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

I started using maple around 1995 on the Inverse Symbolic Calculator to discover the MRB constant and got put on this list.

Do you consider yourself to be one?

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This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics.

• Ahmes (scribe)
• Ashutosh Mukherjee (Lawyer)
• Robert Ammann (programmer and postal worker)
• John Arbuthnot (surgeon and author)
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• Rev. Thomas Bayes (Presbyterian minister)
• Andrew Beal (businessman)
• Isaac Beeckman (candlemaker)
• Chester Ittner Bliss (biologist)
• Napoléon Bonaparte (general)
• Mary Everest Boole (homemaker, librarian)
• William Bourne (innkeeper)
• Nathaniel Bowditch (indentured bookkeeper)
• Achille Brocot (clockmaker)
• Harlan J. Brothers (teacher, inventor, and musician)
• Jost Bürgi (clockmaker)
• Marvin Ray Burns (veteran)

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.

I'm trying to create a custom component in MapleSim 2021, and I want to use Thermal Fluid Flow Ports. However, they don't show up as a type of port in the port Type dropdown.  How can I create a thermal fluid flow port using the Custom Component Template?

Let.Find the equation of the circle touching the graph  at three points?

dsolve accept system of first order ode's in the form x'=A x, where x' is vector, A is matrix of coefficients and x are the dependent variables. This is convenient since one does not have to convert things to a list.

But  dfieldplot and phaseportrait and DEplot do not accept this form. One must convert things to list first.

Here is an example

restart;
sys:=Vector([diff(x(t),t),diff(y(t),t)]) = Matrix([[1,2],[0,3]]).Vector([x(t),y(t)]);
dsolve(sys)

But

DEtools:-dfieldplot(sys,[x(t),y(t)],t=0..4,x=-4..4, y=-4..4);

Error, (in DEtools/dfieldplot) system must have same number of dependent variables as DE's.

workaround is to write the system as list

new_sys:=[diff(x(t), t)=x(t) + 2*y(t),diff(y(t), t)=3*y(t)];
DEtools:-dfieldplot(new_sys,[x(t),y(t)],t=0..4,x=-4..4, y=-4..4);

I know one can automate the conversion. But still, it would be better if dfieldplot would accept sys as dsolve did.

Same for 

DEtools:-phaseportrait(sys,[x(t),y(t)],t=0..4,[[x(0)=1,y(0)=0]],x=-4..4, y=-4..4);
#
DEtools:-DEplot(sys,[x(t),y(t)],t=0..4,[[x(0)=1,y(0)=0]],x=-4..4, y=-4..4);

They gives same error.

Since dsolve can do it, may be these other functions can also support taking a system of ode's in vector/matrix form? Any reason why not?

Maple 2021.1