jksuom

Groups defined by generators (and relators) are analogous to polynomial rings (and their quotient rings). In SymPy there are three different ways of representing polynomials: general expressions, and then dense and sparse representations. Expressions are convenient to use as they are essentially self-contained. But they are less efficient in computations while the other two are each best for specific purposes.

There could also be three types of representations for elements of groups.

jksuom

It seems that implementation of polynomials in sympy and symengine could be closely parallel.

There should be three kinds of polynomials: (standard) polynomials, Laurent polynomials, and Puiseux polynomials, thus adding a "fourth dimension" to the classification in the wiki (https://github.com/sympy/symengine/wiki/En-route-to-Polynomial). They can also be used for representing (truncated) series of respective types.

jksuom

Linear diophantine equations

A general linear nonhomogeneous diophantine equation is of the form

a_0x_0 + a_1x_1 +\cdots+ a_nx_n = c

where the coefficients a_i and the constant c are integers. The components x_i of its solutions are also expected to be integers.

jksuom

Interpretation of

M 210.11173,460.41281 C 167.68532,274.54475 107.07617,197.77315 290.92393,304.84932 474.77169,411.92549 610.13214,541.22502 408.10163,444.25038 206.07112,347.27573 597.03099,636.66328 367.69552,609.91539 21.255008,569.50929 228.75342,542.08117 210.11173,460.41281 Z

The M command sets the starting point.

The C command defines a series of consecutive cubic Bézier curves.

The Z command closes the path.