Perform algebraic manipulations on symbolic expressions.

via 2.10. Sympy : Symbolic Mathematics in Python — Scipy lecture notes

Perform algebraic manipulations on symbolic expressions.

via 2.10. Sympy : Symbolic Mathematics in Python — Scipy lecture notes

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python.

via SymPy

SQLite is a database that is stored in a single file on disk. SQLite is built into Python

in IPython qtconsole (which one could embed inside a custom PyQt/PySide application, and keep track of all the defined symbols

via math – Mathematical equation manipulation in Python – Stack Overflow

Using SymPy, your example would go something like this:

via math – Mathematical equation manipulation in Python – Stack Overflow

Putting Expressions into Different Forms

via Putting Expressions into Different Forms—Wolfram Language Documentation

Can I check if an expression is positive using assumptions?

via Can I check if an expression is positive using assumptions? – Mathematica Stack Exchange

down vote

Backsubstitution is an option often ignored when people use Reduce. In the op’s case it gives:

Reduce[a == b + c && a >= 2 && b <= 10 && c == 5, {a, b, c}, Backsubstitution -> True]

2 <= a <= 15 && b == -5 + a && c == 5

via equation solving – Solve the system of equalities and inequalities – Mathematica Stack Exchange

torus is a surface having genus one

x = (c+acosv)cosu

(2)

y = (c+acosv)sinu

(3)

z = asinv

WeightedAdjacencyGraph

is there a possibility to “transform” a matrix (inheriting the input-output “weights”) into a graph object inheriting the matrix relations?

you can convert it to an edge-weighted graph using `WeightedAdjacencyGraph`

. This will give you a complete graph (a `Graph`

expression) in which each vertex is also connected *to itself*. I am not sure how much sense it makes treat this matrix as a graph, given the full connectivity.

Since you have a fully connected graph, it does not matter in your case, but be aware that `WeightedAdjacencyGraph`

represents missing edges with `Infinity`

, not with zero. This is somewhat annoying because it is inconsistent with `WeightedAdjacencyMatrix`

, which uses `0`

. While `Infinity`

does make sense in *some* (not all) applications, it is much more common to see data that uses 0.

via [✓] Convert matrix into “Graph object”? – Online Technical Discussion Groups—Wolfram Community

Surface Intersection

Highlight the Intersection of Two Surfaces

SliceDensityPlot3D[f, surf, {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}] generates a density plot of f over the slice surface surf as a function of x, y, and z. SliceDensityPlot3D[f, surf, {x, y, z} \[Element] reg] restricts the surface to be within region reg. SliceDensityPlot3D[f, {surf1, surf2, …}, …] generates density plots over several slices.

Rotations

Source: Geometry of Linear Transformations of the Plane – HMC Calculus Tutorial

If V=R2 and W=R2, then T:R2R2 is a linear transformation if and only if there exists a 22 matrix A such that T(v)=Av for all vR2. Matrix A is called the standard matrix for T. The columns of A are T01 and T10 , respectively. Since each linear transformation of the plane has a unique standard matrix, we will identify linear transformations of the plane by their standard matrices. It can be shown that if A is invertible, then the linear transformation defined by A maps parollelograms to parallelograms. We will often illustrate the action of a linear transformation T:R2R2 by looking at the image of a unit square under T

Source: Geometry of Linear Transformations of the Plane – HMC Calculus Tutorial

the image T(P) of any point P is determined by noting that T(A) = A′, T applied to the line segment AB is A′B′, T applied to the line segment AC is A′C′, and T respects scalar multiples of vectors based at A. [If A, E, F are collinear then the ratio length(AF)/length(AE) is equal to length(A′F′)/length(A′E′).] Geometrically T transforms the grid based on ABCD to that based in A′B′C′D′.Affine transformations do not respect lengths or angles; they multiply area by a constant factor

Search ResultsIn mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick’s theorem in the Euclidean plane.

Minkowski’s ConvexBody Theorem

Source: badly approximable convex body Mahler – Google Scholar

The Flatness Theorem

good circle packing density and converges to the hexagonal lattice

Source: On similarity classes of well-rounded sublattices of Z2 (PDF Download Available)

lattice

Source: Bravais lattice – Wikipedia

On the number of lattice points in convex symmetric bodies and their duals

Source: On the number of lattice points in convex symmetric bodies and their duals (PDF Download Available)

H. Gillet and C. Soulé

Source: On the number of lattice points in convex symmetric bodies and their duals | SpringerLink