Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I have asked this before but am still confused. I have a half-dozen procedures I want to save. Don't want them in a module/package. I am using windows 10.

I just can't get the syntax correct on this.

Obviously after saving restart and load to test.

libname;
       "C:\Program Files\Maple 2018\lib", 

         "C:\Users\Ronan\maple\toolbox\CodeBuilder\lib", 

         "C:\Users\Ronan\maple\toolbox\OEIS\lib", 

         "C:\Users\Ronan\maple\toolbox\personal\lib", 

         "C:\Users\Ronan\maple\toolbox\UTF8\lib"
libdir := "C:/Users/Ronan/maple/toolbox/personal/lib";
     libdir := "C:/Users/Ronan/maple/toolbox/personal/lib"
NULL;

LibraryTools:-Save(Pedal, cat(kernelopts(homedir), "/maple/toolbox/personal/lib/Pedal.mpl"));
Error, (in LibraryTools:-Save) could not open `C:\Users\Ronan/maple/toolbox/personal/lib/Pedal.mpl\Pedal.m` for writing

 

Please tell me where I go wrong

And I have not even tried lamda in nanometers

Since theata is small I repalce sin(theta) by theta because, with units, sin did not compute

Anyone know a good reference (book/website) explaing Maple units?

Many thanks


TelescopeUnits.mw

Hi

I hope everyone is fine.

Here is a nice question :

I have an inequality ( please see maple code) if I assume a special condition (on |f(u,s)| used in the code )

how can I get an upper bound of the function |x(t)| and is the upper bound converges to zero when t goes to infinity.

Maybe this is can be done using maple because by hand up to know I can't find an upper bound which converges to zero as t goes to infinity.

Maybe, there is  a good, nice and appropriate answer using maple.

Below, please find the upper_bound.mw code.

Many thinks

 

Upper_bound.mw


 

``

restart; assume*(0 < gamma); assume*(0 < M)

(0 < gamma)*assume

 

(0 < M)*assume

(1)

abs(x(t)) <= exp(-gamma*t)*abs(x(0))+int(abs(x(s))*(int(exp(-gamma*(t-u))*abs(f(u, s)), u = s .. t)), s = 0 .. t);

abs(x(t)) <= exp(-gamma*t)*abs(x(0))+int(abs(x(s))*(int(exp(-gamma*(t-u))*abs(f(u, s)), u = s .. t)), s = 0 .. t)

(2)

assume*(int(abs(f(u, s)), u = 0 .. infinity) < M)

(int(abs(f(u, s)), u = 0 .. infinity) < M)*assume

(3)

``

 

(I*Can*get*an*upper*bound*of*abs(x(t))*when*I)*assume; int(abs(f(u, s)), u = 0 .. infinity) < M


 

Download Upper_bound.mw

I am curious how one can fine the whattype of operation in expression when two variables are actually doing difference or division operation

like

whattype(a-b);
whattype(a/b);

is there any better method to find out actually for all five operations exactly.

1. a-b;  should tell the operation is difference(substraction(`-`))
2. a+b; should tell the operation is addition(`+`)
3. a*b;  should tell the operation is multiplication(`*`)
4. a/b;  should tell the operation is division(`/`)
5. a^b;  should tell the operation is power(`^`)

I understood that maple is reading a-b as a+(-b) and same a/b as a*(1/b). but, for programing it is very much comfortable to know exactly the operation. Especially when solving partial differentiation it is easy if I know exactly.

would be very grateful if I can get this thing solved. Any suggestions and coments are welcomed and thanks in advance
 

Hi,

      I need to compute something involved with the pseudo differential operators.

https://en.wikipedia.org/wiki/Pseudo-differential_operator

Specifically, I need to calculate the inverse of a pseudo differential operator, the multiplication of two pseudo differential operators, and the n-th root of a pseudo differential operator. 

I don't know whether Maple could handle these. 

Thanks.

Respected sir,

I have attached a file that contain integration . Sir I am unable to solve please give me some hint.

PLease note followings 

1. I want to get final expression , want to get the value of constant from boundary condition.

2.I want to get the final expression (.......+c1)

3.I will put boundary condition to determine the value of c1

Dear all;

I need a help to get a simple code about the null hypothesis test.

A drug is administrad to a population X of size 50 while a  placebo is given to a population Y of size 25.

Observed results of good bad and no effects are given in the following vectors for both population.

X=[ 20,11,19];

Y=[4,4,17];

test the null hypothesis H0: population independent of treatment versus the one tailed alternative that they are dependent by computing the theoretical contingency table with entries T[i,j] where i=1,2

for the two rows and j=1,2,3 for the three columns. At what p-value can we reject H0.

Many thanks

There is a simulation of a T handle in space done in matlab https://rotations.berkeley.edu/a-tumbling-t-handle-in-space/

Would like to see someone do this in Maple. More specifically how the Matlab code would look like translated to Maple

restart;
sign(-v1+a);
sign(-V1+a);

my respective outputs are

1
-1

I cannot understand what is the difference between using lowercase and uppercase variable. Could Someone Explain me please.

I have to Two Lists with Equal size. Each element in one List is an variable and Each element in second List is an Value of the variable corresponds to First List.

Now when Ever I call a variable I need the script to read its value and Compute.

For Example:

List1 := [v1,v2,v3,v4];
List2 := [a*b/c, a/c,a*b-2,d];

computation := v1*diff(expression,x)+v3*diff(expression,y)+ v3*v4;

but I need the script to read it as

requiredComputation :=(a*b/c)*diff(expression,x)+(a*b-2)*diff(expression,y)+ a*b-2*d;

I used to do this kind of computation in matlab using containers and map. Is there any thing similar??

I was trying some calculations for a solar installation.

4.9kW system. 3.5 h sun/day.  $0.27/kWh

restart:
with(Units:-Standard):
                     "maple init loaded..."
4.9*Unit(kW)*3.5*Unit(h/day)

714.583333333333*Unit('W')

but I want it to output 17.15 kWh/day

I looked up previous questions, and got this rather convoluted solution:

restart: 
Units[AddSystem]( NewSI, Units[GetSystem](SI), kWh/day );
 Units[UseSystem]( NewSI ); 
combine( 4.9*Unit(kW)*3.5*Unit(h/day), units ); 


17.15*Unit('kWh'/'d')

Hi. I hope this question is not a duplicate of my previous question. Fundiff function results in dirac terms in an equation. Are there commands that simply differentiates a term that is a function of (t) in an equation without involving diracs?

Can we change the color of the units measure?

ie 5 m (5 meters - where m is default black) can the m be changed to a different color for all unit measure entries?

MY CODE:
 

with(Physics);
Setup(mathematicalnotation = true);
Setup(Coordinatesystem = (X = [x, y, z, t]), metric = 4*dx*dt-dy^2-dz^2+4*u*(dt^2));
    * Partial match of  'Coordinatesystem' against keyword 

       'coordinatesystems'
    Systems of spacetime Coordinates are: (Xequals(x,y,z,t))
[coordinatesystems = {X}, 

  metric = {(1, 4) = 2, (2, 2) = -1, (3, 3) = -1, (4, 4) = 4 u}]
g_[];      (here g is diplayed in matrix form)

Weyl[alpha, beta, mu, nu, nonzero];
            Physics:-Weyl[alpha, beta, mu, nu] = {}

So basically i'm trying to find the nonzero components of the weyl tensor which returns the empty set, i.e the weyl tensor apparently equals zero but I know this is not the case, can anyone see if I have input something wrong? Thanks in advance

g_[] in matrix form is 
0 0 0 2
0 -1 0 0
0 0 -1 0
2 0 0 4u

UPDATE: u is a function of all varibles and I have not considered this which might be causing the problem


I trying to get a proc to work. In the 1st half of the document, I derive four sections for a pedal curve and plot them fine. In the second I try doing it with a procedure called Pedal. Am having problems. I think it might be something to do with the for.. do loop. 

restart

NULLNULL

Typesetting:-mrow(Typesetting:-mi("Trunc", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("proc", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("F", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&Proportion;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("procedure", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("`+`", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odr", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&Proportion;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("posint", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("2", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("v", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&Proportion;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("list", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("name", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("y", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mi(""), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("description", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-ms(" Truncates an algebraic equation to required degree"), Typesetting:-mo(";", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo("local", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("f", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("`if`", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("F", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&Proportion;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("procedure", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("F", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("v", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("F", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(";", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("print", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("F", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(";", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("if", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("not", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("f", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&Proportion;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("`+`", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("then", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("error", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-ms("Can't truncate 1-term expression"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("else", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("select", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("q", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&srarr;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("degree", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("q", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("v", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("&leq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odr", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("f", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mi(""), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("fi", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("proc", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"))

NULLNULLNULL

NULL

a := 3; b := -1; c := -1

C := (x^2+y^2+12*x+9)^2-4*(2*x+3)^3

(x^2+y^2+12*x+9)^2-4*(2*x+3)^3

(1)

p21 := plots:-implicitplot(C, x = -3 .. 3, y = -5 .. 5, colour = "Salmon", gridrefine = 2, size = [300, 300])

 

sol1 := [solve(C, y)]

[(-x^2-12*x-9+2*(8*x^3+36*x^2+54*x+27)^(1/2))^(1/2), -(-x^2-12*x-9+2*(8*x^3+36*x^2+54*x+27)^(1/2))^(1/2), (-x^2-12*x-9-2*(8*x^3+36*x^2+54*x+27)^(1/2))^(1/2), -(-x^2-12*x-9-2*(8*x^3+36*x^2+54*x+27)^(1/2))^(1/2)]

(2)

NULL

f1 := expand(eval(C, [x = X+r, y = Y+s]))

X^4+4*X^3*r+2*X^2*Y^2+4*X^2*Y*s+6*X^2*r^2+2*X^2*s^2+4*X*Y^2*r+8*X*Y*r*s+4*X*r^3+4*X*r*s^2+Y^4+4*Y^3*s+2*Y^2*r^2+6*Y^2*s^2+4*Y*r^2*s+4*Y*s^3+r^4+2*r^2*s^2+s^4-8*X^3-24*X^2*r+24*X*Y^2+48*X*Y*s-24*X*r^2+24*X*s^2+24*Y^2*r+48*Y*r*s-8*r^3+24*r*s^2+18*X^2+36*X*r+18*Y^2+36*Y*s+18*r^2+18*s^2-27

(3)

ltg1 := simplify(expand(eval(Trunc(f1, 1, [Y, X]), [X = x-r, Y = y-s])))

-3*r^4+(4*x+16)*r^3+(-6*s^2+4*s*y-24*x-18)*r^2+((4*x-48)*s^2+48*s*y+36*x)*r-27-3*s^4+4*s^3*y+(24*x-18)*s^2+36*s*y

(4)

NULLThis*section*works*out*the*pedal*curve

This*section*works*out*the*pedal*curve

(5)

xp1 := 1; yp1 := 2; lprp1 := -coeff(ltg1, y)*x+coeff(ltg1, x)*y+K1; for i to nops(sol1) do s := eval(sol1[i], x = r); print("s  ", s); K1 := solve(eval(lprp1, [x = xp1, y = yp1]), K1); print("K1  ", K1); sol2 := solve([ltg1, lprp1], [x, y]); Pedal || i := [rhs(sol2[1, 1]), rhs(sol2[1, 2])]; p9 || i := plot([op(Pedal || i), r = -20 .. 20], colour = "MediumSeaGreen"); unassign('K1', 'sol2') end do

"K1  ", -4*(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(3/2)-4*r^2*(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(1/2)+16*(8*r^3+36*r^2+54*r+27)^(1/2)*r-48*r*(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(1/2)+192*r^2+96*(8*r^3+36*r^2+54*r+27)^(1/2)-36*(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(1/2)+576*r+432

(6)

seq(simplify(Pedal || i), i = 1 .. nops(sol1))

[((((2*r+3)^3)^(1/2)+6*r+9)*(-r^2-12*r-9+2*((2*r+3)^3)^(1/2))^(1/2)-2*(r-3)*(r^2+(5/2)*r-((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18), ((-2*r^2-3*r-((2*r+3)^3)^(1/2))*(-r^2-12*r-9+2*((2*r+3)^3)^(1/2))^(1/2)+6*(r-3)*(r-(1/6)*((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18)], [((-((2*r+3)^3)^(1/2)-6*r-9)*(-r^2-12*r-9+2*((2*r+3)^3)^(1/2))^(1/2)-2*(r-3)*(r^2+(5/2)*r-((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18), ((2*r^2+((2*r+3)^3)^(1/2)+3*r)*(-r^2-12*r-9+2*((2*r+3)^3)^(1/2))^(1/2)+6*(r-3)*(r-(1/6)*((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18)], [((6*r-((2*r+3)^3)^(1/2)+9)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)-2*(r-3)*(r^2+(5/2)*r+((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18), ((-2*r^2+((2*r+3)^3)^(1/2)-3*r)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+6*(r-3)*(r+(1/6)*((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18)], [((((2*r+3)^3)^(1/2)-6*r-9)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)-2*(r-3)*(r^2+(5/2)*r+((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18), ((2*r^2-((2*r+3)^3)^(1/2)+3*r)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+6*(r-3)*(r+(1/6)*((2*r+3)^3)^(1/2)+3/2))/(4*r^2-6*r-18)]

(7)

plots:-display(p21, seq(p9 || i, i = 1 .. nops(sol1)), size = [600, 600], scaling = constrained, caption = " Curve and it's Pedal curve")

 

This I can't get to work. All 4 sections of the pedal curve are the same and should not be.

Parse:-ConvertTo1D, "`%1` is not a module or member", RonanRoutines

Pedal2 := Pedal(C, xp1, yp1)

"K||i", -8*r^3+(-4*(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(1/2)+48)*r^2-8*(-(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(1/2)-3)^2*r-4*(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(3/2)+48*r^2+576*r+432+96*(8*r^3+36*r^2+54*r+27)^(1/2)-36*(-r^2-12*r-9-2*(8*r^3+36*r^2+54*r+27)^(1/2))^(1/2)

(8)

seq(simplify(Pedal2[i]), i = 1 .. nops(sol1))

[((4*r^2+6*((2*r+3)^3)^(1/2)+30*r+36)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(-r^2-34*r-69)*((2*r+3)^3)^(1/2)-26*r^3-243*r^2-540*r-351)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162), (((r+9)*((2*r+3)^3)^(1/2)+14*r^2+51*r+45)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(12*r+72)*((2*r+3)^3)^(1/2)+4*r^3+126*r^2+432*r+378)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162)], [((4*r^2+6*((2*r+3)^3)^(1/2)+30*r+36)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(-r^2-34*r-69)*((2*r+3)^3)^(1/2)-26*r^3-243*r^2-540*r-351)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162), (((r+9)*((2*r+3)^3)^(1/2)+14*r^2+51*r+45)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(12*r+72)*((2*r+3)^3)^(1/2)+4*r^3+126*r^2+432*r+378)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162)], [((4*r^2+6*((2*r+3)^3)^(1/2)+30*r+36)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(-r^2-34*r-69)*((2*r+3)^3)^(1/2)-26*r^3-243*r^2-540*r-351)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162), (((r+9)*((2*r+3)^3)^(1/2)+14*r^2+51*r+45)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(12*r+72)*((2*r+3)^3)^(1/2)+4*r^3+126*r^2+432*r+378)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162)], [((4*r^2+6*((2*r+3)^3)^(1/2)+30*r+36)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(-r^2-34*r-69)*((2*r+3)^3)^(1/2)-26*r^3-243*r^2-540*r-351)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162), (((r+9)*((2*r+3)^3)^(1/2)+14*r^2+51*r+45)*(-r^2-2*((2*r+3)^3)^(1/2)-12*r-9)^(1/2)+(12*r+72)*((2*r+3)^3)^(1/2)+4*r^3+126*r^2+432*r+378)/((2*r+30)*((2*r+3)^3)^(1/2)+36*r^2+162*r+162)]

(9)

for i to nops(sol1) do p9 || i := plot([op(Pedal2[i]), r = -20 .. 20], colour = "MediumSeaGreen") end do

 

``

NULL

NULL

``


 

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