Ronan

942 Reputation

14 Badges

11 years, 358 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are questions asked by Ronan

The overloaded  procedure here test returns based on 2 lists or 3 lists entered. The two list has a mixed input type with a default value. The default value of "a" can cause a problem if an explicit value in not entered for "a" in foo1. I not sure is the mixed input type is adding to the problem.
By changing the order of the procedures the problem is avoidable here. But this just a simple example. When there are 6 or so procedures it can be very difficult to select a correct ordering.

Is there a way around this, apart from don't have default values?

I could experiment with changing the input order in each proc but that would break up some logical input sequences on me.

restart

 

foo:=overload([
                        proc(P1::list,P2::list,a::algebraic:=4,$)
                         option overload;
                         print("2 lists");
                          end proc,

                       proc(P1::list,P2::list,P3::list,$)
                         option overload;
                         print("3 lists");
                          end proc
                       ]);

proc () option overload; [proc (P1::list, P2::list, a::algebraic := 4, ` $`) option overload; print("2 lists") end proc, proc (P1::list, P2::list, P3::list, ` $`) option overload; print("3 lists") end proc] end proc

(1)

foo([1,2],[3,4])

"2 lists"

(2)

foo([1,2],[3,4],[4,7])

"3 lists"

(3)

 

 

 

foo1:=overload([
                        

                       proc(P1::list,P2::list,P3::list,$)
                         option overload;
                         print("3 lists");
                          end proc,

                        proc(P1::list,P2::list,a::algebraic:=4,$)
                         option overload;
                         print("2 lists");
                          end proc
                       ]);

proc () option overload; [proc (P1::list, P2::list, P3::list, ` $`) option overload; print("3 lists") end proc, proc (P1::list, P2::list, a::algebraic := 4, ` $`) option overload; print("2 lists") end proc] end proc

(4)

foo1([1,2],[3,4]); #incorrect output

"3 lists"

(5)

foo1([1,2],[3,4],4)

"2 lists"

(6)

foo1([1,2],[3,4],[4,7])

"3 lists"

(7)

 

Download 2024-02-3_Q_Overload_proc_.mw

How do i check if an equation or function does not contain an '=' sign, to convert it?

if eq:= a+b=c

If it has an  '=' I can use eq1:=lhs(eq)-rhs(eq).

If eq=d+e+f there is no lhs/rhs and checking produces an error.

eq := a*x^2 + b*x = v;
                               2          
                      eq := a x  + b x = v

eq1 := lhs(eq) - rhs(eq);
                            2          
                         a x  + b x - v

eq2 := a*x^2 + b*x - v;
                               2          
                     eq1 := a x  + b x - v

lhs(eq1);
Error, invalid input: lhs received a*x^2+b*x-v, which is not valid for its 1st argument, expr
NULL;
has(eq,'=');
Error, invalid uneval
        Typesetting:-mambiguous(hasApplyFunction(eqcomma

          Typesetting:-mambiguous((equals), 

          Typesetting:-merror("invalid uneval"))))


has(eq2, rhs(eq2));
Error, invalid input: rhs received eq2, which is not valid for its 1st argument, expr
NULL;

 

I have done a complete clean reinstall of windows 10 and all programs on my pc.

In worksheet mode new files do not have the "default" red/brown text coluor ond the font is different. 

Might not be a problem but thought that was the default?

What have I changed or have Maple defaults changed?

restart

``

2+2

4

(1)

NULL

eq := x^3+x-7

x^3+x-7

(2)

NULL

Download 23-11-23_Q_inputs_to_worksheet_not_brown_red_colour.mw

I am asking this beacuse I am rusty on using animate in plots. Just trying to show the line segment moving.

restart

with(plottools); with(plots)

Trvl := Matrix(5, 18, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 2, (1, 4) = 3, (1, 5) = 4, (1, 6) = 5, (1, 7) = 6, (1, 8) = 7, (1, 9) = 8, (1, 10) = 9, (1, 11) = 10, (1, 12) = 11, (1, 13) = 12, (1, 14) = 13, (1, 15) = 14, (1, 16) = 15, (1, 17) = 16, (1, 18) = 17, (2, 1) = 25.00000000, (2, 2) = 25.62348980, (2, 3) = 26.24697960, (2, 4) = 26.87046941, (2, 5) = 27.49395921, (2, 6) = 28.11744901, (2, 7) = 28.81795052, (2, 8) = 29.70796779, (2, 9) = 30.69482490, (2, 10) = 31.66997559, (2, 11) = 32.64189447, (2, 12) = 33.63901734, (2, 13) = 34.59934793, (2, 14) = 35.46317753, (2, 15) = 36.17679740, (2, 16) = 36.69583812, (2, 17) = 36.98802824, (2, 18) = 37.03520080, (3, 1) = 9.50000000, (3, 2) = 10.28183148, (3, 3) = 11.06366296, (3, 4) = 11.84549445, (3, 5) = 12.62732593, (3, 6) = 13.40915741, (3, 7) = 14.11748988, (3, 8) = 14.56318511, (3, 9) = 14.69313898, (3, 10) = 14.49329251, (3, 11) = 14.26929209, (3, 12) = 14.29271187, (3, 13) = 14.56209574, (3, 14) = 15.06069470, (3, 15) = 15.75750830, (3, 16) = 16.60921202, (3, 17) = 17.56285107, (3, 18) = 18.55913279, (4, 1) = 26.55872458, (4, 2) = 27.18221431, (4, 3) = 27.80570411, (4, 4) = 28.44091912, (4, 5) = 29.26771501, (4, 6) = 30.27132826, (4, 7) = 31.26754127, (4, 8) = 32.19797655, (4, 9) = 33.15526524, (4, 10) = 34.16855668, (4, 11) = 35.08363639, (4, 12) = 35.87210441, (4, 13) = 36.48493760, (4, 14) = 36.88403298, (4, 15) = 37.04457671, (4, 16) = 36.95658698, (4, 17) = 36.62553455, (4, 18) = 36.06730316, (5, 1) = 11.45457880, (5, 2) = 12.23641019, (5, 3) = 13.01824167, (5, 4) = 13.79066482, (5, 5) = 14.38908368, (5, 6) = 14.67833203, (5, 7) = 14.61699479, (5, 8) = 14.33989949, (5, 9) = 14.25015666, (5, 10) = 14.40907532, (5, 11) = 14.80585186, (5, 12) = 15.41668792, (5, 13) = 16.20360467, (5, 14) = 17.11767545, (5, 15) = 18.10206776, (5, 16) = 19.09557685, (5, 17) = 20.03643114, (5, 18) = 20.86416514})

_rtable[36893489645234278260]

(1)

display(seq(line([Trvl[2, i], Trvl[3, i]], [Trvl[4, i], Trvl[5, i]], color = green), i = 1 .. 18))

 

animate(line([Trvl[2, i], Trvl[3, i]], [Trvl[4, i], Trvl[5, i]], color = green), i = 1 .. 18)

Error, bad index into Matrix

 

NULL

Download 23-11-03_Q_Animate_a_line.mw

If if solve for two circles intersecting the general solution conteint a factor of (xc1-xc2) i.e. x co-ors of the circle centres in both numerator and denominator. So the solution fails if they are equal i.e circles vertically aligned.
I can get arount the problem using  "RealDomain" but that introduces Signum which I dont like and is much slower to solve. I substitued out substitued signum out signum(xc1-xc2)=1. Works.

Just looking for is neater solution approach.
 

restart

NULL

eq1 := (x-xc1)^2+(y-yc1)^2 = R1^2

(x-xc1)^2+(y-yc1)^2 = R1^2

(1)

eq2 := (x-xc2)^2+(y-yc2)^2 = R2^2

(x-xc2)^2+(y-yc2)^2 = R2^2

(2)

eq3 := (xc1-xc2)^2-(yc1-yc2)^2 < (R1+R2)^2

(xc1-xc2)^2-(yc1-yc2)^2 < (R1+R2)^2

(3)

Sol1 := `~`[simplify](solve({eq1, eq2}, [x, y], explicit))[]

[x = (1/2)*((-yc1+yc2)*(-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)-(xc1-xc2)*(-xc1^3+xc1^2*xc2+(R1^2-R2^2+xc2^2-yc1^2+2*yc1*yc2-yc2^2)*xc1-xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2)))/((xc1^2-2*xc1*xc2+xc2^2+(yc1-yc2)^2)*(xc1-xc2)), y = ((-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+yc1^3-yc1^2*yc2+(-R1^2+R2^2+xc1^2-2*xc1*xc2+xc2^2-yc2^2)*yc1+yc2^3+(R1^2-R2^2+xc1^2-2*xc1*xc2+xc2^2)*yc2)/(2*yc1^2-4*yc1*yc2+2*yc2^2+2*(xc1-xc2)^2)], [x = (1/2)*((yc1-yc2)*(-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)-(xc1-xc2)*(-xc1^3+xc1^2*xc2+(R1^2-R2^2+xc2^2-yc1^2+2*yc1*yc2-yc2^2)*xc1-xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2)))/((xc1^2-2*xc1*xc2+xc2^2+(yc1-yc2)^2)*(xc1-xc2)), y = (-(-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+yc1^3-yc1^2*yc2+(-R1^2+R2^2+xc1^2-2*xc1*xc2+xc2^2-yc2^2)*yc1+yc2^3+(R1^2-R2^2+xc1^2-2*xc1*xc2+xc2^2)*yc2)/(2*yc1^2-4*yc1*yc2+2*yc2^2+2*(xc1-xc2)^2)]

(4)

eval(Sol1[1], [R1 = 85, R2 = 30, xc2 = 200, yc2 = 144.85, xc1 = 130, yc1 = 95.7071])

[x = 178.3493912, y = 165.6165872]

(5)

eval(Sol1[2], [R1 = 85, R2 = 30, xc2 = 200, yc2 = 144.85, xc1 = 130, yc1 = 95.7071])

[x = 212.1767210, y = 117.4323513]

(6)

NULL

NULL

NULL

NULL

Sol2 := `assuming`([`~`[simplify](solve({eq1, eq2}, [x, y], explicit))[]], [eq3])

[x = (1/2)*((-yc1+yc2)*(-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)-(xc1-xc2)*(-xc1^3+xc1^2*xc2+(R1^2-R2^2+xc2^2-yc1^2+2*yc1*yc2-yc2^2)*xc1-xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2)))/((xc1^2-2*xc1*xc2+xc2^2+(yc1-yc2)^2)*(xc1-xc2)), y = ((-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+yc1^3-yc1^2*yc2+(-R1^2+R2^2+xc1^2-2*xc1*xc2+xc2^2-yc2^2)*yc1+yc2^3+(R1^2-R2^2+xc1^2-2*xc1*xc2+xc2^2)*yc2)/(2*yc1^2-4*yc1*yc2+2*yc2^2+2*(xc1-xc2)^2)], [x = (1/2)*((yc1-yc2)*(-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)-(xc1-xc2)*(-xc1^3+xc1^2*xc2+(R1^2-R2^2+xc2^2-yc1^2+2*yc1*yc2-yc2^2)*xc1-xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2)))/((xc1^2-2*xc1*xc2+xc2^2+(yc1-yc2)^2)*(xc1-xc2)), y = (-(-(xc1-xc2)^2*(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+yc1^3-yc1^2*yc2+(-R1^2+R2^2+xc1^2-2*xc1*xc2+xc2^2-yc2^2)*yc1+yc2^3+(R1^2-R2^2+xc1^2-2*xc1*xc2+xc2^2)*yc2)/(2*yc1^2-4*yc1*yc2+2*yc2^2+2*(xc1-xc2)^2)]

(7)

NULL

NULL

NULL

NULL

NULL

NULL

NULL

NULL

with(RealDomain)

Sol3 := `~`[simplify](solve({eq1, eq2}, [x, y], explicit))[]

[x = (-(yc1-yc2)*signum(xc1-xc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+xc1^3-xc1^2*xc2+(-R1^2+R2^2-xc2^2+yc1^2-2*yc1*yc2+yc2^2)*xc1+xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2), y = (signum(xc1-xc2)*(xc1-xc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+(yc1+yc2)*xc1^2-2*xc2*(yc1+yc2)*xc1+(yc1+yc2)*xc2^2-(yc1-yc2)*(R1^2-R2^2-yc1^2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2)], [x = ((yc1-yc2)*signum(xc1-xc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+xc1^3-xc1^2*xc2+(-R1^2+R2^2-xc2^2+yc1^2-2*yc1*yc2+yc2^2)*xc1+xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2), y = (-signum(xc1-xc2)*(xc1-xc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+(yc1+yc2)*xc1^2-2*xc2*(yc1+yc2)*xc1+(yc1+yc2)*xc2^2-(yc1-yc2)*(R1^2-R2^2-yc1^2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2)]

(8)

eval(Sol3[1], [R1 = 85, R2 = 30, xc2 = 200, yc2 = 144.85, xc1 = 130, yc1 = 95.7071])

[x = 178.3493912, y = 165.6165871]

(9)

eval(Sol3[2], [R1 = 85, R2 = 30, xc2 = 200, yc2 = 144.85, xc1 = 130, yc1 = 95.7071])

[x = 212.1767209, y = 117.4323512]

(10)

Sol3a := subs(signum(xc1-xc2) = 1, Sol3[1])

[x = (-(yc1-yc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+xc1^3-xc1^2*xc2+(-R1^2+R2^2-xc2^2+yc1^2-2*yc1*yc2+yc2^2)*xc1+xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2), y = ((xc1-xc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+(yc1+yc2)*xc1^2-2*xc2*(yc1+yc2)*xc1+(yc1+yc2)*xc2^2-(yc1-yc2)*(R1^2-R2^2-yc1^2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2)]

(11)

Sol3b := subs(signum(xc1-xc2) = 1, Sol3[2])

[x = ((yc1-yc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+xc1^3-xc1^2*xc2+(-R1^2+R2^2-xc2^2+yc1^2-2*yc1*yc2+yc2^2)*xc1+xc2*(R1^2-R2^2+xc2^2+yc1^2-2*yc1*yc2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2), y = (-(xc1-xc2)*(-(-xc1^2+2*xc1*xc2-xc2^2+(R1-R2+yc1-yc2)*(R1-R2-yc1+yc2))*(-xc1^2+2*xc1*xc2-xc2^2+(R1+R2+yc1-yc2)*(R1+R2-yc1+yc2)))^(1/2)+(yc1+yc2)*xc1^2-2*xc2*(yc1+yc2)*xc1+(yc1+yc2)*xc2^2-(yc1-yc2)*(R1^2-R2^2-yc1^2+yc2^2))/(2*xc1^2-4*xc1*xc2+2*xc2^2+2*(yc1-yc2)^2)]

(12)

eval(Sol3a, [R1 = 85, R2 = 30, xc2 = 200, yc2 = 144.85, xc1 = 130, yc1 = 95.7071])

[x = 212.1767209, y = 117.4323512]

(13)

eval(Sol3b, [R1 = 85, R2 = 30, xc2 = 200, yc2 = 144.85, xc1 = 130, yc1 = 95.7071])

[x = 178.3493912, y = 165.6165871]

(14)

NULL


 

Download 28-10-28_Q_Circles_Intersect.mw

 

1 2 3 4 5 6 7 Last Page 2 of 25