Algebraic simplification

Moses, Joel

doi:10.1145/362637.362648

Cited by 105 publications

(6 citation statements)

References 25 publications

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“…Consider, for example, the following simple program to sort an array Beyond this, there are a number of defects in the current system whose solutions are understood. The algebraic manipulation subsystem could be augmented with a radical simplification package [13]. Similarly, the methods used for solution of difference equations could be extended.…”

Section: Discussionmentioning

confidence: 99%

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Mechanical program analysis

1975

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One means of analyzing program performance is by deriving closed-form expressions for their execution behavior. This paper discusses the mechanization of such analysis, and describes a system, Metric, which is able to analyze simple Lisp programs and produce, for example, closed-form expressions for their running time expressed in terms of size of input. This paper presents the reasons for mechanizing program analysis, describes the operation of Metric, explains its implementation, and discusses its limitations.

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Section: Discussionmentioning

confidence: 99%

“…If J?,'s are present, their first and second derivatives are represented formally. The only complication is the pervasive use of algebraic simplification to control the size of the expressions [13]. Evaluating at z = 1 and using the known values of the zeroth, first, and second derivatives of the Rt's yields the desired results.…”

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confidence: 98%

Mechanical program analysis

1975

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“…We can attempt to set reasonable defaults, but a useful system should probably allow the user to make intelligent choices. It is very difficult to define meaningful canonical forms for general symbolic expressions, and the optimal form often depends on the application [5,19]. A classical problem is whether it makes sense to expand (π + 1) 1000 in Q(π ) or whether the result should be represented in Q((π + 1) 1000 ) (in Calcium, this is configurable).…”

Section: Choosing Extension Numbersmentioning

confidence: 99%

Calcium

Johansson¹

2021

Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation

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Calcium is a C library for real and complex numbers in a form suitable for exact algebraic and symbolic computation. Numbers are represented as elements of fields Q(a 1 , . . . , a n ) where the extension numbers a k may be algebraic or transcendental. The system combines efficient field operations with automatic discovery and certification of algebraic relations, resulting in a practical computational model of R and C in which equality is rigorously decidable for a large class of numbers.

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“…1981) and MACSYMA (Moses 1971) are invaluable to an engineer, but only provide a partial answer to automating the explanation skill, since they tell us what a device does, but not why. Thus the essential goal of work like ENVISION (de Kleer 1984;de Kleer and Brown 1984), temporal qualitative analysis (Williams 19841, qualitative process theory (Forbus 1984), and temporal constraint propagation (Roylance 1980) was causal explanation, not, as Sacks and Doyle claim, SPQR.…”

Section: "Experts Focus On Asymptotic Behavior While Spqr Focuses Onmentioning

confidence: 99%

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Williams

Shirley

Raiman

et al. 1992

Computational Intelligence

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One can respond to "Prolegomena to any Future Qualitative Physics" at several levels. As practitioners in the field, it is easy to become incensed and respond to every minute misrepresentation and error. This would unfortunately miss the forest for the trees. Unfortunate, because there is a much simpler story to be told here. Sacks and Doyle make two high-level claims as the basic theme of their paper. First, they state that the field of qualitative reasoning is roughly equivalent to SPQR. In other words, the principal goal of the qualitative reasoning enterprise is to (1) produce abstract state transition diagrams of system behavior (i.e., simulations) which are (2) solely for the purpose of predicting behavior. Second, in reasoning about such systems' behavior, "experts" are predominantly concerned with their asymptotic, dynamical properties.As stated, we view both points as incorrect, misleading, and quite surprising coming from Sacks, who, as a frequent attendee of the qualitative reasoning workshops, should have a better understanding of the field. However, there is another, less controversial interpretation of the paper which we obtained from personal conversations with Sacks at the most recent workshop. First, their argument was intended to address work on the SPQR subset of the field rather than suggest that all of qualitative reasoning is SPQR. Second, their reference to the concerns of an expert was refemng to an expert academic dynamicist, and was a suggestion about how to compare the relative merits of SPQR and dynamical analysis.Given this interpretation shift, Sacks and Doyle's paper raises an interesting, but much narrower, technical issue related to acausal simulation, a small portion of the work going on in the field of qualitative reasoning. One argument in favor of qualitative simulation (SPQR) is that qualitative differential equations enable reasoning about entire classes of functions and is thus a more efficient way to perform certain tasks, such as the preliminary stages of design. Alternatively, Sacks and Doyle argue that it is better to pick a specific differential equation, analyze its solutions using conventional techniques, and if these are undesirable (for the task, say diagnosis or design) to pick another one. We believe that neither has demonstrated clear superiority for the kinds of tasks qualitative simulation is intended to address and we think it is perfectly reasonable that researchers in qualitative simulation explore and evaluate both approaches.Rather than focus on that debate in our response, we instead address the broader issues that have arisen while discussing this paper. We try to clarify what we see as the goals of the field and describe some of the major research efforts. 'We were told that they could not make these clarifying changes because some people had already invested significant effort responding to the original paper.

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Algebraic simplification

Cited by 105 publications

References 25 publications

Mechanical program analysis

Mechanical program analysis

Calcium

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