
ode:=diff(y(x),x) = 2*(2*y(x)-x)/(x+y(x));
ic:=y(0)=2;
sol:=dsolve([ode,ic], y(x),'implicit','Lie');

Another variant which gives book solution but requires one extra step

restart;
ode:=diff(y(x),x) = 2*(2*y(x)-x)/(x+y(x));
ic:=y(0)=2;
sol:=dsolve([ode,ic], y(x),'implicit','Lie',way=all,fat);
simplify(exp( (lhs-rhs)(sol)))=1

ps. corrected above now, thanks to comment below by Carl.

Maple 2021.1