## How do we plot the least integer function [x]?...

How do we plot the least integer function [x]?

I am referring to a function with the following graph

## What is the best way to have a type declaration fo...

Declaring types of arguments of a procedure or checking type of something when working with lists or Arrays is easy. For example one can easily use A :: list( posint ) or type( B :: 'Array'( polynom ) ), but with MutableSet, the same approach ends with an error;

Error, module does not have a ModuleType member to accept structured type arguments.

I guess it is the same for other objects defined as a module with option object. Is there a recommended way to have type declaration for such objects or MutableSet in specific?

## coefficient of nonlinear terms...

Dear Mapler

I have an expression that consist of power of main variable x. I aim to fetch the coefficient of square root of x for example. I get an error when I am using COEFF(esp, sqrt(x))

Is there any solution?

## Maple to Latex - empty page pdf only...

When I export a very simple Maple 2018 (MaxOS) document to Latex, this tex file results:

%% Created by Maple 2018.2, Mac OS X

%% Source Worksheet: untitled 3

%% Generated: Sun Jul 03 16:34:49 CEST 2022

\documentclass{article}

\usepackage{maplestd2e}

\def\emptyline{\vspace{12pt}}

\begin{document}

\pagestyle{empty}

\DefineParaStyle{Maple Bullet Item}

\DefineParaStyle{Maple Warning}

\DefineParaStyle{Maple Dash Item}

\DefineParaStyle{Maple Error}

\DefineParaStyle{Maple Title}

\DefineParaStyle{Maple Text Output}

\DefineParaStyle{Maple Normal}

\DefineCharStyle{Maple 2D Output}

\DefineCharStyle{Maple 2D Input}

\DefineCharStyle{Maple Maple Input}

\DefineCharStyle{Maple 2D Math}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{restart; 1}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{maplegroup}

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

\mapleresult

\begin{maplelatex}

\mapleinline{inert}{2d}{a := b^2-2; "_noterminate"}{$\displaystyle$}

\end{maplelatex}

\end{maplegroup}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\begin{maplegroup}

\begin{Maple Normal}{

\mapleinline{inert}{2d}{a := b^2-sqrt(4); "_noterminate"}{$\displaystyle$}

}\end{Maple Normal}

\mapleresult

\begin{maplelatex}

\mapleinline{inert}{2d}{a := b^2-2; "_noterminate"}{$\displaystyle$}

\end{maplelatex}

\end{maplegroup}

\begin{Maple Normal}{

\begin{Maple Normal}{

\mapleinline{inert}{2d}{}{$\displaystyle$}

}\end{Maple Normal}

}\end{Maple Normal}

\end{document}

However, when trying to process the tex file in both Overleaf and TexShop the pdf output is only an empty page. No error occurs, i.e. the maplestd2e.sty file is recognised by both Overleaf and TexShop.

What is going wrong here?

## resolution of the equation of degree 3...

restart:
eq := a*x^3 + b*x^2 + c*x + d;
s := x1 + x2 + x3 = -b/a;
sp := x1*x2 + x1*x3 + x2*x3 = c/a;
p := x1*x2*x3 = -d/a;
sol:=solve({eq, p, s, sp}, {x1, x2, x3},explicit);
a := 1;
b := -5;
c := 6;
d := -1;
sol;

why is not successfull ?   Thank you.

## unable to implicit plot a procedure...

I have a problem in plotting bellow function. actually because my main program is not working so I decided to do it in simple way. I found that my program in maple can't plot the function I introduced it as a procudure and is an implicit function. can you help me please?

>EQ := proc(x, t) local y, m, func;
m := 3;
func := m*x^2 + t*y^2 = 4;
end proc;

>eq := EQ(x, 10);
eq := 3*x^2  + 10*y^2  = 4

>implicitplot(eq, x = -1 .. 1, y = 0 .. 2)
Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {y}

## How to construct a multiple layered arrow procedur...

Given this "pattern" to transfporm an expression into an arrow procedure

e := 1/b:
f := unapply(e, b):
f(3)
1
-
3


I would like now to use this same "pattern" to transform an expression e which depends on 2 indeterminates a and b into a "double layered arrow procedure" f.
Here is a notional example

e := a/b:
f := unapply(unapply(e, b), a);
a
a -> b -> -
b

f(A)(B)
a
-
B


How can I proceed in order that f(A)(B) gives A/B ?

TIA

## implicitplot doesn't recognize the constant Pi...

I was surprised to learn that implicitplot doesn't recognize the constant Pi.  I attach a simple example to illustrate.

 (1)

 (2)

 (3)

## how to make a new function from a derivative?...

dgdx := (x, T) -> diff(g(x, T), x);

g := (x, T) -> T*x + x^2;#just an example

dgdx(1, 2);
Error, (in dgdx) invalid input: diff received 1, which is not valid for its 2nd argument

So, I like to introduce a new function dgdx(x,T) from the x-derivative of g(x,T) but if I insert a value for x I get an error message. It would be great if you can help me out!

## Is it possible to stack to dataframe columns?...

Perhaps a silly question but is it possible to stack two dataframe columns? When I use the Vector command the columns are stacked but nested.

## Why adding noise mu(t) to y_a not working in plot?...

5_6190449716501677775.pdf

I ahve a signal y_a to which adding mu(t) doesn't seem to give any plot but error , what is missing here?.

And also in second k(x,t) pdf file I want the value of k(x,t) after I did the integration. When I type k(x,t) and hit enter it's not giving me the value of k(x,t) but returns k(x,t) as it is.K(x_t).pdf

## how to use odetest to very series solution with ex...

I do not remember now if this was asked before. Doing search here is hard.

But I am trying this now on 2022.1 and this gives FAIL.

What is the correct syntax to use odetest to verify solution to ode using series method with expansion around infinity? Why do I get FAIL here?

 > interface(version)

 > Physics:-Version()

 > restart;
 > ode:=x^3*diff(y(x),x$2)+x^2*diff(y(x),x)+y(x)=0; sol:=dsolve(ode,y(x),'series',x=infinity); odetest(sol,ode,'series','point'=infinity) Warning, unable to compute series necessary to test the given solution  > Download odetest_series.mw Update I've testsed methods given below on 6 random ode's using Maple odetest, VV method and Axel method. THis is the result obtained using Maple 2022.1 odetest was able to verify the solution zero out of 6 times. VV method was able to verify the solution 3 out of 6 times. Axel method was able to verify the solution 5 out of 6 times. So based on this small test, Axel method seems to do the best. Attached worksheet. I will use this method to verify my series solution to ode's instead of Maple's odetest but will use Maple's odetest for non-series method solutions.  > interface(version);  > Physics:-Version();  > restart; Example 1 Regular singular point. Complex roots  > Order:=6; ode:=sin(x)*diff(y(x),x$2)+cos(x)*diff(y(x),x)+1/x*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0)

VV method

 > odetest(sol,ode): asympt(%,x);

odetest method

 > odetest(sol,ode,'series','point'=0);

Axel method

 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

Example 2 Regular singular point. Dierence is integer

 > Order:=6; ode:=sin(x)*diff(y(x),x$2)+cos(x)*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0): VV method  > odetest(sol,ode): asympt(%,x); convert(%,polynom); odetest method  > odetest(sol,ode,'series','point'=0);  Axel method  > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom); Example 3 Regular singular point. Repeated root  > Order:=6; ode:=(exp(x)-1)*diff(y(x),x$2)+exp(x)*diff(y(x),x)+y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x): convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

Example 4 Regular singular point. Repeated root

 > Order:=6;   ode:=(exp(x)-1)*diff(y(x),x$2)+exp(x)*diff(y(x),x)+y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0): VV method  > odetest(sol,ode): asympt(%,x): convert(%,polynom); odetest method  > odetest(sol,ode,'series','point'=0);  Axel method  > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom); Example 5 . Regular singular point. Complex roots  > Order:=6; ode:=x^3*diff(y(x),x$2)+sin(x^3)*diff(y(x),x)+x*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x); #convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): #convert(%,polynom);

Error, (in MultiSeries:-multiseries) need to determine the sign of -I*3^(1/2)

Example 6 . Regular singular point. Complex roots

 > Order:=6;   ode:=x^2*diff(y(x),x\$2)+x*diff(y(x),x)+(x+1)*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0):

VV method

 > odetest(sol,ode): asympt(%,x); #convert(%,polynom);

odetest method

 > odetest(sol,ode,'series','point'=0);

 Axel method
 > rhs(sol): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);

 >
 >

## Maple's WeierstrassP vs Weierstrass' P-function...

What is the [explict] relation between Maple's WeierstrassP and Weierstrass' P-function (e.g. https://en.wikipedia.org/wiki/Weierstrass_elliptic_function) ?

## Specify unit system?...

How can I specify english units as the default in Flow?  Rather than Newtons (N), pound force (lbf)?

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