11 problems

Algebraic-to-Ritt conjecture. If one can solve the problem of computing a characteristic decomposition of a radical differential ideal from generators completely algebraically—by f…

Rational integrating-factor conjecture. For the algorithm proposed in the earlier work, the integrating factor $R$ should necessarily be rational whenever the corresponding second-…

A generalized polylogarithm (GPL) is defined iteratively by … with $G(;x)=1$ and $G(\vec{0}_n;x)=\frac{1}{n!}\ln^n(x)$. Its transcendentality is its weight, namely the number of it…

Let $\Delta_n\in\mathbb{Z}_{>0}$, and let $r\in\mathbb{Z}_{>0}$ be a divisor of $\Delta_n$. Consider the parametrized formulas for $A,B,C,D$ constructed in Sections 2.1 and 2.2, an…

Iterative Hermite-reduction complexity conjecture. The theoretical worst-case complexity of this procedure should be asymptotically the same as that of applying classical Hermite r…

Let $F(x,y)$ be the integer-coefficient polynomial corresponding to the numerically computed polynomial curve that passes through the 16 line segments, with its coefficients normal…

Let $(G,\kappa^*)$ be a mass-action system with $n$ species and rational-number rate constants, and let $I$ be its steady-state ideal. For each species $X_i$, Algorithm computes a…

Let generalized polylogarithms be defined by iterated integrals … with the all-zero index case defined by $H(\vec{0};x):=\frac{1}{n!}\log^n x$ for weight $n$. The symbol is an alge…

Four-function conjecture. Each such double sum can be expressed as a linear combination of the four functions

Let ${\sf RealDet}$ denote the algorithm discussed in the paper, and let the stated bounds refer to the degree bounds for the rational parametrizations it computes. Degree-bound no…

Zero-sum conjecture. The associated summation