Ronan

1371 Reputation

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13 years, 226 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are answers submitted by Ronan

  This might help. In Maple 2024 under Format Styles  you can alter the font and other settings. Different Styles sets can be exported and imported using Manage Styles Sets.

I am not exactly sure frm you wording of "k consecutive random characters". Is this what you want?

restart

NULL

randomize

randomize

(1)

[seq(StringTools:-Char(i), i = 30 .. 128)]

["", "", " ", "!", """, "#", "$", "%", "&", "'", "(", ")", "*", "+", ",", "-", ".", "/", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", ":", ";", "<", "=", ">", "?", "@", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z", "[", "\", "]", "^", "_", "`", "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "{", "|", "}", "~", "", "�"]

(2)

num := rand(30 .. 128)

proc () (proc () option builtin = RandNumberInterface; end proc)(6, 99, 7)+30 end proc

(3)

k := 25

25

(4)

[seq(StringTools:-Char(num()), i = 1 .. k)]

["O", "L", "%", "K", "I", "&", "j", "X", "-", "", "c", "j", "D", "y", "d", "`", "k", "P", "R", ")", "0", "\", "E", "w", " "]

(5)

NULL

Download 2025-10-12_A_Random_Characters.mw

You can do this .

evalc(D11)

To get real part only.

evalc(Re(D11))

Or imaginary part only.

evalc(Im(D11))

It i seasiest to use Equal fr0m the LlinearAlgebra package for this.

V1 := <2, 3, -7>;
                             [    2     ]
                             [          ]
                       V1 := [    3     ]
                             [          ]
                             [&uminus0;7]

V2 := <2, 3, -7>;
                             [    2     ]
                             [          ]
                       V2 := [    3     ]
                             [          ]
                             [&uminus0;7]

Equal(V1, V2);
                              true

The is something to do with how maple evaluates Vectors and Matrices.  delay evaluation quotes  '...... help here. There may be nicer ways to do this though.

{'Matrix'([1])} union {'Matrix'([1])};
                         {Matrix([1])}

eval({'Matrix'([1])} union {'Matrix'([1])});
                             {[1]}



 

One of your simpler puzzles. 

restart

NULL

NULL

A := Matrix(4, 7, {(1, 1) = 343, (1, 2) = 0, (1, 3) = 15625, (1, 4) = 0, (1, 5) = 32, (1, 6) = 0, (1, 7) = 36, (2, 1) = 0, (2, 2) = x, (2, 3) = 0, (2, 4) = 15657, (2, 5) = 0, (2, 6) = 68, (2, 7) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 31625, (3, 4) = 0, (3, 5) = y, (3, 6) = 0, (3, 7) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = z, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0})

Matrix(%id = 36893489885763238716)

(1)

The rows appear to be sums of of pairs above.

x := A[1, 1]+A[1, 3]

15968

(2)

x+A[2, 4]

31625

(3)

y := A[2, 4]+A[2, 6]

15725

(4)

z := A[3, 3]+y

47350

(5)

evalm(A)

array( 1 .. 4, 1 .. 7, [( 4, 5 ) = (0), ( 1, 2 ) = (0), ( 2, 4 ) = (15657), ( 1, 5 ) = (32), ( 1, 6 ) = (0), ( 3, 6 ) = (0), ( 1, 3 ) = (15625), ( 3, 4 ) = (0), ( 3, 2 ) = (0), ( 2, 3 ) = (0), ( 4, 2 ) = (0), ( 4, 1 ) = (0), ( 1, 1 ) = (343), ( 3, 7 ) = (0), ( 2, 2 ) = (15968), ( 4, 6 ) = (0), ( 2, 1 ) = (0), ( 2, 6 ) = (68), ( 2, 5 ) = (0), ( 2, 7 ) = (0), ( 1, 7 ) = (36), ( 4, 3 ) = (0), ( 1, 4 ) = (0), ( 3, 1 ) = (0), ( 3, 5 ) = (15725), ( 4, 4 ) = (47350), ( 4, 7 ) = (0), ( 3, 3 ) = (31625)  ] )

(6)

NULL

Download 5-05-25_A_sums.mw

This works. Nothing fancy.

plot(rhs(sol_1),x=0.15..5)

If the file doesn't use new features it willl open with a warning that it was created in a newer version of Maple. It should run ok. I opened one from a 2025 answer earlier.

9/2=4.5   Gives a similar triangle to the yellow one

sqrt(4.5/2)=sqrt( 2.25)=1.5   square root of ratio of areas gives sides ratio

(1.5+1)^2*2=12.5 ( total ratio of side length to mid point)^2 times yellow area gives size of triangle to midpoint of side AD.

12.5+12.5-2 =23 (green area)  

For some reason I can't upload the worksheet.
It is just the 3,4,5 triangle.

restart

sph:=(x-3)^2+(y-7)^2+(z-4)^2-25

plxy:=z=0
plyz:=x=0
ctr:=[3,7,4]
R:=5
ctrplxy:=[3,7,0]
4^2+Rxy^2=5^2
fsolve( ?? );
Rxy:=3
ctrplyz:=[0,7,4]
3^2+Ryz^2=5^2

fsolve( ?? );
Ryz:=4
#Center  and Radius on xy plane
ctrplxy;
Rxy
#Center  and Radius on yz plane
ctrplyz;
Ryz

This is just a quick test. I drew it in a CAD system to see. And  another possible assumption is the side slopes are equal.

 

On my pc Maple docs are here. Or are you asking about windows File History?

If memory serves me correctly, I think I specified Home User. As I have a Personal Edition license.

Hope this is correct
 

restart

L:=1

1

(1)

E:=[0,0]

[0, 0]

(2)

A:=[-1/2*L,L*sqrt(3)/2]

 

[-1/2, (1/2)*3^(1/2)]

(3)

D1:=[L,0]

[1, 0]

(4)

C:=[L,L]

[1, 1]

(5)

AC:=C-A

[3/2, -(1/2)*3^(1/2)+1]

(6)

AB:=L

1

(7)

BC:=L

1

(8)

expn1:=2*L*cos(theta)=sqrt(AC[1]^2+AC[2]^2)

2*cos(theta) = (1/2)*(9+4*(-(1/2)*3^(1/2)+1)^2)^(1/2)

(9)

theta:=solve(expn1,theta)

arccos((1/4)*(9+4*(-(1/2)*3^(1/2)+1)^2)^(1/2))

(10)

b:=2*Pi-(Pi-2*theta)

Pi+2*arccos((1/4)*(9+4*(-(1/2)*3^(1/2)+1)^2)^(1/2))

(11)

simplify( (11) );

2*Pi-2*arcsin((1/2)*(4-3^(1/2))^(1/2))

(12)

expn2:=L-L*cos(c)=L*sin(2*Pi/3)-L*sin(a+Pi/3)

1-cos(c) = (1/2)*3^(1/2)-sin(a+(1/3)*Pi)

(13)

expn3:=L-L*sin(c)=L*cos(2*Pi/3)+L(a+Pi/3)

1-sin(c) = 1/2

(14)

c:=solve(expn3,c)

(1/6)*Pi

(15)

a:=solve(expn2,a)

-(1/3)*Pi+arcsin(3^(1/2)-1)

(16)

simplify( (16) );

-(1/3)*Pi+arcsin(3^(1/2)-1)

(17)

B[1]:=L-L*sin(c)

1/2

(18)

B[2]:=L-L*cos(c)

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

(19)

B:=[B[1],B[2]]

[1/2, -(1/2)*3^(1/2)+1]

(20)


plots:-display(plottools:-polygon([E,D1,C,B,A]),colour=yellow)

1

 

 

 


 

Download Fun-Angles.mw

In you expression

test := subs(a = 2, x^2/2 + x*a + a^2*ln(x - a))

ln(x-a) becomes complex with x<a.

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