Equality in Computer Algebra and Beyond
نویسندگان
چکیده
منابع مشابه
Effective Set Membership in Computer Algebra and Beyond
In previous work, we showed the importance of distinguishing “I know that X = Y ” from “I don’t know that X = Y ”. In this paper we look at effective set membership, starting with Gröbner bases, where the issues are well-expressed in algebra systems, and going on to integration and other questions of ‘computer calculus’. In particular, we claim that a better recognition of the role of set membe...
متن کاملA Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy
How do we recognize when an answer is “right”? This is a question that has bedevilled the use of computer systems in mathematics (as opposed to arithmetic) ever since their introduction. A computer system can certainly say that some answers are definitely wrong, in the sense that they are provably not an answer to the question posed. However, an answer can be mathematically right without being ...
متن کاملThe Algebra of Equality Proofs
Proofs of equalities may be built from assumptions using proof rules for reflexivity, symmetry, and transitivity. Reflexivity is an axiom proving x=x for any x; symmetry is a 1-premise rule taking a proof of x=y and returning a proof of y=x; and transitivity is a 2-premise rule taking proofs of x=y and y=z, and returning a proof of x=z. Define an equivalence relation to hold between proofs iff ...
متن کاملALGEBRA , COMPUTER ALGEBRA , AND MATHEMATICAL THINKING Paul
Mathematical symbolism generally—and symbolic algebra in particular—is among mathematics’ most powerful intellectual and practical tools. Knowing mathematics well enough to use it effectively requires a degree of comfort and ease with basic symbolics. Helping students acquire symbolic fluency and intuition has traditionally been an important, and sometimes daunting, goal of mathematics educatio...
متن کاملAlgebra , Computer Algebra , and Mathematical Thinking
Mathematical symbolism in general—and symbolic algebra in particular—is among mathematics’ most powerful intellectual and practical tools. Knowing mathematics well enough to use it effectively requires a degree of comfort and ease with basic symbolics. Helping students acquire symbolic fluency and intuition has traditionally been an important, but often daunting, goal of mathematics education. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2002
ISSN: 0747-7171
DOI: 10.1006/jsco.2002.0551