sympy/sympy

A computer algebra system written in pure Python http://sympy.org/ . To get started to with contributing https://github.com/sympy/sympy/wiki/Introduction-to-contributing

Kalevi Suominen

@jksuom

I think that is true though I'm not sure what you mean by 'compose'.

Micah

@micahscopes

I'm not sure either, I don't think "compose" is the mathematically correct term, but I'd like to do multiple "base changes"

I'd like to be able to construct some of these division algebras: https://core.ac.uk/download/pdf/25253839.pdf

Kalevi Suominen

@jksuom

Those tensor products of algebras can be represented by products of tensors (taking proper care of the indices).

Ayushman Koul

@ayushmankoul

@jksuom As you pointed if I am not wrong we need to amend subclasses of BaseSeries containing 2D lines series.Please can you tell me how should I proceed further on this issue ?

Kalevi Suominen

@jksuom

You could probably start by adding methods that would create instances of List2DSeries to some geometric classes such as Segment and Triangle, and also Polygon. (Those could then be appended to a suitable Plot object for showing.)

Micah

@micahscopes

@jksuom I think I'm starting to get some intuition for this idea

Kalevi Suominen

@jksuom

The components

a_{ijk}

of the tensor associated with the bilinear product in an algebra can be found as follows. If

(e_i)

is a basis of the algebra, then the components are the coefficients of the pairwise products

e_i e_j = \sum_k a_{ijk} e_k

Kalevi Suominen

@jksuom

For example, if

\Bbb{C}

is considered as an

\Bbb{R}

-algebra with basis

(1, i)

, then

a_{110}=-1

is the coefficient of

1

ii

and

a_{111}=0

Micah

@micahscopes

@jksuom !thank you so much!

basically then, to construct the tensor of a finite k-algebra, I just need to get the coefficients in k of pairwise products of basis elements of the algebra

Micah

@micahscopes

I think I need to really play with the summation notation

(and the concept of summation/contraction)

Kalevi Suominen

@jksuom

It seems to me that tensor.array might be the best module for handling algebras and their tensor products.

Micah

@micahscopes

yeah, that's my intuition too. I didn't realize how malleable tensor contraction could be... basically it's very important to keep track of the indices

the indices aren't inherently ordered, so it's gonna be up to me to keep them structured

I had been getting caught up on thinking about duality and covariance/contravariance, but for this problem it's maybe not so necessary to worry about that aspect for now

Micah

@micahscopes

by the way... one of my motivations for this is to be able to do automatic differentiation with "dual numbers". have you heard of this?

https://matiasmorant.wordpress.com/2017/12/29/dual-numbers/

Kalevi Suominen

@jksuom

It is a standard construction in algebra. To any ring

A

, one can associate the "dual ring"

A[\delta]

where

\delta^2 = 0

Micah

@micahscopes

awesome

I didn't realize that

what is that square bracket notation?

is that a "ring extension"?

Kalevi Suominen

@jksuom

Yes, extension of

A

\delta

Its elements are polynomials in

\delta

with coefficients in

A

. In this case, only linear polynomials.

Micah

@micahscopes

that makes sense

you can use the dual ring to do automatic differentiation

in my case, I'd like to use it to render fractals made out of clifford algebras and other interesting algebras

with automatic differentiation, you can create a "distance estimator" that can be used to render the surface of a fractal set

(theoretically)

so far I've only been able to render these fractals using a "brute force" approach, which actually goes and tests each point to see if it's in the fractal

this doesn't scale well for large dimensional algebras

http://blog.hvidtfeldts.net/index.php/2011/12/distance-estimated-3d-fractals-vii-dual-numbers/

Abhigyan Khaund

@abhigyank

Hey, I am trying to plot a scatter of points using the Plot module in sympy. From the documention I am unable to figure out how do I plot a scatter of points as we do in matplotlib.

I have 2 arrays; call them A and B. I can do a scatter plot using matplotlib like this:
plt.plot(A,B)

How do I do the same in Sympy?

Aaron Meurer

@asmeurer

Sympy only deals with plotting of sympy expressions. If you want to plot a dataset, you should use matplotlib, just as you have already done

Abhigyan Khaund

@abhigyank

Ok thanks!

Is there a way to plot the dataset in matplot lib and plot the sympy expression using sympy and somehow display the two plots in a single window?

Aaron Meurer

@asmeurer

I think you might be able to access the figure from the sympy plot. I'm not sure.

Another way is to lambdify the sympy expression and plot it manually with np.linspace

udit4

@udit4

Hello all, i am new to the SymPy project.. Can anyone help me where can i find complete documentation of SymPy and some other relevant sources, so that i can get some more insights about project and then start contributing to the same. Thanks in advance.

Malkhan Singh

@Malkhan52

Docs

I would recommend before start contribution go through documents and tutorials, you will definitely get idea how to start contribution

udit4

@udit4

@Malkhan52 thank you so much..

Kalevi Suominen

@jksuom

25 in sieve is a membership test operation in Python. It evaluates to False as sieve is the list of prime numbers and 25 is not a prime.

S.Y. Lee

@sylee957

Hello, I want to write a test case to check if a certain function is called.
But I the closest one I could find, is to make an arbitrary function which can raise a mock exception when called, and catching up via raises().
However, I think this method cannot be used to check whether the function can call any default APIs from sympy.
I need some help about this

Sudarshan Kamath

@sudz123

Hi while running the doc tests, there are a sequence of tests which give :

"ttk::ThemeChanged"
can't invoke "event" command: application has been destroyed
    while executing
"event generate $w <<ThemeChanged>>"
    (procedure "ttk::ThemeChanged" line 6)
    invoked from within

namely test_plot.py and test_plot_implicit.py . Are these necessary if the application has been destroyed? Or can they be removed?

Kalevi Suominen

@jksuom

@sylee957 What kind of test are you thinking of. Is it not possible to run the code in a debugger to see if a function is called?

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