[fricas-devel] Re: Some questions about Fricas

[Erik Eidsvig]

Thanks!

-But what about n-root of a numer? As an example, the 5th-root of 32?

(I have tried commands like root(32,5), nrot(32,5) etc.)



-The angle between two vectors?
(For example [2,3] and [-3,4])



-If I know the x-value of the function, is it possible to make Axiom find
the tangent line in this point?

(Something like this:(1) -> f(x)==2*x^4-2*x^2
Type:
Void
(2) -> Tangent(1, f(x))
Compiling function f with type Variable(x) -> Polynomial(Integer)
There are no library operations named Tangent
Use HyperDoc Browse or issue
)what op Tangent
to learn if there is any operation containing " Tangent " in its
name.

Cannot find a definition or applicable library operation named
Tangent with argument type(s)
PositiveInteger
Polynomial(Integer)

Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.


-Is it possible to find the (shortest) distance between the line and a
point?

(For example the distance between the line 3x-4 and the point (6,4))


-The lenght of a vector?

For example the length of [2,3]

[Bill Page]

Post by Erik Eidsvig
Thanks!
-But what about n-root of a number? As an example, the 5th-root of 32?
(I have tried commands like root(32,5), nrot(32,5) etc.)

(1) -> )what op root

Operations whose names satisfy the above pattern(s):

alg_split_root0 alg_split_roots
allRootsOf approxNthRoot
charthRoot complexRoots
countRealRoots countRealRootsMultiple
createSceneRoot droot
froot get_rational_roots
inrootof insertRoot!
iroot irootDep
mightHaveRoots nthRoot
nthRootIfCan perfectNthRoot
qroot radicalRoots
realRoots root
root? rootBound
rootFactor rootKerSimp
rootNormalize rootOf
rootOfIrreduciblePoly rootPoly
rootPower rootProduct
rootRadius rootSimp
rootSplit rootSum
rootsOf rroot
scaleRoots shiftRoots

To get more information about an operation such as root? , issue
the command )display op root?
(1) -> nthRoot(32,5)

(1) 2
Type: AlgebraicNumber

Post by Erik Eidsvig
...

[Prof. Dr. Johannes Grabmeier privat]

Post by Erik Eidsvig
Thanks!
-But what about n-root of a numer? As an example, the 5th-root of 32?
(I have tried commands like root(32,5), nrot(32,5) etc.)

(1) -> nthRoot(5,7)

        7+-+
   (1)  \|5
                                                                              
Type: AlgebraicNumber
(2) -> nthRoot(5.0,7)

   (2)  1.2584989506_41826735
                                                                                        
Type: Float

Post by Erik Eidsvig
-The angle between two vectors?
(For example [2,3] and [-3,4])

(4) -> v := vector [2,3]

   (4)  [2, 3]
                                                                      
Type: Vector(PositiveInteger)

(5) -> length v

         +--+
   (5)  \|13
                                                                              
Type: AlgebraicNumber
(6) -> w := vector [-3,4]

   (6)  [- 3, 4]
                                                                              
Type: Vector(Integer)
(7) -> length w

   (7)  5
                                                                              
Type: AlgebraicNumber
(8) -> angle(v,w) == acos( dot(v,w) / length(v) / length(w))
                                                                                         
Type: Void
(9) -> angle(v,w)
   Compiling function angle with type (Vector(PositiveInteger),
Vector(Integer)) -> Expression
      (Integer)

                +--+
             6 \|13
   (9)  acos(-------)
                65
                                                                          
Type: Expression(Integer)
(10) -> numeric %

   (10)  1.2315037123_40851938

Post by Erik Eidsvig
-If I know the x-value of the function, is it possible to make Axiom
find the tangent line in this point?
(Something like this:(1) -> f(x)==2*x^4-2*x^2
                                                                 
 Type: Void
(2) -> Tangent(1, f(x))
   Compiling function f with type Variable(x) -> Polynomial(Integer)
   There are no library operations named Tangent
      Use HyperDoc Browse or issue
                              )what op Tangent
      to learn if there is any operation containing " Tangent " in its
      name.
   Cannot find a definition or applicable library operation named
      Tangent with argument type(s)
                               PositiveInteger
                             Polynomial(Integer)
      or "$" to specify which version of the function you need.

(18) -> f := 2*x^4-2*x^2

            4      2
   (18)  2 x  - 2 x
                                                                          
Type: Polynomial(Integer)
(19) -> tangent(f,x0) == eval(D(f,x),x=x0)*x - eval(f,x=x0) -
eval(D(f,x),x=x0)*x0
   1 old definition(s) deleted for function or rule tangent
                                                                                         
Type: Void
(20) -> tangent(f,1)
   Compiling function tangent with type (Polynomial(Integer),
PositiveInteger) -> Polynomial(
      Integer)

   (20)  4 x - 4
                                                                          
Type: Polynomial(Integer)

Post by Erik Eidsvig
-Is it possible to find the (shortest) distance between the line and a
point? 
(For example the distance between the line 3x-4 and the point (6,4))
-The lenght of a vector?
For example the length of [2,3]
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Johannes Grabmeier

Prof. Dr. Johannes Grabmeier
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