Despite the recent successes of deep neural networks in various fields such as image and speech recognition, natural language processing, and reinforcement learning, we still face big challenges in bringing the power of numeric optimization to symbolic reasoning. Researchers have proposed different avenues such as neural machine translation for proof synthesis, vectorization of symbols and expr...

In this paper we make use of the power series facility of Scratchpad2 , a symbolic computer language under development at the IBM Research Mathematics Department , to construct algebraic ECC on the elliptic Riemann surface of genus one. The construction method described uses products of elliptic theta series with rational characteristics and finite field coefficients to define the projective co...

The lazy evaluation protocol defers the evaluation of a function arguments until the moment, when the function uses them. If such a function constructs composite data structures, it is possible to manipulate “infinite”, recursively open objects. We use these techniques to manipulate power series, to construct Padé approximants, to implement the differentiation of programs, etc. in a compact and...

A scheme is presented to extract detailed dynamical signatures from successive measurements of complex systems. Relative entropy based time series tools are used to quantify the gain in predictive power of increasing past knowledge. By lossy compression, data is represented by increasingly coarsened symbolic strings. Each compression resolution is modeled by a machine: a finite memory transitio...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

We use a combination of both symbolic and numerical techniques to construct a degree bounded C-continuous, rational B-spline -approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points we use the classical Newton power series factorizations to determine the distinct branches of the spac...

the renewable energy resources such as wind power have recently attracted more researchers’ attention. it is mainly due to the aggressive energy consumption, high pollution and cost of fossil fuels. in this era, the future fluctuations of these time series should be predicted to increase the reliability of the power network. in this paper, the dynamic characteristics and short-term predictabili...

The tanh method is a powerful solution method; various extension forms of the tanh method have been developed with a computerized symbolic computation and is used for constructing the exact travelling wave solutions, of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. First a power series in tanh was used as an ansatz t...

In this paper we propose refinements for optimal search with symbolic pattern databases in deterministic statespace planning. As main memory is limited, external heuristic search is combined with the power of symbolic representation. We start with an external version of symbolic breadth-first search. Then an alternative and external implementation for BDDA* to include different heuristic evalua...