Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi all,

Wrote some Maple code, and want to share.

I put less than eight hours into this exploration.

I have been running a computer to find Fermat factors for over ten years now.  Want support.

This is an exploration in some mostly composite whole numbers.

see 2_to_the_exponent_p_3.pdf

also see 

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/2_to_the_exponent_p_3.mw .
 

Download 2_to_the_exponent_p_3.mw

Have a look.

Regards

 

Matt

 

 

ff := dsolve({eq1, Vt(0)=0}, Vt(t), type=numeric, method=classical, start=0, stepsize=.00001);

this is a old syntax of maple 5, with maple 2017 version it is not working, is it possible to solve non linear equatins with maple

When I click on the "install" option for the update to the Physics Package, get the following error message:

Fetching package "Physics Updates" from MapleCloud...
ID: 5137472255164416
Version: 988
URL: https://maple.cloud

An error occurred, the package was not installed: 
Unable to log into Maplesoft account: Forbidden (403)

In Maple 2021.1

restart;
int(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x)

gives

Error, (in SumTools:-DefiniteSum:-ClosedForm) numeric exception: division by zero

But in Maple 2020.2 it works OK giving an answer. (A very long one)

btw, the answer should be

3/4*arcsin(2/3*sin(x)*3^(1/2))-3/4*arctan(sin(x)/(-1+4*cos(x)^2)^(1/2))-3/4*arctan(sin(x)/(-1+8*cos(x)^2)^(1/2
))+5/8*arcsin(2/7*sin(x)*14^(1/2))*2^(1/2)-1/2*sin(x)*(-1+4*cos(x)^2)^(1/2)-1/2*sin(x)*(-1+8*cos(x)^2)^(1/2)

 

Is this a known issue? I know Maple int has went some changes and improvements in Maple 2021 from the release notes. May be this was caused by some of these changes?

https://www.maplesoft.com/products/maple/new_features/

  • Integration has been enhanced with improved algorithms for indefinite integration, and the ability to easily specify which integration method should be used and to compare the results from different methods."

Maple 2021.1 on windows 10


 

Hi all,

Do some of you know the form of all primes greater than five?

Is it 6*p +/- 1?

maple_about_primes.pdf



Maple Worksheet - Error

et/convert/                                  Maple_prime_expository_number_one_for_sharing.mw .
 

Download Maple_prime_expository_number_one_for_sharing.mwmaple_about_primes.pdf

 

Regards,

Matt

 

We consider a triangle ABC, its circumscribed circle (O), of radius R, its inscribed circle (I) of centre I. We designate by α, β, γ the points of contact of BC, CA, AB with the circle (I), by A', B', C' the points of meeting other than A, B, C, of AI, BI, CI with the circle (O), by the media of BC, CA, AB.
.Establish that there is a conic (E), focus I, tangent to βγ, γα, αβ.
My code : 

restart;
with(geometry);
with(plots); _local(gamma);
_EnvHorizontalName := x; _EnvVerticalName := y;
alias(coor = coordinates);
point(A, -5, -5); point(B, 7, -1); point(C, 1, 5);
triangle(ABC, [A, B, C]); circumcircle(_O, ABC, 'centername' = OO); incircle(_I, ABC, 'centername' = Io);
line(lBC, [B, C]); sol := solve({Equation(_I), Equation(lBC)}, {x, y}); point(alpha, subs(sol, x), subs(sol, y));
line(lCA, [C, A]); sol := solve({Equation(_I), Equation(lCA)}, {x, y}); point(beta, subs(sol, x), subs(sol, y));
line(lAB, [A, B]); sol := solve({Equation(_I), Equation(lAB)}, {x, y}); point(gamma, subs(sol, x), subs(sol, y));
line(lAO, [A, OO]); intersection(Ap, lAO, lBC);
line(lBO, [B, OO]); intersection(Bp, lBO, lCA);
line(lCO, [C, OO]); intersection(Cp, lCO, lAB);
midpoint(l, B, C); midpoint(m, A, C); midpoint(n, A, B);
triangle(T, [alpha, beta, gamma]);
dr := draw([ABC(color = blue), _O(color = red), _I(color = magenta), lAO(color = black), lBO(color = black), lCO(color = black), T(color = red), alpha, beta, gamma, Ap, Bp, Cp, l, m, n], printtext = true);
display([dr], axes = normal, scaling = constrained, size = [800, 800]);
How to find the Equation of (E); Thank you.

The command

plots[textplot]({[4.2,1.9,typeset(sin(30°))]},
symbol=point,color=black,font=["Arial","Bold",25]);

will output

Can we have the number 30 in a non-italic format?
Thank you!
mapleatha


 

Why is the minus sign so weak even in the bold font case? My students sometimes miss it in online tests.
How do we make the minus sign bolder?
Thank you!

mapleatha

 

Hi, 

First question
Let P1 the logical proposition

restart
with(Logic):
local O
P1 := (&not O) &and (&not C) &implies (&not Q);

Is it possible to obtain its contraposition P2  in a form that contains &implies?

# P2 := (Q) &implies &not ((&not O) &and (&not C));


Second question
Why does the modulo 2 canonical form of proposition P5 above contains "1" "plus" other terms:
(if 1 is present this means 1 + something = 1 and then that P5 is a tautology, which is obviously wrong as Tautology(P5) shows)

restart
with(Logic):
local O
P1 := (&not O) &and (&not C) &implies (&not Q);-
P2 := (Q) &implies &not ((&not O) &and (&not C));
P3 := op(1, P2) &and (&not C);
P4 := op(2, P2) &and (&not C);
P5 := P3 &implies P4:

Canonicalize(P5, {O, C, Q}, form=MOD2)

                   C O Q + C Q + O Q + Q + 1


Verificaion of what the modulo 2 canonical form of a proposition including an "addititive" tautology is

T := O &or (&not O):
Canonicalize(T, {O}, form=MOD2);
Canonicalize(T &or S, {O, S}, form=MOD2);
                               1
                               1

Is it that I missed something or is iot a bug?

Watchout: this result has been obtained with Maple 2015.2

TIA
 

Is there any command for defining piecewise functions in 2 dimensional domain (x, y)

Say (x,y) such that ((0,0)<(x,y)<(1,1), x+y, (1,1)<(x,y)<(2,1), x-y), x=0..2, y=0..1)

 

Thanks for help.

Ramakrishnan

Hi, I want to animate the motion of an electrond around a negative-source electric field. The trajectory would be iperbolic, however I've encountered one problem: I have to compose the movemente with 4 different animate pointplot3d, and they all start at a certain point at the same time and end in another at the same time. Can I make it so that they all start when another one has finished and only the moving one is shown?

display(
animate(pointplot3d, [[A, sqrt(A^2 - 1), 0], symbol = solidsphere, symbolsize = 15, color = "Blue"], A = 1 .. 3), 
pointplot3d([0, 0, 0], symbol = solidsphere, color = "Blue", symbolsize = 15), 
animate(pointplot3d, [[-A, -sqrt(-1 + (-A)^2), 0], symbol = solidsphere, symbolsize = 15, color = "Blue"], A = -3 .. -1), 
animate(pointplot3d, [[A, 3*sqrt(2)/4*A - sqrt(2)/4, 0], symbol = solidsphere, symbolsize = 15, color = "Blue"], A = 3 .. 6), 
animate(pointplot3d, [[-A, 3*sqrt(2)/4*A - sqrt(2)/4, 0], symbol = solidsphere, symbolsize = 15, color = "Blue"], A = -6 .. -3), 
implicitplot3d(x^2 + y^2 + z^2 = 17, x = -6 .. 6, y = -10 .. 10, z = -10 .. 10, color = "Green", style = wireframe), 
scaling = constrained)

This is the code I've come up with, the blue still point is the elctron which powers the field, the moving blue point (there are 4 of them but all represent the same thing) is the moving electron and the green ball is a representation of the electric field.

Edit: I'll use the code for interactive components.

Thanks in advance to everyone!

 

I have a list of 1's and 2's. Something like [1,1,1,2,2,2]. I want to remove 1 or 2 from the list (only once), without needing to mention at which place. The remove command removes all of the occurrences, I need something similar which remove the given element only once.
>L:[1,1,1,2]
>remove(has, L, 1)
[2]

I want the output to be [1,1,2]

Does Maple support nested modules, to better organize library code?

Hi,

I have created a simple command which extracts the term containing the input. It works fine when I have more than one term in the expression but fails when there is the only one term in the expression. See below.

LT:= (expr, term)-> select(has, expr, term) #extract the operand containing the "term" in the given expression "expr"


>A:=t*u[1,1,1]*u[1,1,1,2]+2;
             

(input)>LT(A, u[1,1,1]);# works as expected, extracting the operand containing u[1,1,1]
 (output) t u[1, 1, 1] u[1, 1, 1, 2]

>op(A);#works, there are two operands
 t u[1, 1, 1] u[1, 1, 1, 2], 2

>A:=t*u[1,1,1]*u[1,1,1,2];
 

>LT(A, u[1,1,1]);#doesn't work, expected output is tu[1,1,1]u[1,1,1,2]
 u[1, 1, 1]

>op(A); doesn't work, expected output is tu[1,1,1]u[1,1,1,2]
t, u[1, 1, 1], u[1, 1, 1, 2]

Find the sum of the degrees of the Neighbors of a vertex say u in a graph G. Kind help with writing a function.

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