Computer algebra is an alternative and complement to numerical mathematics. Its importance is steadily increasing. This volume is the first systematic and complete treatment of computer algebra. It presents the basic problems of computer algebra and the best algorithms now known for their solution with their mathematical foundations, and complete references to the original literature. The volume follows a top-down structure proceeding from very high-level problems which will be well-motivated for most readers to problems whose solution is needed for solving the problems at the higher level. The volume is written as a supplementary text for a traditional algebra course or for a general algorithms course. It also provides the basis for an independent computer algebra course.

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The nitrogen-sulfur linkage in compounds of the type R-NSO is capable of undergoing addition. For N-sulfinylsulfonamides in particular, the reactivity is increased so greatly that new types of compounds may be obtained by cyclic addition or migration of the sulfinyl group.In 1890, Michaelis and Herz [l) identified "thionylaniline" C~HSNSO as a product of the reaction of aniline with SOC4:(1) QHsNHz + SOClz + GHsNSO + 2 HCL This substance has been described earlier by Bottinger [2] but with no statement concerning its structure. In a large number of subsequent publications, Michaelis has described the preparation of approximately seventy-five N-sulfinylamines of the type R-NSO and their reactions. This thorough exploration of the field, as well as the fact that the described reactions either led back to the amines, or else to products which could be obtained more easily by another route, explains why very little work was done with the N-sulfinyl compounds in the subsequent period. Only in the last few years have various groups made renewed studies of the structure and behavior of the organic N-sulfinyl compounds, and it is these studies in particular which are described here. The literature up to June 1958 is summarized in Houben-Weyl [3a] and is therefore only treated briefly; a survey of earlier works is also given by Kennard [3 b]. A summary of the properties of the unsubstituted thionylimide has been given by Goehring [4].Most N-sulhyl compounds known up to the present time are amine or bydrazine derivatives and are prepared from them.

Zwei neue Wege zu N-Arylsulfonyl-iminen bzw. -formamidinen werden beschrieben. Im Rahmen unserer Arbeiten iiber Diensynthesen, die zu Heterocyclen fiihren, haben wir uns auch mit den Sulfonyliminen RSOzN=CHR beschtiftigt, da diese a h C =N-Dienophile von Inter-sein konnen. Diese Schiffschen Basen von Sulfonamiden sind seit einigen Jahren bekannt. J. LICHTEN-BERGER und Mitarbb.1) bzw. A. J. KRETOW und JE. A. ABRASHANOWA~) erreichten die Kondensation von Arylsulfonamiden mit Aldehyden mit AlCl3 bzw. ZnClz als Kondensationsmittel.

Detection of molecular alterations is of potential significance for diagnosis and prognosis in bladder cancer. Fluorescence in situ hybridization (FISH) allows visualization and quantitation of genes and chromosomes on a cell by cell level and can easily be applied to urinary cells. To evaluate the sensitivity of FISH for detection of DNA aberrations in bladder cancer, formalin-fixed tissues of 293 tumors were examined by FISH and flow cytometry (FCM). Centromere probes for the chromosomes X, Y, 1, 7, 9, and 17 were used for FISH analysis. FISH was more sensitive for detection of quantitative DNA aberrations than FCM. An aberration of at least one chromosome was found in 107 of 108 tumors (99%), which were tetraploid, aneuploid, or multiploid, and in 29 of 49 tumors (59%), which were diploid, by FCM. The frequency of FISH aberrations showed greater differences between pTa (47%) and pT 1 tumors (85 %; P < 0.0001) than between stages pT 1 and pT2-4 (98%). The marked genetic difference between pTa and pT1 tumors argues against the concept of grouping pTa and pTl tumors together as "superficial bladder cancer." The frequency of tumors with chromosomal aberrations detected by FISH increased with the number of chromosomes examined. Aneusomy was seen in 68% of grade 1 tumors examined for >4 chromosomes, suggesting that the cytological diagnosis of bladder cancer recurrences could be substantially improved by FISH.