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Ronan

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13 years, 43 days
East Grinstead, United Kingdom
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These are questions asked by Ronan

Implicitplot empty, Why?...

Ronan 1331 Maple 2018
October 19 2018
2 6

Why does the implicit plot return empty?

plots:-implicitplot((x^2+y^2 = 1)^2, x = -3 .. 3, y = -3 .. 3);# plots
   plots:-implicitplot((x^2+y^2-1)^2, x = -3 .. 3, y = -3 .. 3) # empty plot

 

Assume and Signum problem...

Ronan 1331 Maple 2018
assume signum
September 27 2018
1 0


I have assumed lambda <-1 yet signum(lambda) returns lambda~.  It should be -1. I need to show that the expression lambda is used in is negative. 

restart

NULL

assume(t > 0, k > 1, lambda = 'real', mu = 'real', mu = 'real', lambda+mu+nu = 1)

about(lambda)

Originally lambda, renamed lambda~:

  Involved in the following expressions with properties
    -real+lambda assumed `property/object`[0]
    lambda+mu+nu assumed `property/object`[1]
  also used in the following assumed objects
  [-real+lambda] assumed 0
  [lambda+mu+nu] assumed 1

  

signum(lambda)

signum(lambda)

 (1)

additionally(lambda <= -1)

about(lambda)

Originally lambda, renamed lambda~:

  Involved in the following expressions with properties
    -real+lambda assumed `property/object`[0]
    lambda+mu+nu assumed `property/object`[1]
  is assumed to be: RealRange(-infinity,-1)
  also used in the following assumed objects
  [-real+lambda] assumed 0
  [lambda+mu+nu] assumed 1

  

signum(lambda)

signum(lambda)

 (2)

sCDB := (4*(k-1))*(k+1)*`&lambda;`*t^3/((t^2+1)^2*(k^2*t^2+1))

4*(k-1)*(k+1)*lambda*t^3/((t^2+1)^2*(k^2*t^2+1))

 (3)

signum(sCDB)

signum(lambda)

 (4)

``


 

Download signum_problem.mw

Simplify What assumptions to treat a,b a...

Ronan 1331 Maple 2018
simplify
August 31 2018
2 0 
A := (a^6)^(1/3)*(-b^3)^(1/3)/a^3

I Can't get this to simplify to -b/a. 

How to get procedure to handle f or f(x,...

Ronan 1331 Maple 2018
polynomial degree
August 13 2018
3 3

I have a procedure to truncate algebraic equations. Found the basic answer hrere. I would like to make it handle equations and functions i.e f:=a x^2 +b y... and f(x,y):=c x y^2.... I can make it handle the first type but not the second.

restart

``

NULL

NULL

Trunc := proc (eq, odr := 2, v::list := [x, y, z]) local a, b, q; description " Truncates an algebraic equation to required degree"; a := eq; b := v; map(select, proc (q) options operator, arrow; evalb(degree(q, b) <= odr) end proc, a) end proc

proc (eq, odr := 2, v::list := [x, y, z]) local a, b, q; description " Truncates an algebraic equation to required degree"; a := eq; b := v; map(select, proc (q) options operator, arrow; evalb(degree(q, b) <= odr) end proc, a) end proc

 (1)

"E1(x,y,z):=2+3 x-y+5 x^(2)y+4 x y+x y^(3)+3 a^(2)+z+z^(2)"

proc (x, y, z) options operator, arrow, function_assign; 2+3*x-y+5*x^2*y+4*y*x+x*y^3+3*a^2+z+z^2 end proc

 (2)

Trunc(E1, 2, [x, y, z])

E1

 (3)

``

E2 := E1(x, y, z)

x*y^3+5*x^2*y+3*a^2+4*x*y+z^2+3*x-y+z+2

 (4)

Trunc(E2, 1, [x, y])

3*a^2+z^2+3*x-y+z+2

 (5)

Trunc(E2, 1, [x, y, z])

3*a^2+3*x-y+z+2

 (6)

``whattype(E1(x, y, z))

`+`

 (7)

whattype(E2)

`+`

 (8)

``


 

Download Truncate.mw

How to convert to sum?...

Ronan 1331 Maple 2018
sum eval series
August 09 2018
1 4

I am trying to evaluate some functions when u=v so function goes to 0/0

Example given below of the expansion series I need to produce first. But I can't produce it.
 

restart

"How do I get this expansion and sum"?""

````

``

eq := (u^m-v^m)/(u-v)

(u^m-v^m)/(u-v)

 (1)

eval(eq, u = v)

Error, numeric exception: division by zero

  

``

eq1 := convert(eq, Sum, method = rational, include = powers)

(Sum((1-u)^_k1*binomial(-m+_k1-1, _k1), _k1 = 0 .. m)-(Sum((1-v)^_k1*binomial(-m+_k1-1, _k1), _k1 = 0 .. m)))*(Sum((-1)^_k1*(-1+u-v)^_k1, _k1 = 0 .. infinity))

 (2)

"(=)"

-(Sum((-1)^_k1*(-1+u-v)^_k1, _k1 = 0 .. infinity))*m*(Sum((1-u)^_k1*binomial(-m+_k1, _k1)/(-m+_k1), _k1 = 0 .. m))+(Sum((-1)^_k1*(-1+u-v)^_k1, _k1 = 0 .. infinity))*m*(Sum((1-v)^_k1*binomial(-m+_k1, _k1)/(-m+_k1), _k1 = 0 .. m))

 (3)

"(=)"

-(Sum((-1)^_k1*(-1+u-v)^_k1, _k1 = 0 .. infinity))*m*(Sum((1-u)^_k1*binomial(-m+_k1, _k1)/(-m+_k1), _k1 = 0 .. m))+(Sum((-1)^_k1*(-1+u-v)^_k1, _k1 = 0 .. infinity))*m*(Sum((1-v)^_k1*binomial(-m+_k1, _k1)/(-m+_k1), _k1 = 0 .. m))

 (4)

eval(eq1, u = v)

0

 (5)

for m to 5 do m, " ", simplify(eq); eval(simplify(eq), u = v) end do

5*v^4

 (6)

unassign('m')

``eq2 := sum(u^(m-1-i)*v^i, i = 0 .. m-1)

-u^(m-1)*(v/u)^m*u/(u-v)+u^(m-1)*u/(u-v)

 (7)

"(=)"

-u^m*((v/u)^m-1)/(u-v)

 (8)

eval(eq2, u = v)

Error, numeric exception: division by zero

  

``

``

u := v

v

 (9)

eq3 := sum(u^(m-1-i)*v^i, i = 0 .. m-1)

v^m*m/v

 (10)

"(=)"

v^(m-1)*m

 (11)

``


 

Download Convert_to_Sum.mw

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