Measurements of jet production rates in association with W and Z bosons for jet transverse momenta above 30 GeV are reported, using a sample of proton-proton collision events recorded by CMS at √ s = 7 TeV, corresponding to an integrated luminosity of 36 pb −1 . The study includes the measurement of the normalized inclusive rates of jets σ(V+ ≥ n jets)/σ(V), where V represents either a W or a Z. In addition, the ratio of W to Z cross sections and the W charge asymmetry as a function of the number of associated jets are measured. A test of scaling at √ s = 7 TeV is also presented. The measurements provide a stringent test of perturbative-QCD calculations and are sensitive to the possible presence of new physics. The results are in agreement with the predictions of a simulation that uses explicit matrix element calculations for final states with jets.

Computer algebra systems (CASs) and automated theorem provers (ATPs) exhibit complementary abilities. CASs focus on efficiently solving domain-specific problems. ATPs are designed to allow for the formalization and solution of wide classes of problems within some logical framework. Integrating CASs and ATPs allows for the solution of problems of a higher complexity than those confronted by each class alone. However, most experiments conducted so far followed an ad-hoc approach, resulting in solutions tailored to specific problems. A structured and principled approach is necessary to allow for the sound integration of systems in a modular way. The Open Mechanized Reasoning Systems (OMRS) framework was introduced for the specification and implementation of mechanized reasoning systems, e.g. ATPs. In this paper, we introduce a generalization of OMRS, named OMSCS (Open Mechanized Symbolic Computation Systems). We show how OMSCS can be used to soundly express CASs, ATPs, and their integration, by formalizing a combination between the Isabelle prover and the Maple algebra system. We show how the integrated system solves a problem which could not be tackled by each single system alone.

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Abstract. The combination of logical and symbolic computation systems has recently emerged from prototype extensions of stand-alone systems to the study of environments allowing interaction among several systems. Communication and cooperation mechanisms of systems performing any kind of mathematical service enable to study and solve new classes of problems and to perform e cient computation by distributed specialized packages.The classi cation of communication and cooperation methods for logical and symbolic computation systems given in this paper provides and surveys di erent methodologies for combining mathematical services and their characteristics, capabilities, requirements, and di erences. The methods are illustrated by r e c e n t w ell-known examples.We separate the classi cation into communication and cooperation methods. The former includes all aspects of the physical connection, the ow of mathematical information, the communication language(s) and its encoding, encryption, and knowledge sharing. The latter concerns the semantic aspects of architectures for cooperative problem solving.

Solving sophisticated mathematical problems often requires algebraic algorithms and theorems.