On Saturday, February 4, 2017 at 4:46:38 PM UTC-6, Dima Pasechnik wrote:
>
>
>
> On Saturday, February 4, 2017 at 8:48:22 PM UTC, valer...@gmail.com wrote:
>>
>> I would like to know the right way to do in SAGE what I am currently
>> doing with Mathematica in these two examples (I actually know how to do the
>> first one in SAGE, but probably not in the best way):
>> 1) Finding the intersection of a generic tangent line to f(x) with f(x):
>> f[x_]:= x^2(x^2-1)
>> L[a_,x_]:=f[a]+f'[a](x-a)
>> Solve[L[a,x]==f[x],x]
>> Here the main issue for me is how use the derivative f'(x) without having
>> to define a new function g(x)=derivative(f(x))
>>
>
> Are your f always polynomials? Sage can do much more with polynomials then
> with "generic" symbolic functions.
> (e.g. for intersecting plane curves an exact approach would be to compute
> the resultant, etc)
>
> Regarding your last question, certainly there is no need to define a new
> named function for everything, e.g.
> sage: f(x)=x^2
> sage: f.diff(x)
> x |--> 2*x
> sage: f.diff(x)(5)
> 10
>
> works
>
f is not always a polynomial, but the above surely answers my question,
thank you
>
>
>>
>> 2) Testing if |f(z)| < f(|z|) for various choices of f:
>> Pl[f_,r_]:=Plot[Abs[f[r Exp[I t]]]/f[r],{t,0,2Pi}]
>> Here I am mostly interested in how to write a command that uses a
>> function as a variable.
>>
>
> Sage has two different types of "functions": 1) native Python functions 2)
> symbolic functions;
> certainly both of these can be passed around as parameters.
>
I have not been able to use f as a parameter. To use a simpler example,
what is the SAGE code corresponding to this Mathematica code:
f[x_]:=1+x+x^2
g[x_]:=1+x+x^2+x^3
Ex[f_]:=Expand[f[x]^2]
Ex[f]
1 + 2 x + 3 x^2 + 2 x^3 + x^4
Ex[g]
1 + 2 x + 3 x^2 + 4 x^3 + 3 x^4 + 2 x^5 + x^6
etc.
>
>
>>
>> Thanks for any suggestions.
>>
>
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