Symbolic algebra elaboration?

General Usage
1

Hi all …

My daughter is in the first scientific high school, here in Italy. Yesterday, we were to see the expansion of (x+y)^7 with tartaglia triangle method … very nice … but I’d like to use Julia to do other symbolic algebric expansions …

So, what package i could use in Julia?

Thank you very much for help.

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2

You can use SymEngine.jl

julia> using SymEngine

julia> @vars x,y
(x, y)

julia> expand((x+y)^7 )
7*x*y^6 + 21*x^2*y^5 + 35*x^3*y^4 + 35*x^4*y^3 + 21*x^5*y^2 + 7*x^6*y + x^7 + y^7
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Thank you very much, it works perfectly …
but i have another question. How can i print the result, this one …

julia> expand( ( a * b^2 + a^2 * b) ^ 7 )
a^7*b^14 + 7*a^8*b^13 + 21*a^9*b^12 + 35*a^10*b^11 + 35*a^11*b^10 + 21*a^12*b^9 + 7*a^13*b^8 + a^14*b^7

… in a better graphically pretty print … as if the professor had written it on the blackboard ?

Many thanks.

4

If you are using Jupyter you can try Latexify:

julia> using Latexify

julia> latexify(expand( ( a * b^2 + a^2 * b) ^ 7 ))
L"$a^{7} \cdot b^{14} + 7 \cdot a^{8} \cdot b^{13} + 21 \cdot a^{9} \cdot b^{12} + 35 \cdot a^{10} \cdot b^{11} + 35 \cdot a^{11} \cdot b^{10} + 21 \cdot a^{12} \cdot b^{9} + 7 \cdot a^{13} \cdot b^{8} + a^{14} \cdot b^{7}$"

(Jupyter should render it nicely, at least according to the docs!)

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5

Another package you can use is my Reduce.jl package for this:

julia> using Reduce; expand(:((x+y)^7))
:(x ^ 7 + 7 * x ^ 6 * y + 21 * x ^ 5 * y ^ 2 + 35 * x ^ 4 * y ^ 3 + 35 * x ^ 3 * y ^ 4 + 21 * x ^ 2 * y ^ 5 + 7 * x * y ^ 6 + y ^ 7)

It allows you to symbolically manipulate Julia Expr objects directly.

4 Likes
6

Symata.jl will do this as well

symata
symata971×304 23.4 KB

2 Likes
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I had never been able to find the documentation for SymEngine… is it the same as SymPy at user level?

8

The documentation is README.md

9

Well, it seems way, way shorter than the SymPy.jl one (not to speak of the original SymPy one)… for example there is no limits nor solve described, no way to specify the domain of the variables… is it because at the moment the functionality of SymEngine is constrained to the functions in the readme, or because a more exhaustive documentation has not yet been wrote (or maybe there is no need if it is the same as SymPy.jl)

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Sorry, I think I can answer myself looking at the code, I don’t see indeed much more than what reported in the README… my next question is then if the common features of a CAS are still missing at the level of the SymEngine library, or “simply” need to be implemented in the SymEngine.jl wrapper…

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For me, all I need is explained in the README.md, I don’t know if all functions of SymEngine (C++) were implemented :confused: .