Ramakrishnan

Ramakrishnan Vaidyanathan

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8 years, 309 days

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With twenty years of Industrial experience and twenty years of teaching experience, I am now as retired Professor, using Maple to teach mathematics subject for students studying X to XII standards. Published XII Mathematics books.

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These are questions asked by Ramakrishnan

Fractional part of a negative number is always positive. But maple command frac(-7.8) gives -0.8 instead of 0.2. Why is this? Though we can find it by using 1-frac(x), maple command may be there to give fractional part for all real numbers as per definition.

Like frac(9.8)=0.8 and frac(-9.8)=0.2.

Is there a command in maple?

Thanks. Ramakrishnan V

A polynomial divided by another polynomial of lower degree. I want to find the remainder and quotient. How do I get.

The question is what should I add to the numerator get perfect division when x-3 x  -12 x+19 is divided by x2+x-6.

I shd get the answer as 2x+5 to be added since the remainder is -2x-5.   (Note that x-3 x  -10 x+24 is excatly divided by 2+x-6.

Can any one state the code to get the answer.

Quotient ( ) and Remainder (  ) codes , i tried, donot know how to use them.

Thanks for help. Cheers. RK

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 am not getting the hemisphere which I thought was my expression (equation) represents.

Can anyone help me find my mistake.

with(plots);
implicitplot3d(z <= sqrt(-x^2 - y^2 + 9), x = -3 .. 3, y = -3 .. 3, z = 0 .. 3, coords = spherical);

Thanks in advance.

Doubt_ImplicitPlot.mw

I have recently received a doc from my friend in privete group in maple cloud, the table showed both eye(view) icon and download icon).When I downloaded and run, the document does not run (maple 2019). 

When I sign in maple cloud and see the doc (only view button is ahow), the same document works fine. What could be the error?

I attach  a document extract showing the errors (unable to delimt   .../  identifiers).

Can any one help us please?

Thanks. Ramki.
 

``

"Refraction Demonstration          restart:with(plots):  RefractionDemo:=proc(theta1, n2)  local theta2,ainput,ainside,aoutput,box,line1,line2,H,n2text,theta1text,theta2text;   if(theta1<0)or(theta1>Pi/(2.0001)) then return end if;   #theta1:=theta01*Pi180.;   theta2:=arcsin(1/(n2)*sin(theta1));   ainput:=arrow(?&ndash;cos(theta1),&ndash;sin(theta1)?,?cos(theta1),sin(theta1)?,color="Red"):   ainside:=arrow(?0,0?,?1,tan(theta2)?,color="DarkBlue",width=[0.05,relative=false]):   aoutput:=arrow(?1,tan(theta2)?,?cos(theta1),sin(theta1)?,color="Red"):   line1:=plot(0,x=&ndash;1..0,thickness=4,color=black);   line2:=plot(tan(theta2),x=1..2,thickness=4,color=black);   H:=1.8:   box:=plottools:&ndash;rectangle([0,&ndash;H],[1,H],color="LightBlue"):   n2text:=textplot([0.5,1.5,sprintf("n_2=%1.3 g",n2)]);   theta1text:=textplot([&ndash;0.5,0.4,sprintf("theta_1=%4.3 g",theta1)]);   theta2text:=textplot([0.5,&ndash;0.4,sprintf("theta_2=%4.3 g",theta2)]);   display([ainput,ainside,aoutput,box,line1,line2,n2text,theta1text,theta2text],scaling=constrained,view=[&ndash;1..2,&ndash;1..H]);   endproc:        Light enters from the air into a medium at an angle of theta1 relative to the normal. It is refracted to an angle of theta2and travels through the medium, returning back to the air.      You can vary two parameters:       theta1the angle of incidence       n2the index of refraction of the medium*(assuming the index of refraction of the air is essentially 1.0).     To do: Let it execute and start manipulating the sliders.     >Explore(RefractionDemo(theta1,n2),parameters=[theta1=0..Pi2.0015,n2=1..3.]);6""

Error, unable to delimit strings/identifiers

"Refraction Demonstration          restart:with(plots):  RefractionDemo:=proc(theta1, n2)  local theta2,ainput,ainside,aoutput,box,line1,line2,H,n2text,theta1text,theta2text;   if(theta1<0)or(theta1>Pi/2.0001) then return end if;   #theta1:=theta01*Pi180.;   theta2:=arcsin(1/n2*sin(theta1));   ainput:=arrow(&acirc;ï¿&frac12;&uml;&ndash;cos(theta1),&ndash;sin(theta1)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):   ainside:=arrow(&acirc;ï¿&frac12;&uml;0,0&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,color="DarkBlue",width=[0.05,relative=false]):   aoutput:=arrow(&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):   line1:=plot(0,x=&ndash;1..0,thickness=4,color=black);   line2:=plot(tan(theta2),x=1..2,thickness=4,color=black);   H:=1.8:   box:=plottools:&ndash;rectangle([0,&ndash;H],[1,H],color="LightBlue"):   n2text:=textplot([0.5,1.5,sprintf("n_2=%1.3 g",n2)]);   theta1text:=textplot([&ndash;0.5,0.4,sprintf("theta_1=%4.3 g",theta1)]);   theta2text:=textplot([0.5,&ndash;0.4,sprintf("theta_2=%4.3 g",theta2)]);   display([ainput,ainside,aoutput,box,line1,line2,n2text,theta1text,theta2text],scaling=constrained,view=[&ndash;1..2,&ndash;1..H]);   endproc:        Light enters from the air into a medium at an angle of theta1 relative to the normal. It is refracted to an angle of theta2and travels through the medium, returning back to the air.      You can vary two parameters:       theta1the angle of incidence       n2the index of refraction of the medium*(assuming the index of refraction of the air is essentially 1.0).     To do: Let it execute and start manipulating the sliders.     >Explore(RefractionDemo(theta1,n2),parameters=[theta1=0..Pi2.0015,n2=1..3.]);"

 

``

``

``

``Dear Prof.

The following code seems not copying properly (my communication error be allowed please)

 

"ainput:=arrow(?&"

Error, unable to delimit strings/identifiers

"ainput:=arrow(&acirc;ï¿&frac12;&uml;&ndash;cos(theta1),&ndash;sin(theta1)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):ainside:=arrow(&acirc;ï¿&frac12;&uml;0,0&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,color="DarkBlue",width=[0.05,relative=false]):aoutput:=arrow(&acirc;ï¿&frac12;&uml;1,tan(theta2)&acirc;ï¿&frac12;&copy;,&acirc;ï¿&frac12;&uml;cos(theta1),sin(theta1)&acirc;ï¿&frac12;&copy;,color="Red"):"

 

``

``

"I checked by typing separately. It works as below."

``

``

a1 := arrow([-cos(theta1), -sin(theta1)], color = "LightBlue")

 

``ainput := arrow([-1, 0], color = "Red")

 

"But the copied from your code does not work."

"ainput:=arrow([-1, 0],color= "`Red"`)"

Error, unable to delimit strings/identifiers

"ainput:=arrow([-1, 0],color= "`Red"`)"

 

``


 

Download forScotgould_Error_arrow.mw

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