SageMath

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Discuss everything about maths at the SageMath forum with other mathematics enthusiasts.

SageMath

49m ago

After installing Sagemath through WSL+conda-forge on Windows. Is there a way to use Jupyterlab desktop on windows with sagemath ..read more

SageMath

16h ago

I have the following problem. I want to define expression which contains elements of several Weyl Character Rings. The problem comes from physics. I have expression for theory with several symmetries, which can be of the same or different groups which involves characters of these groups representations. Let's take a simplest example of such expression $x = \chi_{R_1}(U)\chi_{R_2}(V)$ where $U\in G_1 $, $V\in G_2 $ are matrices in groups $G_1$ and $G_2$ and $R_{1,2}$ are corresponding representations. Let's say I want to find $x^2$ (or any other power) expanded in terms of irreps. If $G_1 \neq ..read more

SageMath

3d ago

I am trying to write a code using SAGE to find all subgroups of $\mathbb{Z}^*_n$ where the elements of subgroups are elements of $\mathbb{Z}_n$. To elaborate, when I am using the command .subgroups(), it returns the subgroups in generator-relator form and not as integers. Is there anyway to do it ..read more

SageMath

3d ago

I have the following problem. I want to define expression which contains elements of several Weyl Character Rings. The problem comes from physics. I have expression for theory with several symmetries, which can be of the same or different groups which involves characters of these groups representations. Let's take a simplest example of such expression $x = \chi_{R_1}(U)\chi_{R_2}(V)$ where $U\in G_1 $, $V\in G_2 $ are matrices in groups $G_1$ and $G_2$ and $R_{1,2}$ are corresponding representations. Let's say I want to find $x^2$ (or any other power) expanded in terms of irreps. If $G_1 \neq ..read more

SageMath

3d ago

I have defined a function G such that G(alpha) is in QSym = QuasisymmetricFunctions(K) for alpha in Compositions. Is there a way to declare G as a basis of QSym, so that I can access functions like G(f) to give me the G-expansion of f where f is in QSym ..read more

SageMath

5d ago

I know that ``PolynomialRing`` has the keyword ``"sparse"`` which defaults to ``False``. sage: S = PolynomialRing(QQ, "x", sparse=False) sage: S is PolynomialRing(QQ, "x") True But the output of ``.coefficients()`` is still sparse in the sense that it does only show non-zero coefficients sage: p = S([1, 0, 2]) sage: p.coefficients() [1, 2] I know that I could reconstruct the polynomial using ``.exponents()`` sage: p.exponents() [0, 2] sage: x = S.gen() sage: p == sum(coef*x**exp for coef, exp in zip(p.coefficients(), p.exponents()) True But is there an easy way to make ``.coefficients()`` retu ..read more

SageMath

1w ago

I'm using Sagemath in Jupyter lab. Some of my cells contain cython code, and I keep getting the following warnings: ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored ld: warning: duplicate -rpath '/private/var/tmp/sage-10.3-current/local/lib' ignored ld: warning: passed two min versions (10.9, 10.9) for platform macOS. Using 10.9. ld: warning: passed two min versions (10.9, 10.9) for platform ..read more

SageMath

1w ago

I'm trying to find the inverse of the polynomial \( 7X^2 + 1 \) in the Galois ring \( GR(2^3, 3) \) where the modulus polynomial is \( h(X) = X^3 + X + 1 \). However, I keep encountering the error "Flint exception (Impossible inverse): Cannot invert modulo \(2 4\)." Here is the SageMath code I'm using: k = 3 d = 3 R = IntegerModRing(2**k) GR = PolynomialRing(R, 'X') X = GR.gen() h = X^3 + X + 1 GaloisRing = GR.quotient(h, 'X') poly = GaloisRing(7*X^2 + 1) poly_elem = poly.lift() poly_modulus = h g, u, v = xgcd(poly_elem, poly_modulus) if g != 1: raise ValueError(f"The element {elem} does not h ..read more

SageMath

1w ago

Let's start with sage: x,p,q = var('x p q') sage: ( exp(p*x - q*x)^(1/(p-q)) ).full_simplify() e^x So far so good. Let's bring an extra factor to the picture: sage: ( (exp(p*x - q*x)/q)^(1/(p-q)) ).full_simplify() (e^(p*x - q*x)/q)^(1/(p - q)) There is no simplification here. Why? Also: sage: ( (exp(p*x - q*x)/q)^(1/(p-q)) ).factor() (e^(p*x - q*x)/q)^(1/(p - q)) does not produce the expected `exp(x)*q^(-1/(p-q))`. How to get that result ..read more

SageMath

1w ago

How do I get PIL images to display in SageMath on JupyterLab 4.2.4? I tried this... from IPython.display import display from PIL import Image img1 = toimage(data) # PIL image display(img1) All I get for the output is... PIL.Image.Image image mode=RGB size=720x360 at 0x184D1AE10 Any advice? Thanks. Eric ..read more